Various changes to day 4

diff --git a/04-08-amidakuji/04-lines.txt b/04-08-amidakuji/04-lines.txt
deleted file mode 100644 (file)
index c859642..0000000
--- a/04-08-amidakuji/04-lines.txt
+++ /dev/null
@@ -1,10135 +0,0 @@
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\ No newline at end of file

diff --git a/04-08-amidakuji/04-small.txt b/04-08-amidakuji/04-small.txt
deleted file mode 100644 (file)
index 75e0d3d..0000000
--- a/04-08-amidakuji/04-small.txt
+++ /dev/null
@@ -1,15 +0,0 @@
-(2, 5)
-(1, 4)
-(0, 3)
-(0, 3)
-(0, 5)
-(3, 5)
-(0, 2)
-(3, 4)
-(2, 4)
-(1, 2)
-(0, 4)
-(1, 2)
-(2, 4)
-(0, 4)
-(1, 4)
\ No newline at end of file

diff --git a/04-08-amidakuji/amidakuji-creation.ipynb b/04-08-amidakuji/amidakuji-creation.ipynb
deleted file mode 100644 (file)
index 65d9751..0000000
--- a/04-08-amidakuji/amidakuji-creation.ipynb
+++ /dev/null
@@ -1,2514 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import collections\n",
-    "import random\n",
-    "import string\n",
-    "import itertools"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "Link = collections.namedtuple('Link', 'height left right')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def link_ends(link):\n",
-    "    return set((link.left, link.right))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def can_add(link, links):\n",
-    "    ends = link_ends(link)\n",
-    "    same_height_links = [l for l in links if l.height == link.height]\n",
-    "    return all(ends.isdisjoint(link_ends(l)) for l in same_height_links)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def make_net(num_links, lines=10, height=50):\n",
-    "    links = set()\n",
-    "    while len(links) < num_links:\n",
-    "        a = random.randrange(lines)\n",
-    "        b = random.randrange(lines)\n",
-    "        if a != b:\n",
-    "            l = min(a, b)\n",
-    "            r = max(a, b)\n",
-    "            h = random.randrange(height)\n",
-    "            link = Link(h, l, r)\n",
-    "            if can_add(link, links):\n",
-    "                links.add(link)\n",
-    "    return links"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{Link(height=4, left=0, right=3),\n",
-       " Link(height=8, left=1, right=5),\n",
-       " Link(height=16, left=0, right=4),\n",
-       " Link(height=17, left=1, right=5),\n",
-       " Link(height=18, left=3, right=5),\n",
-       " Link(height=20, left=0, right=1),\n",
-       " Link(height=25, left=0, right=3),\n",
-       " Link(height=30, left=1, right=4),\n",
-       " Link(height=33, left=0, right=4),\n",
-       " Link(height=34, left=4, right=5),\n",
-       " Link(height=35, left=0, right=3),\n",
-       " Link(height=36, left=1, right=4),\n",
-       " Link(height=37, left=2, right=5),\n",
-       " Link(height=45, left=4, right=5),\n",
-       " Link(height=46, left=2, right=5)}"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "net = make_net(15, lines=6)\n",
-    "net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow(initial_line, links):\n",
-    "    line = initial_line\n",
-    "    heights = sorted(set(l.height for l in links))\n",
-    "    for h in heights:\n",
-    "        for l in [l for l in links if l.height == h]:\n",
-    "            if line in link_ends(l):\n",
-    "                line = [e for e in link_ends(l) if e != line][0]\n",
-    "#                 print(l, line)\n",
-    "    return line"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "3"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "follow(4, net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def pack(net):\n",
-    "    packed_links = []\n",
-    "    line_heights = collections.defaultdict(lambda: -1)\n",
-    "    for link in sorted(net):\n",
-    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
-    "        line_heights[link.left] = link_height\n",
-    "        line_heights[link.right] = link_height\n",
-    "        packed_links += [Link(link_height, link.left, link.right)]\n",
-    "    return sorted(packed_links)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow_many_slow(in_sequence, links):\n",
-    "    out_sequence = [(follow(i, links), term) \n",
-    "                    for i, term in enumerate(in_sequence)]\n",
-    "    return [term for i, term in sorted(out_sequence)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow_many(in_sequence, net):\n",
-    "    height_groups = [list(g) for _, g in itertools.groupby(pack(net), lambda l: l.height)]\n",
-    "    seq = list(in_sequence)\n",
-    "    for links in height_groups:\n",
-    "        for link in links:\n",
-    "#             l = seq[link.left]\n",
-    "#             r = seq[link.right]\n",
-    "#             seq[link.right] = l\n",
-    "#             seq[link.left] = r\n",
-    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
-    "    return seq"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10000 loops, best of 3: 39.2 µs per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many('abcdef', net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# %%timeit\n",
-    "# follow_many_slow('abcdefghij', net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def show_net(links, randomise=False, pair_sep=', '):\n",
-    "    if randomise:\n",
-    "        output = []\n",
-    "        heights = sorted(set(l.height for l in links))\n",
-    "        for h in heights:\n",
-    "            ls = [l for l in links if l.height == h]\n",
-    "            random.shuffle(ls)\n",
-    "            output += ['({}, {})'.format(l.left, l.right) for l in ls]\n",
-    "        return pair_sep.join(output)\n",
-    "    return pair_sep.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'(0, 3), (1, 5), (0, 4), (1, 5), (3, 5), (0, 1), (0, 3), (1, 4), (0, 4), (4, 5), (0, 3), (1, 4), (2, 5), (4, 5), (2, 5)'"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "show_net(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'(0, 3), (1, 5), (0, 4), (1, 5), (3, 5), (0, 1), (0, 3), (1, 4), (0, 4), (4, 5), (0, 3), (1, 4), (2, 5), (4, 5), (2, 5)'"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "show_net(net, randomise=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'(0, 3) : (1, 5) : (0, 4) : (1, 5) : (3, 5) : (0, 1) : (0, 3) : (1, 4) : (0, 4) : (4, 5) : (0, 3) : (1, 4) : (2, 5) : (4, 5) : (2, 5)'"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "show_net(net, pair_sep=' : ')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'(0, 3)\\n(1, 5)\\n(0, 4)\\n(1, 5)\\n(3, 5)\\n(0, 1)\\n(0, 3)\\n(1, 4)\\n(0, 4)\\n(4, 5)\\n(0, 3)\\n(1, 4)\\n(2, 5)\\n(4, 5)\\n(2, 5)'"
-      ]
-     },
-     "execution_count": 53,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "show_net(net, pair_sep='\\n')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "(0, 3)\n",
-      "(1, 5)\n",
-      "(0, 4)\n",
-      "(1, 5)\n",
-      "(3, 5)\n",
-      "(0, 1)\n",
-      "(0, 3)\n",
-      "(1, 4)\n",
-      "(0, 4)\n",
-      "(4, 5)\n",
-      "(0, 3)\n",
-      "(1, 4)\n",
-      "(2, 5)\n",
-      "(4, 5)\n",
-      "(2, 5)\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(show_net(net, pair_sep='\\n'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# open('04-small.txt', 'w').write(show_net(net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'(0, 3), (1, 5), (0, 4), (1, 5), (3, 5), (0, 1), (0, 3), (1, 4), (0, 4), (4, 5), (0, 3), (1, 4), (2, 5), (4, 5), (2, 5)'"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "show_net(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "ls = [l for l in net if l.height == 1]\n",
-    "ls"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "random.shuffle(ls)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def read_net(net_string):\n",
-    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def extract_pairs(net_string):\n",
-    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "net = read_net('(1, 5), (2, 4), (0, 2), (0, 4), (0, 1), (0, 2), (1, 5), (0, 3), (1, 2), (4, 5), (0, 5), (3, 5), (1, 4), (0, 1), (2, 3)')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=1, right=5),\n",
-       " Link(height=1, left=2, right=4),\n",
-       " Link(height=2, left=0, right=2),\n",
-       " Link(height=3, left=0, right=4),\n",
-       " Link(height=4, left=0, right=1),\n",
-       " Link(height=5, left=0, right=2),\n",
-       " Link(height=6, left=1, right=5),\n",
-       " Link(height=7, left=0, right=3),\n",
-       " Link(height=8, left=1, right=2),\n",
-       " Link(height=9, left=4, right=5),\n",
-       " Link(height=10, left=0, right=5),\n",
-       " Link(height=11, left=3, right=5),\n",
-       " Link(height=12, left=1, right=4),\n",
-       " Link(height=13, left=0, right=1),\n",
-       " Link(height=14, left=2, right=3)]"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "read_net(show_net(net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=1, right=5),\n",
-       " Link(height=0, left=2, right=4),\n",
-       " Link(height=1, left=0, right=2),\n",
-       " Link(height=2, left=0, right=4),\n",
-       " Link(height=3, left=0, right=1),\n",
-       " Link(height=4, left=0, right=2),\n",
-       " Link(height=4, left=1, right=5),\n",
-       " Link(height=5, left=0, right=3),\n",
-       " Link(height=5, left=1, right=2),\n",
-       " Link(height=5, left=4, right=5),\n",
-       " Link(height=6, left=0, right=5),\n",
-       " Link(height=6, left=1, right=4),\n",
-       " Link(height=7, left=0, right=1),\n",
-       " Link(height=7, left=3, right=5),\n",
-       " Link(height=8, left=2, right=3)]"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pack(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=1, right=5),\n",
-       " Link(height=0, left=2, right=4),\n",
-       " Link(height=1, left=0, right=2),\n",
-       " Link(height=2, left=0, right=4),\n",
-       " Link(height=3, left=0, right=1),\n",
-       " Link(height=4, left=0, right=2),\n",
-       " Link(height=4, left=1, right=5),\n",
-       " Link(height=5, left=0, right=3),\n",
-       " Link(height=5, left=1, right=2),\n",
-       " Link(height=5, left=4, right=5),\n",
-       " Link(height=6, left=0, right=5),\n",
-       " Link(height=6, left=1, right=4),\n",
-       " Link(height=7, left=0, right=1),\n",
-       " Link(height=7, left=3, right=5),\n",
-       " Link(height=8, left=2, right=3)]"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pack(read_net(show_net(net)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(True, True)"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pnet = pack(net)\n",
-    "rrnet = read_net(show_net(net, randomise=True))\n",
-    "rnet = read_net(show_net(net))\n",
-    "rnet == rrnet, pack(rrnet) == pnet"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "lnet = make_net(10207, 26, 100000)\n",
-    "plnet = pack(lnet)\n",
-    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, plnet)\n",
-    "# for i in range(204):\n",
-    "#     assert follow(i, lnet) == follow(i, plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "rlnet = read_net(show_net(lnet))\n",
-    "prlnet = pack(rlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2239"
-      ]
-     },
-     "execution_count": 68,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "99989"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10206"
-      ]
-     },
-     "execution_count": 70,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in rlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2239"
-      ]
-     },
-     "execution_count": 71,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in prlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, prlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 25.9 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many(string.ascii_lowercase, lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# %%timeit\n",
-    "# follow_many_slow(string.ascii_lowercase, lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pairs_slow(net):\n",
-    "    eps = []\n",
-    "    for l in net:\n",
-    "        o = Link(l.height + 1, l.left, l.right)\n",
-    "        if o in net:\n",
-    "            eps += [(l, o)]\n",
-    "    return eps    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pairs(net):\n",
-    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "    eps = []\n",
-    "    for h in range(1, max(height_groups.keys())):\n",
-    "        for l in height_groups[h]:\n",
-    "            o = Link(l.height - 1, l.left, l.right)\n",
-    "            if o in height_groups[h-1]:\n",
-    "                eps += [(l, o)]\n",
-    "    return eps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 24.1 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "eliminable_pairs(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pair(net):\n",
-    "    for l in net:\n",
-    "        o = Link(l.height + 1, l.left, l.right)\n",
-    "        if o in net:\n",
-    "            return l, o\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pair_hg(height_groups):\n",
-    "    for h in range(1, max(height_groups.keys())):\n",
-    "        for l in height_groups[h]:\n",
-    "            o = Link(l.height - 1, l.left, l.right)\n",
-    "            if o in height_groups[h-1]:\n",
-    "                return l, o\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_pairs_slow(net):\n",
-    "    eliminable_links = eliminable_pair(net)\n",
-    "    while eliminable_links:\n",
-    "        net = pack(l for l in net if l not in eliminable_links)\n",
-    "        eliminable_links = eliminable_pair(net)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_pairs(net):\n",
-    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "    eliminable_links = eliminable_pair_hg(height_groups)\n",
-    "    while eliminable_links:\n",
-    "        net = pack(l for l in net if l not in eliminable_links)\n",
-    "        height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "        eliminable_links = eliminable_pair_hg(height_groups)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10207\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(10207, 9813)"
-      ]
-     },
-     "execution_count": 82,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "print(len(plnet))\n",
-    "elnet = eliminate_pairs(plnet)\n",
-    "len(plnet), len(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "eliminable_pairs(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase,  lnet) == follow_many(string.ascii_lowercase, elnet)\n",
-    "assert follow_many(string.ascii_lowercase, plnet) == follow_many(string.ascii_lowercase, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 6.08 s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "elnet = eliminate_pairs(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# for i in range(26):\n",
-    "#     assert follow(i, plnet) == follow(i, elnet)\n",
-    "#     assert follow(i,  lnet) == follow(i, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# follow(0, plnet), follow(0, elnet), follow(0, lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def triple_slow(net):\n",
-    "    x = None\n",
-    "    y = None\n",
-    "    ts = []\n",
-    "    for a in net:\n",
-    "        bs = [l for l in net if l.height == a.height + 1 \n",
-    "              if l.left == a.right or l.right == a.left]\n",
-    "        for b in bs:\n",
-    "            c = Link(a.height + 2, a.left, a.right)\n",
-    "            if c in net:\n",
-    "                ts += [(a, b, c)]\n",
-    "    return ts"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def triple_pair_slow(net):\n",
-    "    ts = []\n",
-    "    for a in net:\n",
-    "        a_ends = link_ends(a)\n",
-    "        bs = [l for l in net if l.height == a.height + 1 \n",
-    "              if link_ends(l) & a_ends]\n",
-    "        if len(bs) == 1:\n",
-    "            b = bs[0]\n",
-    "            lines = set((a.left, a.right, b.left, b.right))\n",
-    "            cs = [l for l in net \n",
-    "                  if l.height == a.height + 2\n",
-    "                  if link_ends(l) & lines]\n",
-    "            if len(cs) == 1:\n",
-    "                c = Link(a.height + 2, a.left, a.right)\n",
-    "                if c in cs:\n",
-    "                    ds = [l for l in net \n",
-    "                          if l.height == a.height + 3\n",
-    "                          if link_ends(l) & lines]\n",
-    "                    d = Link(a.height + 3, b.left, b.right)\n",
-    "                    if d in ds:\n",
-    "                        ts += [(a, b, c, d)]\n",
-    "    return ts"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def find_height_groups(net):\n",
-    "    return {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def triple_pair_hg(height_groups, debug=False):\n",
-    "    ts = []\n",
-    "    for h in range(3, max(height_groups.keys())):\n",
-    "        for d in height_groups[h]:\n",
-    "            if debug: print('d:', d)\n",
-    "            ch = h - 1\n",
-    "            cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
-    "            if debug: print('cs:', cs)\n",
-    "            while ch > 2 and not cs:\n",
-    "                ch -= 1\n",
-    "                cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
-    "                if debug: print('cs:', cs)\n",
-    "            if len(cs) == 1:\n",
-    "                c = cs[0]\n",
-    "                lines = set((d.left, d.right, c.left, c.right))\n",
-    "                if debug: print('c:', '; lines:', lines)\n",
-    "                bs = [l for l in height_groups[ch-1] if link_ends(l) & lines]\n",
-    "                b = Link(ch - 1, d.left, d.right)\n",
-    "                if debug: print('b:', b, '; bs:', bs)\n",
-    "                if len(bs) == 1 and b in bs:\n",
-    "                    ah = b.height - 1\n",
-    "                    als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
-    "                    if debug: print('ah:', ah, '; als:', als)\n",
-    "                    while ah > 0 and not als:\n",
-    "                        ah -= 1\n",
-    "                        als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
-    "                        if debug: print('ah:', ah, '; als:', als)\n",
-    "                    a = Link(ah, c.left, c.right)\n",
-    "                    if debug: print('a:', a)\n",
-    "                    if a in als:\n",
-    "                        if debug: print('adding:', a, b, c, d)\n",
-    "                        ts += [(a, b, c, d)]\n",
-    "    return ts"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_a_triple_pair_slow(net, debug=False):\n",
-    "    tps = triple_pair_slow(net)\n",
-    "    if debug: print('eatp', tps)\n",
-    "\n",
-    "    if tps:\n",
-    "        a, b, c, d = tps[0]\n",
-    "#         x = Link(a.height, b.left, b.right)\n",
-    "#         y = Link(b.height, a.left, a.right)\n",
-    "        x = Link(b.height - 0.5, b.left, b.right)\n",
-    "        y = Link(b.height, a.left, a.right)\n",
-    "        if debug: print('removing', a, b, c, d, '; adding', x, y)\n",
-    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_a_triple_pair(net, debug=False):\n",
-    "    height_groups = find_height_groups(net)\n",
-    "\n",
-    "    tps = triple_pair_hg(height_groups)\n",
-    "    if debug: print('eatp', tps)\n",
-    "    if tps:\n",
-    "        a, b, c, d = tps[0]\n",
-    "        x = Link(b.height - 0.5, b.left, b.right)\n",
-    "        y = Link(b.height, a.left, a.right)\n",
-    "        if debug: print('removing', a, b, c, d, '; adding', x, y)\n",
-    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=1126, left=8, right=17),\n",
-       "  Link(height=1127, left=1, right=8),\n",
-       "  Link(height=1128, left=8, right=17),\n",
-       "  Link(height=1129, left=1, right=8)),\n",
-       " (Link(height=1952, left=12, right=25),\n",
-       "  Link(height=1953, left=10, right=12),\n",
-       "  Link(height=1954, left=12, right=25),\n",
-       "  Link(height=1955, left=10, right=12))]"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "height_groups = find_height_groups(elnet)\n",
-    "triple_pair_hg(height_groups)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 98.7 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "height_groups = find_height_groups(elnet)\n",
-    "triple_pair_hg(height_groups)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_triple_pairs_slow(net):\n",
-    "    print(len(net))\n",
-    "    new_net = eliminate_a_triple_pair_slow(net)\n",
-    "    while new_net:\n",
-    "        print(len(net))\n",
-    "        net = new_net\n",
-    "        new_net = eliminate_a_triple_pair_slow(net)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_triple_pairs(net):\n",
-    "    print(len(net))\n",
-    "    new_net = eliminate_a_triple_pair(net)\n",
-    "    while new_net:\n",
-    "        print(len(net))\n",
-    "        net = new_net\n",
-    "        new_net = eliminate_a_triple_pair(net)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "etlnet = eliminate_a_triple_pair(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "9813\n",
-      "9813\n",
-      "9811\n"
-     ]
-    }
-   ],
-   "source": [
-    "setlnet = eliminate_triple_pairs(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9809"
-      ]
-     },
-     "execution_count": 101,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(setlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'ypetfugkzdsacbvwjohqlnirmx'"
-      ]
-     },
-     "execution_count": 103,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, etlnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'ypetfugkzdsacbvwjohqlnirmx'"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, setlnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'ypetfugkzdsacbvwjohqlnirmx'"
-      ]
-     },
-     "execution_count": 105,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, elnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'ypetfugkzdsacbvwjohqlnirmx'"
-      ]
-     },
-     "execution_count": 106,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 107,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "eliminable_pairs(etlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(10207, 9811)"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(lnet), len(etlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def simplify(net0):\n",
-    "    netp = eliminate_pairs(net0)\n",
-    "    new_net = eliminate_a_triple_pair(netp)\n",
-    "    while new_net:\n",
-    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
-    "        netp = eliminate_pairs(new_net)\n",
-    "        new_net = eliminate_a_triple_pair(netp)\n",
-    "    return netp"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "simple_lnet = simplify(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, simple_lnet)) == ''.join(follow_many(string.ascii_lowercase, lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'ypetfugkzdsacbvwjohqlnirmx'"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, simple_lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'ypetfugkzdsacbvwjohqlnirmx'"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9809"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(simple_lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 115,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def add_triple_pair(net, max_lines=None, trace=False):\n",
-    "    if not max_lines:\n",
-    "        max_lines = max(l.right for l in net)\n",
-    "    a, b, c = 0, 0, 0\n",
-    "    while len(set((a, b, c))) != 3:\n",
-    "        a = random.randrange(max_lines)\n",
-    "        b = random.randrange(max_lines)\n",
-    "        c = random.randrange(max_lines)\n",
-    "    tp = [(min(a, b), max(a, b)), (min(b, c), max(b, c))] * 2\n",
-    "    \n",
-    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
-    "    i = random.randrange(len(pairs))\n",
-    "    if trace: print(i, tp)\n",
-    "    new_pairs = pairs[:i] + tp + pairs[i:]\n",
-    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 116,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def add_pair(net, max_lines=None, trace=False):\n",
-    "    if not max_lines:\n",
-    "        max_lines = max(l.right for l in net)\n",
-    "\n",
-    "    a, b = 0, 0\n",
-    "    while a == b:\n",
-    "        a = random.randrange(max_lines)\n",
-    "        b = random.randrange(max_lines)\n",
-    "    p = [(min(a, b), max(a, b))] * 2\n",
-    "    \n",
-    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
-    "    i = random.randrange(len(pairs))\n",
-    "    \n",
-    "    if trace: print(i, p)\n",
-    "    new_pairs = pairs[:i] + p + pairs[i:]\n",
-    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 117,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 117,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 118,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 118,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "lnettp = simple_lnet\n",
-    "for _ in range(10):\n",
-    "    lnettp = add_pair(lnettp)\n",
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 119,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=301, left=7, right=23),\n",
-       "  Link(height=302, left=16, right=23),\n",
-       "  Link(height=303, left=7, right=23),\n",
-       "  Link(height=304, left=16, right=23)),\n",
-       " (Link(height=362, left=11, right=23),\n",
-       "  Link(height=363, left=3, right=23),\n",
-       "  Link(height=364, left=11, right=23),\n",
-       "  Link(height=365, left=3, right=23)),\n",
-       " (Link(height=363, left=3, right=23),\n",
-       "  Link(height=364, left=11, right=23),\n",
-       "  Link(height=365, left=3, right=23),\n",
-       "  Link(height=366, left=11, right=23)),\n",
-       " (Link(height=595, left=12, right=15),\n",
-       "  Link(height=596, left=10, right=15),\n",
-       "  Link(height=597, left=12, right=15),\n",
-       "  Link(height=598, left=10, right=15)),\n",
-       " (Link(height=796, left=12, right=21),\n",
-       "  Link(height=797, left=4, right=12),\n",
-       "  Link(height=798, left=12, right=21),\n",
-       "  Link(height=799, left=4, right=12)),\n",
-       " (Link(height=879, left=0, right=18),\n",
-       "  Link(height=880, left=0, right=8),\n",
-       "  Link(height=881, left=0, right=18),\n",
-       "  Link(height=882, left=0, right=8)),\n",
-       " (Link(height=930, left=3, right=17),\n",
-       "  Link(height=931, left=3, right=21),\n",
-       "  Link(height=932, left=3, right=17),\n",
-       "  Link(height=933, left=3, right=21)),\n",
-       " (Link(height=1120, left=5, right=19),\n",
-       "  Link(height=1121, left=18, right=19),\n",
-       "  Link(height=1122, left=5, right=19),\n",
-       "  Link(height=1123, left=18, right=19)),\n",
-       " (Link(height=2040, left=9, right=21),\n",
-       "  Link(height=2041, left=9, right=15),\n",
-       "  Link(height=2042, left=9, right=21),\n",
-       "  Link(height=2043, left=9, right=15)),\n",
-       " (Link(height=2110, left=13, right=21),\n",
-       "  Link(height=2111, left=13, right=24),\n",
-       "  Link(height=2112, left=13, right=21),\n",
-       "  Link(height=2113, left=13, right=24))]"
-      ]
-     },
-     "execution_count": 119,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "lnettp = simple_lnet\n",
-    "for _ in range(10):\n",
-    "    lnettp = add_triple_pair(lnettp)\n",
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 120,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=49, left=10, right=20),\n",
-       "  Link(height=50, left=2, right=20),\n",
-       "  Link(height=51, left=10, right=20),\n",
-       "  Link(height=52, left=2, right=20)),\n",
-       " (Link(height=54, left=2, right=24),\n",
-       "  Link(height=55, left=3, right=24),\n",
-       "  Link(height=56, left=2, right=24),\n",
-       "  Link(height=57, left=3, right=24)),\n",
-       " (Link(height=62, left=2, right=15),\n",
-       "  Link(height=63, left=0, right=15),\n",
-       "  Link(height=64, left=2, right=15),\n",
-       "  Link(height=65, left=0, right=15)),\n",
-       " (Link(height=114, left=14, right=18),\n",
-       "  Link(height=115, left=3, right=18),\n",
-       "  Link(height=116, left=14, right=18),\n",
-       "  Link(height=117, left=3, right=18)),\n",
-       " (Link(height=138, left=13, right=19),\n",
-       "  Link(height=139, left=8, right=19),\n",
-       "  Link(height=140, left=13, right=19),\n",
-       "  Link(height=141, left=8, right=19)),\n",
-       " (Link(height=160, left=12, right=13),\n",
-       "  Link(height=161, left=4, right=12),\n",
-       "  Link(height=162, left=12, right=13),\n",
-       "  Link(height=163, left=4, right=12)),\n",
-       " (Link(height=315, left=23, right=24),\n",
-       "  Link(height=320, left=20, right=23),\n",
-       "  Link(height=321, left=23, right=24),\n",
-       "  Link(height=322, left=20, right=23)),\n",
-       " (Link(height=324, left=3, right=18),\n",
-       "  Link(height=325, left=16, right=18),\n",
-       "  Link(height=326, left=3, right=18),\n",
-       "  Link(height=327, left=16, right=18)),\n",
-       " (Link(height=342, left=21, right=22),\n",
-       "  Link(height=345, left=1, right=22),\n",
-       "  Link(height=346, left=21, right=22),\n",
-       "  Link(height=347, left=1, right=22)),\n",
-       " (Link(height=405, left=8, right=19),\n",
-       "  Link(height=406, left=4, right=8),\n",
-       "  Link(height=407, left=8, right=19),\n",
-       "  Link(height=408, left=4, right=8)),\n",
-       " (Link(height=468, left=11, right=22),\n",
-       "  Link(height=469, left=15, right=22),\n",
-       "  Link(height=470, left=11, right=22),\n",
-       "  Link(height=471, left=15, right=22)),\n",
-       " (Link(height=549, left=1, right=2),\n",
-       "  Link(height=550, left=1, right=6),\n",
-       "  Link(height=551, left=1, right=2),\n",
-       "  Link(height=552, left=1, right=6)),\n",
-       " (Link(height=568, left=16, right=21),\n",
-       "  Link(height=569, left=11, right=21),\n",
-       "  Link(height=570, left=16, right=21),\n",
-       "  Link(height=571, left=11, right=21)),\n",
-       " (Link(height=608, left=17, right=20),\n",
-       "  Link(height=609, left=2, right=17),\n",
-       "  Link(height=610, left=17, right=20),\n",
-       "  Link(height=611, left=2, right=17)),\n",
-       " (Link(height=613, left=18, right=21),\n",
-       "  Link(height=618, left=18, right=19),\n",
-       "  Link(height=619, left=18, right=21),\n",
-       "  Link(height=620, left=18, right=19)),\n",
-       " (Link(height=635, left=2, right=4),\n",
-       "  Link(height=636, left=4, right=20),\n",
-       "  Link(height=637, left=2, right=4),\n",
-       "  Link(height=638, left=4, right=20)),\n",
-       " (Link(height=681, left=7, right=20),\n",
-       "  Link(height=682, left=20, right=22),\n",
-       "  Link(height=683, left=7, right=20),\n",
-       "  Link(height=684, left=20, right=22)),\n",
-       " (Link(height=750, left=23, right=24),\n",
-       "  Link(height=751, left=18, right=24),\n",
-       "  Link(height=752, left=23, right=24),\n",
-       "  Link(height=753, left=18, right=24)),\n",
-       " (Link(height=760, left=12, right=18),\n",
-       "  Link(height=761, left=17, right=18),\n",
-       "  Link(height=762, left=12, right=18),\n",
-       "  Link(height=763, left=17, right=18)),\n",
-       " (Link(height=765, left=0, right=9),\n",
-       "  Link(height=766, left=0, right=14),\n",
-       "  Link(height=767, left=0, right=9),\n",
-       "  Link(height=768, left=0, right=14)),\n",
-       " (Link(height=805, left=16, right=22),\n",
-       "  Link(height=806, left=0, right=16),\n",
-       "  Link(height=807, left=16, right=22),\n",
-       "  Link(height=808, left=0, right=16)),\n",
-       " (Link(height=834, left=1, right=6),\n",
-       "  Link(height=835, left=3, right=6),\n",
-       "  Link(height=836, left=1, right=6),\n",
-       "  Link(height=837, left=3, right=6)),\n",
-       " (Link(height=881, left=2, right=12),\n",
-       "  Link(height=882, left=2, right=23),\n",
-       "  Link(height=883, left=2, right=12),\n",
-       "  Link(height=884, left=2, right=23)),\n",
-       " (Link(height=904, left=12, right=23),\n",
-       "  Link(height=905, left=12, right=14),\n",
-       "  Link(height=906, left=12, right=23),\n",
-       "  Link(height=907, left=12, right=14)),\n",
-       " (Link(height=936, left=7, right=17),\n",
-       "  Link(height=937, left=15, right=17),\n",
-       "  Link(height=938, left=7, right=17),\n",
-       "  Link(height=939, left=15, right=17)),\n",
-       " (Link(height=1010, left=4, right=6),\n",
-       "  Link(height=1011, left=6, right=17),\n",
-       "  Link(height=1012, left=4, right=6),\n",
-       "  Link(height=1013, left=6, right=17)),\n",
-       " (Link(height=1030, left=1, right=12),\n",
-       "  Link(height=1031, left=1, right=20),\n",
-       "  Link(height=1032, left=1, right=12),\n",
-       "  Link(height=1033, left=1, right=20)),\n",
-       " (Link(height=1197, left=2, right=9),\n",
-       "  Link(height=1198, left=9, right=22),\n",
-       "  Link(height=1199, left=2, right=9),\n",
-       "  Link(height=1200, left=9, right=22)),\n",
-       " (Link(height=1222, left=2, right=3),\n",
-       "  Link(height=1223, left=2, right=5),\n",
-       "  Link(height=1224, left=2, right=3),\n",
-       "  Link(height=1225, left=2, right=5)),\n",
-       " (Link(height=1318, left=12, right=23),\n",
-       "  Link(height=1319, left=4, right=12),\n",
-       "  Link(height=1320, left=12, right=23),\n",
-       "  Link(height=1321, left=4, right=12)),\n",
-       " (Link(height=1341, left=17, right=22),\n",
-       "  Link(height=1342, left=11, right=17),\n",
-       "  Link(height=1343, left=17, right=22),\n",
-       "  Link(height=1344, left=11, right=17)),\n",
-       " (Link(height=1396, left=4, right=9),\n",
-       "  Link(height=1397, left=3, right=9),\n",
-       "  Link(height=1398, left=4, right=9),\n",
-       "  Link(height=1399, left=3, right=9)),\n",
-       " (Link(height=1426, left=18, right=24),\n",
-       "  Link(height=1427, left=17, right=18),\n",
-       "  Link(height=1428, left=18, right=24),\n",
-       "  Link(height=1429, left=17, right=18)),\n",
-       " (Link(height=1456, left=2, right=15),\n",
-       "  Link(height=1457, left=3, right=15),\n",
-       "  Link(height=1458, left=2, right=15),\n",
-       "  Link(height=1459, left=3, right=15)),\n",
-       " (Link(height=1505, left=13, right=18),\n",
-       "  Link(height=1506, left=13, right=21),\n",
-       "  Link(height=1507, left=13, right=18),\n",
-       "  Link(height=1508, left=13, right=21)),\n",
-       " (Link(height=1551, left=10, right=12),\n",
-       "  Link(height=1552, left=4, right=12),\n",
-       "  Link(height=1553, left=10, right=12),\n",
-       "  Link(height=1554, left=4, right=12)),\n",
-       " (Link(height=1622, left=4, right=11),\n",
-       "  Link(height=1623, left=11, right=16),\n",
-       "  Link(height=1624, left=4, right=11),\n",
-       "  Link(height=1625, left=11, right=16)),\n",
-       " (Link(height=1653, left=8, right=24),\n",
-       "  Link(height=1654, left=4, right=8),\n",
-       "  Link(height=1655, left=8, right=24),\n",
-       "  Link(height=1656, left=4, right=8)),\n",
-       " (Link(height=1688, left=0, right=5),\n",
-       "  Link(height=1689, left=0, right=23),\n",
-       "  Link(height=1690, left=0, right=5),\n",
-       "  Link(height=1691, left=0, right=23)),\n",
-       " (Link(height=1724, left=10, right=23),\n",
-       "  Link(height=1725, left=10, right=11),\n",
-       "  Link(height=1726, left=10, right=23),\n",
-       "  Link(height=1727, left=10, right=11)),\n",
-       " (Link(height=1863, left=1, right=12),\n",
-       "  Link(height=1864, left=1, right=13),\n",
-       "  Link(height=1865, left=1, right=12),\n",
-       "  Link(height=1866, left=1, right=13)),\n",
-       " (Link(height=1873, left=10, right=22),\n",
-       "  Link(height=1874, left=10, right=15),\n",
-       "  Link(height=1875, left=10, right=22),\n",
-       "  Link(height=1876, left=10, right=15)),\n",
-       " (Link(height=1879, left=18, right=20),\n",
-       "  Link(height=1880, left=17, right=20),\n",
-       "  Link(height=1881, left=18, right=20),\n",
-       "  Link(height=1882, left=17, right=20)),\n",
-       " (Link(height=1916, left=18, right=19),\n",
-       "  Link(height=1917, left=7, right=18),\n",
-       "  Link(height=1918, left=18, right=19),\n",
-       "  Link(height=1919, left=7, right=18)),\n",
-       " (Link(height=1961, left=11, right=20),\n",
-       "  Link(height=1962, left=7, right=20),\n",
-       "  Link(height=1963, left=11, right=20),\n",
-       "  Link(height=1964, left=7, right=20)),\n",
-       " (Link(height=1962, left=9, right=18),\n",
-       "  Link(height=1963, left=18, right=19),\n",
-       "  Link(height=1964, left=9, right=18),\n",
-       "  Link(height=1965, left=18, right=19)),\n",
-       " (Link(height=2031, left=3, right=6),\n",
-       "  Link(height=2032, left=3, right=4),\n",
-       "  Link(height=2033, left=3, right=6),\n",
-       "  Link(height=2034, left=3, right=4)),\n",
-       " (Link(height=2077, left=2, right=9),\n",
-       "  Link(height=2078, left=2, right=23),\n",
-       "  Link(height=2079, left=2, right=9),\n",
-       "  Link(height=2080, left=2, right=23)),\n",
-       " (Link(height=2165, left=1, right=8),\n",
-       "  Link(height=2166, left=4, right=8),\n",
-       "  Link(height=2167, left=1, right=8),\n",
-       "  Link(height=2168, left=4, right=8)),\n",
-       " (Link(height=2185, left=6, right=21),\n",
-       "  Link(height=2186, left=11, right=21),\n",
-       "  Link(height=2187, left=6, right=21),\n",
-       "  Link(height=2188, left=11, right=21))]"
-      ]
-     },
-     "execution_count": 120,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "lnettp = simple_lnet\n",
-    "for _ in range(50):\n",
-    "    lnettp = add_pair(lnettp)\n",
-    "for _ in range(50):\n",
-    "    lnettp = add_triple_pair(lnettp)\n",
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 121,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 121,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "lnettp == pack(lnettp)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 122,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9909"
-      ]
-     },
-     "execution_count": 122,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "lnettps = simplify(lnettp)\n",
-    "len(lnettps)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 123,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(9809, 10109, 9909)"
-      ]
-     },
-     "execution_count": 123,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(simple_lnet), len(lnettp), len(lnettps)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 124,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 124,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, lnet)) == ''.join(follow_many(string.ascii_lowercase, simple_lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 125,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 125,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, lnettps)) == ''.join(follow_many(string.ascii_lowercase, lnettp))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 126,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2285"
-      ]
-     },
-     "execution_count": 126,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in lnettp)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 127,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def simplify_with_checks(net0):\n",
-    "    netp = eliminate_pairs(net0)\n",
-    "    if follow_many(string.ascii_lowercase, net0) != follow_many(string.ascii_lowercase, netp):\n",
-    "        print('pairs', eliminable_pairs(net0))\n",
-    "        return net0\n",
-    "    else:\n",
-    "        print('pairs ok')\n",
-    "    new_net = eliminate_a_triple_pair(netp)\n",
-    "    if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
-    "        hg = find_height_groups(netp)\n",
-    "        print('triple', triple_pair_hg(hg))\n",
-    "        return netp\n",
-    "    else:\n",
-    "        print('triple ok')\n",
-    "    while new_net:\n",
-    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
-    "        netp = eliminate_pairs(new_net)\n",
-    "        if follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
-    "            print('pairs', eliminable_pairs(new_net))\n",
-    "            return new_net\n",
-    "        else:\n",
-    "            print('pairs ok')\n",
-    "        new_net = eliminate_a_triple_pair(netp)\n",
-    "        if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
-    "            hg = find_height_groups(netp)\n",
-    "            print('triple', triple_pair_hg(hg))\n",
-    "            return netp\n",
-    "        else:\n",
-    "            print('triple ok')\n",
-    "    print('** done')\n",
-    "    return netp"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 128,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "** done\n"
-     ]
-    }
-   ],
-   "source": [
-    "lnettps = simplify_with_checks(lnettp)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 129,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 129,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, lnettps)) == ''.join(follow_many(string.ascii_lowercase, lnettp))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 130,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10109"
-      ]
-     },
-     "execution_count": 130,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(lnettp)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 131,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# open('04-lines.txt', 'w').write(show_net(lnettp, randomise=True, pair_sep='\\n'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "139"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# open('04-small.txt', 'w').write(show_net(make_net(20), randomise=True, pair_sep='\\n'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 143,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "8 [(2, 4), (0, 4), (2, 4), (0, 4)]\n",
-      "10 [(1, 2), (1, 2)]\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=2, right=5),\n",
-       " Link(height=1, left=1, right=4),\n",
-       " Link(height=2, left=0, right=3),\n",
-       " Link(height=3, left=0, right=3),\n",
-       " Link(height=4, left=0, right=5),\n",
-       " Link(height=5, left=3, right=5),\n",
-       " Link(height=6, left=0, right=2),\n",
-       " Link(height=7, left=3, right=4),\n",
-       " Link(height=8, left=2, right=4),\n",
-       " Link(height=9, left=1, right=2),\n",
-       " Link(height=10, left=0, right=4),\n",
-       " Link(height=11, left=1, right=2),\n",
-       " Link(height=12, left=2, right=4),\n",
-       " Link(height=13, left=1, right=2),\n",
-       " Link(height=14, left=0, right=4),\n",
-       " Link(height=15, left=1, right=4)]"
-      ]
-     },
-     "execution_count": 143,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "net = make_net(10, lines=6)\n",
-    "net = add_triple_pair(net, trace=True)\n",
-    "net = add_pair(net, trace=True)\n",
-    "net = read_net(show_net(net, randomise=True))\n",
-    "net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 147,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'(2, 5), (1, 4), (0, 3), (0, 3), (0, 5), (3, 5), (0, 2), (3, 4), (2, 4), (1, 2), (0, 4), (1, 2), (2, 4), (1, 2), (0, 4), (1, 4)'"
-      ]
-     },
-     "execution_count": 147,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "show_net(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 149,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=2, right=5),\n",
-       " Link(height=1, left=1, right=4),\n",
-       " Link(height=2, left=0, right=3),\n",
-       " Link(height=3, left=0, right=3),\n",
-       " Link(height=4, left=0, right=5),\n",
-       " Link(height=5, left=3, right=5),\n",
-       " Link(height=6, left=0, right=2),\n",
-       " Link(height=7, left=3, right=4),\n",
-       " Link(height=8, left=2, right=4),\n",
-       " Link(height=9, left=1, right=2),\n",
-       " Link(height=10, left=0, right=4),\n",
-       " Link(height=11, left=1, right=2),\n",
-       " Link(height=12, left=2, right=4),\n",
-       " Link(height=13, left=0, right=4),\n",
-       " Link(height=14, left=1, right=4)]"
-      ]
-     },
-     "execution_count": 149,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "net = read_net('(2, 5), (1, 4), (0, 3), (0, 3), (0, 5), (3, 5), (0, 2), (3, 4), (2, 4), (1, 2), (0, 4), (1, 2), (2, 4), (0, 4), (1, 4)')\n",
-    "net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 150,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=0, right=3),\n",
-       " Link(height=0, left=1, right=4),\n",
-       " Link(height=0, left=2, right=5),\n",
-       " Link(height=1, left=0, right=3),\n",
-       " Link(height=2, left=0, right=5),\n",
-       " Link(height=3, left=0, right=2),\n",
-       " Link(height=3, left=3, right=5),\n",
-       " Link(height=4, left=3, right=4),\n",
-       " Link(height=5, left=2, right=4),\n",
-       " Link(height=6, left=0, right=4),\n",
-       " Link(height=6, left=1, right=2),\n",
-       " Link(height=7, left=1, right=2),\n",
-       " Link(height=8, left=2, right=4),\n",
-       " Link(height=9, left=0, right=4),\n",
-       " Link(height=10, left=1, right=4)]"
-      ]
-     },
-     "execution_count": 150,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pack(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 151,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=1, right=4),\n",
-       " Link(height=0, left=2, right=5),\n",
-       " Link(height=1, left=0, right=5),\n",
-       " Link(height=2, left=0, right=2),\n",
-       " Link(height=2, left=3, right=5),\n",
-       " Link(height=3, left=3, right=4),\n",
-       " Link(height=4, left=2, right=4),\n",
-       " Link(height=5, left=0, right=4),\n",
-       " Link(height=6, left=2, right=4),\n",
-       " Link(height=7, left=0, right=4),\n",
-       " Link(height=8, left=1, right=4)]"
-      ]
-     },
-     "execution_count": 151,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "epnet = eliminate_pairs(net)\n",
-    "pack(epnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 152,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "11\n",
-      "11\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=1, right=4),\n",
-       " Link(height=0, left=2, right=5),\n",
-       " Link(height=1, left=0, right=5),\n",
-       " Link(height=2, left=0, right=2),\n",
-       " Link(height=2, left=3, right=5),\n",
-       " Link(height=3, left=3, right=4),\n",
-       " Link(height=4, left=0, right=4),\n",
-       " Link(height=5, left=2, right=4),\n",
-       " Link(height=6, left=1, right=4)]"
-      ]
-     },
-     "execution_count": 152,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "eptnet = eliminate_triple_pairs(epnet)\n",
-    "pack(eptnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 153,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 153,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, net)) == ''.join(follow_many(string.ascii_lowercase, eptnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 155,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "104"
-      ]
-     },
-     "execution_count": 155,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "open('04-small.txt', 'w').write(show_net(net, pair_sep='\\n'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

diff --git a/04-08-amidakuji/amidakuji-solution-1-slow.ipynb b/04-08-amidakuji/amidakuji-solution-1-slow.ipynb
deleted file mode 100644 (file)
index 345321d..0000000
--- a/04-08-amidakuji/amidakuji-solution-1-slow.ipynb
+++ /dev/null
@@ -1,1881 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import collections\n",
-    "import string\n",
-    "import itertools"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "Link = collections.namedtuple('Link', 'height left right')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def link_ends(link):\n",
-    "    return set((link.left, link.right))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def read_net(net_string):\n",
-    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow(initial_line, links):\n",
-    "    line = initial_line\n",
-    "    heights = sorted(set(l.height for l in links))\n",
-    "    for h in heights:\n",
-    "        for l in [l for l in links if l.height == h]:\n",
-    "            if line in link_ends(l):\n",
-    "                line = [e for e in link_ends(l) if e != line][0]\n",
-    "#                 print(l, line)\n",
-    "    return line"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def pack(net):\n",
-    "    packed_links = []\n",
-    "    line_heights = collections.defaultdict(lambda: -1)\n",
-    "    for link in sorted(net):\n",
-    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
-    "        line_heights[link.left] = link_height\n",
-    "        line_heights[link.right] = link_height\n",
-    "        packed_links += [Link(link_height, link.left, link.right)]\n",
-    "    return sorted(packed_links)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow_many_slow(in_sequence, links):\n",
-    "    out_sequence = [(follow(i, links), term) \n",
-    "                    for i, term in enumerate(in_sequence)]\n",
-    "    return [term for i, term in sorted(out_sequence)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow_many(in_sequence, net):\n",
-    "    height_groups = [list(g) for _, g in itertools.groupby(pack(net), lambda l: l.height)]\n",
-    "    seq = list(in_sequence)\n",
-    "    for links in height_groups:\n",
-    "        for link in links:\n",
-    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
-    "    return seq"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10000 loops, best of 3: 47.5 µs per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many('abcdefghij', net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# %%timeit\n",
-    "# follow_many_slow('abcdefghij', net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def show_net(links, randomise=False):\n",
-    "    if randomise:\n",
-    "        output = []\n",
-    "        heights = sorted(set(l.height for l in links))\n",
-    "        for h in heights:\n",
-    "            ls = [l for l in links if l.height == h]\n",
-    "            random.shuffle(ls)\n",
-    "            output += ['({}, {})'.format(l.left, l.right) for l in ls]\n",
-    "        return ', '.join(output)\n",
-    "    return ', '.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def extract_pairs(net_string):\n",
-    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(True, True)"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "rrnet = read_net(show_net(net, randomise=True))\n",
-    "rnet = read_net(show_net(net))\n",
-    "rnet == rrnet, pack(rrnet) == pnet"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "lnet = make_net(10207, 26, 100000)\n",
-    "plnet = pack(lnet)\n",
-    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, plnet)\n",
-    "# for i in range(204):\n",
-    "#     assert follow(i, lnet) == follow(i, plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "rlnet = read_net(show_net(lnet))\n",
-    "prlnet = pack(rlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2251"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "99998"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10206"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in rlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2251"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(link.height for link in prlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, prlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 24.5 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many(string.ascii_lowercase, lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# %%timeit\n",
-    "# follow_many_slow(string.ascii_lowercase, lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pairs_slow(net):\n",
-    "    eps = []\n",
-    "    for l in net:\n",
-    "        o = Link(l.height + 1, l.left, l.right)\n",
-    "        if o in net:\n",
-    "            eps += [(l, o)]\n",
-    "    return eps    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pairs(net):\n",
-    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "    eps = []\n",
-    "    for h in range(1, max(height_groups.keys())):\n",
-    "        for l in height_groups[h]:\n",
-    "            o = Link(l.height - 1, l.left, l.right)\n",
-    "            if o in height_groups[h-1]:\n",
-    "                eps += [(l, o)]\n",
-    "    return eps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 23.5 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "eliminable_pairs(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 2.33 s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "eliminable_pairs_slow(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert sorted(sorted(p) for p in eliminable_pairs(plnet)) == sorted(sorted(p) for p in eliminable_pairs_slow(plnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pair(net):\n",
-    "    for l in net:\n",
-    "        o = Link(l.height + 1, l.left, l.right)\n",
-    "        if o in net:\n",
-    "            return l, o\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pair_hg(height_groups):\n",
-    "    for h in range(1, max(height_groups.keys())):\n",
-    "        for l in height_groups[h]:\n",
-    "            o = Link(l.height - 1, l.left, l.right)\n",
-    "            if o in height_groups[h-1]:\n",
-    "                return l, o\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_pairs_slow(net):\n",
-    "    eliminable_links = eliminable_pair(net)\n",
-    "    while eliminable_links:\n",
-    "        net = pack(l for l in net if l not in eliminable_links)\n",
-    "        eliminable_links = eliminable_pair(net)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_pairs(net):\n",
-    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "    eliminable_links = eliminable_pair_hg(height_groups)\n",
-    "    while eliminable_links:\n",
-    "        net = pack(l for l in net if l not in eliminable_links)\n",
-    "        height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "        eliminable_links = eliminable_pair_hg(height_groups)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10207\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(10207, 9811)"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "print(len(plnet))\n",
-    "elnet = eliminate_pairs_slow(plnet)\n",
-    "len(plnet), len(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10207\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(10207, 9811)"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "print(len(plnet))\n",
-    "elnet = eliminate_pairs(plnet)\n",
-    "len(plnet), len(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "eliminable_pairs(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert eliminate_pairs_slow(plnet) == eliminate_pairs(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase,  lnet) == follow_many(string.ascii_lowercase, elnet)\n",
-    "assert follow_many(string.ascii_lowercase, plnet) == follow_many(string.ascii_lowercase, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 3min 30s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "elnet = eliminate_pairs_slow(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 6.27 s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "elnet = eliminate_pairs(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# for i in range(26):\n",
-    "#     assert follow(i, plnet) == follow(i, elnet)\n",
-    "#     assert follow(i,  lnet) == follow(i, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# follow(0, plnet), follow(0, elnet), follow(0, lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def triple(net):\n",
-    "    x = None\n",
-    "    y = None\n",
-    "    ts = []\n",
-    "    for a in net:\n",
-    "        bs = [l for l in net if l.height == a.height + 1 \n",
-    "              if l.left == a.right or l.right == a.left]\n",
-    "        for b in bs:\n",
-    "            c = Link(a.height + 2, a.left, a.right)\n",
-    "            if c in net:\n",
-    "                ts += [(a, b, c)]\n",
-    "    return ts"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def triple_pair(net):\n",
-    "    ts = []\n",
-    "    for a in net:\n",
-    "        a_ends = link_ends(a)\n",
-    "        bs = [l for l in net if l.height == a.height + 1 \n",
-    "              if link_ends(l) & a_ends]\n",
-    "        if len(bs) == 1:\n",
-    "            b = bs[0]\n",
-    "            lines = set((a.left, a.right, b.left, b.right))\n",
-    "            cs = [l for l in net \n",
-    "                  if l.height == a.height + 2\n",
-    "                  if link_ends(l) & lines]\n",
-    "            if len(cs) == 1:\n",
-    "                c = Link(a.height + 2, a.left, a.right)\n",
-    "                if c in cs:\n",
-    "                    ds = [l for l in net \n",
-    "                          if l.height == a.height + 3\n",
-    "                          if link_ends(l) & lines]\n",
-    "                    d = Link(a.height + 3, b.left, b.right)\n",
-    "                    if d in ds:\n",
-    "                        ts += [(a, b, c, d)]\n",
-    "    return ts"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 129,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def triple_pair_hg(height_groups, debug=False):\n",
-    "    ts = []\n",
-    "    for h in range(3, max(height_groups.keys())):\n",
-    "        for d in height_groups[h]:\n",
-    "            if debug: print('d:', d)\n",
-    "            ch = h - 1\n",
-    "            cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
-    "            if debug: print('cs:', cs)\n",
-    "            while ch > 2 and not cs:\n",
-    "                ch -= 1\n",
-    "                cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
-    "                if debug: print('cs:', cs)\n",
-    "            if len(cs) == 1:\n",
-    "                c = cs[0]\n",
-    "                lines = set((d.left, d.right, c.left, c.right))\n",
-    "                if debug: print('c:', '; lines:', lines)\n",
-    "                bs = [l for l in height_groups[ch-1] if link_ends(l) & lines]\n",
-    "                b = Link(ch - 1, d.left, d.right)\n",
-    "                if debug: print('b:', b, '; bs:', bs)\n",
-    "                if len(bs) == 1 and b in bs:\n",
-    "                    ah = b.height - 1\n",
-    "                    als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
-    "                    if debug: print('ah:', ah, '; als:', als)\n",
-    "                    while ah > 0 and not als:\n",
-    "                        ah -= 1\n",
-    "                        als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
-    "                        if debug: print('ah:', ah, '; als:', als)\n",
-    "                    a = Link(ah, c.left, c.right)\n",
-    "                    if debug: print('a:', a)\n",
-    "                    if a in als:\n",
-    "                        if debug: print('adding:', a, b, c, d)\n",
-    "                        ts += [(a, b, c, d)]\n",
-    "    return ts"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 132,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_a_triple_pair_slow(net):\n",
-    "    tps = triple_pair(net)\n",
-    "    print('eatp', tps)\n",
-    "\n",
-    "    if tps:\n",
-    "        a, b, c, d = tps[0]\n",
-    "#         x = Link(a.height, b.left, b.right)\n",
-    "#         y = Link(b.height, a.left, a.right)\n",
-    "        x = Link(a.height, b.left, b.right)\n",
-    "        y = Link(b.height, a.left, a.right)\n",
-    "        print('removing', a, b, c, d, '; adding', x, y)\n",
-    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 133,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_a_triple_pair(net):\n",
-    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "\n",
-    "    tps = triple_pair_hg(height_groups)\n",
-    "    print('eatp', tps)\n",
-    "    if tps:\n",
-    "        a, b, c, d = tps[0]\n",
-    "        x = Link(a.height, b.left, b.right)\n",
-    "        y = Link(b.height, a.left, a.right)\n",
-    "        print('removing', a, b, c, d, '; adding', x, y)\n",
-    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=12, left=0, right=5),\n",
-       "  Link(height=13, left=5, right=11),\n",
-       "  Link(height=14, left=0, right=5)),\n",
-       " (Link(height=29, left=2, right=18),\n",
-       "  Link(height=30, left=1, right=2),\n",
-       "  Link(height=31, left=2, right=18)),\n",
-       " (Link(height=40, left=2, right=3),\n",
-       "  Link(height=41, left=3, right=18),\n",
-       "  Link(height=42, left=2, right=3)),\n",
-       " (Link(height=43, left=1, right=10),\n",
-       "  Link(height=44, left=10, right=20),\n",
-       "  Link(height=45, left=1, right=10)),\n",
-       " (Link(height=91, left=5, right=8),\n",
-       "  Link(height=92, left=3, right=5),\n",
-       "  Link(height=93, left=5, right=8)),\n",
-       " (Link(height=91, left=5, right=8),\n",
-       "  Link(height=92, left=8, right=18),\n",
-       "  Link(height=93, left=5, right=8)),\n",
-       " (Link(height=99, left=13, right=17),\n",
-       "  Link(height=100, left=4, right=13),\n",
-       "  Link(height=101, left=13, right=17)),\n",
-       " (Link(height=120, left=18, right=20),\n",
-       "  Link(height=121, left=9, right=18),\n",
-       "  Link(height=122, left=18, right=20)),\n",
-       " (Link(height=147, left=19, right=21),\n",
-       "  Link(height=148, left=7, right=19),\n",
-       "  Link(height=149, left=19, right=21)),\n",
-       " (Link(height=147, left=19, right=21),\n",
-       "  Link(height=148, left=21, right=23),\n",
-       "  Link(height=149, left=19, right=21)),\n",
-       " (Link(height=179, left=13, right=25),\n",
-       "  Link(height=180, left=12, right=13),\n",
-       "  Link(height=181, left=13, right=25)),\n",
-       " (Link(height=265, left=3, right=20),\n",
-       "  Link(height=266, left=20, right=23),\n",
-       "  Link(height=267, left=3, right=20)),\n",
-       " (Link(height=291, left=5, right=23),\n",
-       "  Link(height=292, left=2, right=5),\n",
-       "  Link(height=293, left=5, right=23)),\n",
-       " (Link(height=292, left=18, right=25),\n",
-       "  Link(height=293, left=0, right=18),\n",
-       "  Link(height=294, left=18, right=25)),\n",
-       " (Link(height=302, left=11, right=19),\n",
-       "  Link(height=303, left=6, right=11),\n",
-       "  Link(height=304, left=11, right=19)),\n",
-       " (Link(height=309, left=15, right=20),\n",
-       "  Link(height=310, left=20, right=25),\n",
-       "  Link(height=311, left=15, right=20)),\n",
-       " (Link(height=325, left=13, right=18),\n",
-       "  Link(height=326, left=11, right=13),\n",
-       "  Link(height=327, left=13, right=18)),\n",
-       " (Link(height=362, left=11, right=22),\n",
-       "  Link(height=363, left=22, right=24),\n",
-       "  Link(height=364, left=11, right=22)),\n",
-       " (Link(height=372, left=22, right=23),\n",
-       "  Link(height=373, left=1, right=22),\n",
-       "  Link(height=374, left=22, right=23)),\n",
-       " (Link(height=386, left=4, right=17),\n",
-       "  Link(height=387, left=17, right=21),\n",
-       "  Link(height=388, left=4, right=17)),\n",
-       " (Link(height=393, left=4, right=16),\n",
-       "  Link(height=394, left=0, right=4),\n",
-       "  Link(height=395, left=4, right=16)),\n",
-       " (Link(height=531, left=0, right=4),\n",
-       "  Link(height=532, left=4, right=15),\n",
-       "  Link(height=533, left=0, right=4)),\n",
-       " (Link(height=575, left=5, right=21),\n",
-       "  Link(height=576, left=1, right=5),\n",
-       "  Link(height=577, left=5, right=21)),\n",
-       " (Link(height=639, left=7, right=11),\n",
-       "  Link(height=640, left=11, right=17),\n",
-       "  Link(height=641, left=7, right=11)),\n",
-       " (Link(height=687, left=2, right=4),\n",
-       "  Link(height=688, left=4, right=15),\n",
-       "  Link(height=689, left=2, right=4)),\n",
-       " (Link(height=706, left=8, right=11),\n",
-       "  Link(height=707, left=11, right=22),\n",
-       "  Link(height=708, left=8, right=11)),\n",
-       " (Link(height=722, left=22, right=23),\n",
-       "  Link(height=723, left=21, right=22),\n",
-       "  Link(height=724, left=22, right=23)),\n",
-       " (Link(height=768, left=9, right=11),\n",
-       "  Link(height=769, left=11, right=17),\n",
-       "  Link(height=770, left=9, right=11)),\n",
-       " (Link(height=792, left=5, right=12),\n",
-       "  Link(height=793, left=12, right=17),\n",
-       "  Link(height=794, left=5, right=12)),\n",
-       " (Link(height=805, left=20, right=22),\n",
-       "  Link(height=806, left=19, right=20),\n",
-       "  Link(height=807, left=20, right=22)),\n",
-       " (Link(height=806, left=19, right=20),\n",
-       "  Link(height=807, left=18, right=19),\n",
-       "  Link(height=808, left=19, right=20)),\n",
-       " (Link(height=806, left=19, right=20),\n",
-       "  Link(height=807, left=20, right=22),\n",
-       "  Link(height=808, left=19, right=20)),\n",
-       " (Link(height=882, left=7, right=14),\n",
-       "  Link(height=883, left=14, right=22),\n",
-       "  Link(height=884, left=7, right=14)),\n",
-       " (Link(height=884, left=6, right=11),\n",
-       "  Link(height=885, left=11, right=19),\n",
-       "  Link(height=886, left=6, right=11)),\n",
-       " (Link(height=892, left=12, right=17),\n",
-       "  Link(height=893, left=10, right=12),\n",
-       "  Link(height=894, left=12, right=17)),\n",
-       " (Link(height=916, left=18, right=24),\n",
-       "  Link(height=917, left=16, right=18),\n",
-       "  Link(height=918, left=18, right=24)),\n",
-       " (Link(height=919, left=14, right=17),\n",
-       "  Link(height=920, left=6, right=14),\n",
-       "  Link(height=921, left=14, right=17)),\n",
-       " (Link(height=994, left=0, right=3),\n",
-       "  Link(height=995, left=3, right=24),\n",
-       "  Link(height=996, left=0, right=3)),\n",
-       " (Link(height=1012, left=9, right=12),\n",
-       "  Link(height=1013, left=12, right=24),\n",
-       "  Link(height=1014, left=9, right=12)),\n",
-       " (Link(height=1034, left=1, right=6),\n",
-       "  Link(height=1035, left=6, right=12),\n",
-       "  Link(height=1036, left=1, right=6)),\n",
-       " (Link(height=1035, left=7, right=21),\n",
-       "  Link(height=1036, left=4, right=7),\n",
-       "  Link(height=1037, left=7, right=21)),\n",
-       " (Link(height=1047, left=3, right=10),\n",
-       "  Link(height=1048, left=10, right=11),\n",
-       "  Link(height=1049, left=3, right=10)),\n",
-       " (Link(height=1088, left=7, right=8),\n",
-       "  Link(height=1089, left=8, right=14),\n",
-       "  Link(height=1090, left=7, right=8)),\n",
-       " (Link(height=1104, left=3, right=10),\n",
-       "  Link(height=1105, left=10, right=11),\n",
-       "  Link(height=1106, left=3, right=10)),\n",
-       " (Link(height=1135, left=5, right=8),\n",
-       "  Link(height=1136, left=8, right=19),\n",
-       "  Link(height=1137, left=5, right=8)),\n",
-       " (Link(height=1138, left=1, right=3),\n",
-       "  Link(height=1139, left=3, right=23),\n",
-       "  Link(height=1140, left=1, right=3)),\n",
-       " (Link(height=1146, left=5, right=7),\n",
-       "  Link(height=1147, left=7, right=24),\n",
-       "  Link(height=1148, left=5, right=7)),\n",
-       " (Link(height=1197, left=5, right=14),\n",
-       "  Link(height=1198, left=14, right=15),\n",
-       "  Link(height=1199, left=5, right=14)),\n",
-       " (Link(height=1205, left=7, right=23),\n",
-       "  Link(height=1206, left=3, right=7),\n",
-       "  Link(height=1207, left=7, right=23)),\n",
-       " (Link(height=1276, left=18, right=25),\n",
-       "  Link(height=1277, left=17, right=18),\n",
-       "  Link(height=1278, left=18, right=25)),\n",
-       " (Link(height=1319, left=14, right=20),\n",
-       "  Link(height=1320, left=20, right=24),\n",
-       "  Link(height=1321, left=14, right=20)),\n",
-       " (Link(height=1328, left=8, right=21),\n",
-       "  Link(height=1329, left=1, right=8),\n",
-       "  Link(height=1330, left=8, right=21)),\n",
-       " (Link(height=1329, left=2, right=14),\n",
-       "  Link(height=1330, left=14, right=25),\n",
-       "  Link(height=1331, left=2, right=14)),\n",
-       " (Link(height=1385, left=10, right=14),\n",
-       "  Link(height=1386, left=14, right=15),\n",
-       "  Link(height=1387, left=10, right=14)),\n",
-       " (Link(height=1419, left=2, right=8),\n",
-       "  Link(height=1420, left=8, right=15),\n",
-       "  Link(height=1421, left=2, right=8)),\n",
-       " (Link(height=1465, left=13, right=21),\n",
-       "  Link(height=1466, left=21, right=24),\n",
-       "  Link(height=1467, left=13, right=21)),\n",
-       " (Link(height=1514, left=11, right=15),\n",
-       "  Link(height=1515, left=15, right=21),\n",
-       "  Link(height=1516, left=11, right=15)),\n",
-       " (Link(height=1545, left=3, right=11),\n",
-       "  Link(height=1546, left=11, right=25),\n",
-       "  Link(height=1547, left=3, right=11)),\n",
-       " (Link(height=1561, left=7, right=18),\n",
-       "  Link(height=1562, left=0, right=7),\n",
-       "  Link(height=1563, left=7, right=18)),\n",
-       " (Link(height=1671, left=9, right=15),\n",
-       "  Link(height=1672, left=15, right=23),\n",
-       "  Link(height=1673, left=9, right=15)),\n",
-       " (Link(height=1701, left=13, right=21),\n",
-       "  Link(height=1702, left=4, right=13),\n",
-       "  Link(height=1703, left=13, right=21)),\n",
-       " (Link(height=1706, left=5, right=13),\n",
-       "  Link(height=1707, left=13, right=23),\n",
-       "  Link(height=1708, left=5, right=13)),\n",
-       " (Link(height=1730, left=7, right=16),\n",
-       "  Link(height=1731, left=1, right=7),\n",
-       "  Link(height=1732, left=7, right=16)),\n",
-       " (Link(height=1781, left=0, right=8),\n",
-       "  Link(height=1782, left=8, right=17),\n",
-       "  Link(height=1783, left=0, right=8)),\n",
-       " (Link(height=1784, left=8, right=18),\n",
-       "  Link(height=1785, left=1, right=8),\n",
-       "  Link(height=1786, left=8, right=18)),\n",
-       " (Link(height=1804, left=19, right=24),\n",
-       "  Link(height=1805, left=7, right=19),\n",
-       "  Link(height=1806, left=19, right=24)),\n",
-       " (Link(height=1827, left=3, right=23),\n",
-       "  Link(height=1828, left=23, right=25),\n",
-       "  Link(height=1829, left=3, right=23)),\n",
-       " (Link(height=1837, left=1, right=16),\n",
-       "  Link(height=1838, left=16, right=17),\n",
-       "  Link(height=1839, left=1, right=16)),\n",
-       " (Link(height=1849, left=18, right=25),\n",
-       "  Link(height=1850, left=4, right=18),\n",
-       "  Link(height=1851, left=18, right=25)),\n",
-       " (Link(height=1856, left=6, right=13),\n",
-       "  Link(height=1857, left=13, right=17),\n",
-       "  Link(height=1858, left=6, right=13)),\n",
-       " (Link(height=1875, left=2, right=11),\n",
-       "  Link(height=1876, left=11, right=15),\n",
-       "  Link(height=1877, left=2, right=11)),\n",
-       " (Link(height=1970, left=6, right=24),\n",
-       "  Link(height=1971, left=1, right=6),\n",
-       "  Link(height=1972, left=6, right=24)),\n",
-       " (Link(height=2075, left=20, right=25),\n",
-       "  Link(height=2076, left=5, right=20),\n",
-       "  Link(height=2077, left=20, right=25)),\n",
-       " (Link(height=2081, left=4, right=19),\n",
-       "  Link(height=2082, left=1, right=4),\n",
-       "  Link(height=2083, left=4, right=19)),\n",
-       " (Link(height=2111, left=3, right=25),\n",
-       "  Link(height=2112, left=1, right=3),\n",
-       "  Link(height=2113, left=3, right=25)),\n",
-       " (Link(height=2225, left=3, right=12),\n",
-       "  Link(height=2226, left=12, right=24),\n",
-       "  Link(height=2227, left=3, right=12)),\n",
-       " (Link(height=2242, left=3, right=18),\n",
-       "  Link(height=2243, left=18, right=23),\n",
-       "  Link(height=2244, left=3, right=18))]"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "triple(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=316, left=8, right=17),\n",
-       "  Link(height=317, left=8, right=21),\n",
-       "  Link(height=318, left=8, right=17),\n",
-       "  Link(height=319, left=8, right=21)),\n",
-       " (Link(height=867, left=4, right=11),\n",
-       "  Link(height=868, left=5, right=11),\n",
-       "  Link(height=869, left=4, right=11),\n",
-       "  Link(height=870, left=5, right=11))]"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "triple_pair(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=316, left=8, right=17),\n",
-       "  Link(height=317, left=8, right=21),\n",
-       "  Link(height=318, left=8, right=17),\n",
-       "  Link(height=319, left=8, right=21)),\n",
-       " (Link(height=867, left=4, right=11),\n",
-       "  Link(height=868, left=5, right=11),\n",
-       "  Link(height=869, left=4, right=11),\n",
-       "  Link(height=870, left=5, right=11))]"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(elnet), lambda l: l.height)}\n",
-    "triple_pair_hg(height_groups)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=1368, left=13, right=19),\n",
-       " Link(height=1368, left=14, right=16),\n",
-       " Link(height=1369, left=3, right=6)]"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[l for l in elnet if l.height >= 1367 if l.height <= 1370 if link_ends(l) & set((6, 16, 19))]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 21.3 s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "triple_pair(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 105 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(elnet), lambda l: l.height)}\n",
-    "triple_pair_hg(height_groups)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(elnet), lambda l: l.height)}\n",
-    "assert triple_pair_hg(height_groups) == triple_pair(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=242, left=8, right=9),\n",
-       " Link(height=242, left=15, right=21),\n",
-       " Link(height=243, left=1, right=9),\n",
-       " Link(height=243, left=8, right=14),\n",
-       " Link(height=243, left=11, right=15),\n",
-       " Link(height=244, left=1, right=18),\n",
-       " Link(height=244, left=6, right=8),\n",
-       " Link(height=244, left=9, right=20),\n",
-       " Link(height=244, left=15, right=25),\n",
-       " Link(height=245, left=0, right=15),\n",
-       " Link(height=245, left=1, right=16),\n",
-       " Link(height=245, left=9, right=12),\n",
-       " Link(height=245, left=18, right=21)]"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[l for l in elnet if l.height >= 242 if l.height <= 245 ] #if l.left in [13, 17, 20] or l.right in [13, 17, 20]]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_triple_pairs_slow(net):\n",
-    "    print(len(net))\n",
-    "    new_net = eliminate_a_triple_pair_slow(net)\n",
-    "    while new_net:\n",
-    "        print(len(net))\n",
-    "        net = new_net\n",
-    "        new_net = eliminate_a_triple_pair_slow(net)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 118,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_triple_pairs(net):\n",
-    "    print(len(net))\n",
-    "    new_net = eliminate_a_triple_pair(net)\n",
-    "    while new_net:\n",
-    "        print(len(net))\n",
-    "        net = new_net\n",
-    "        new_net = eliminate_a_triple_pair(net)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 134,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "9811\n",
-      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
-      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=316, left=8, right=21) Link(height=317, left=8, right=17)\n",
-      "9811\n",
-      "eatp [(Link(height=866, left=4, right=11), Link(height=867, left=5, right=11), Link(height=868, left=4, right=11), Link(height=869, left=5, right=11))]\n",
-      "removing Link(height=866, left=4, right=11) Link(height=867, left=5, right=11) Link(height=868, left=4, right=11) Link(height=869, left=5, right=11) ; adding Link(height=866, left=5, right=11) Link(height=867, left=4, right=11)\n",
-      "9809\n",
-      "eatp []\n"
-     ]
-    }
-   ],
-   "source": [
-    "etlnet = eliminate_triple_pairs(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
-      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=317, left=8, right=17) Link(height=318, left=8, right=21)\n"
-     ]
-    }
-   ],
-   "source": [
-    "etlnet = eliminate_a_triple_pair(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 135,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 136,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=315, left=17, right=20),\n",
-       " Link(height=316, left=8, right=17),\n",
-       " Link(height=317, left=8, right=21),\n",
-       " Link(height=318, left=8, right=17),\n",
-       " Link(height=319, left=8, right=21),\n",
-       " Link(height=319, left=14, right=17),\n",
-       " Link(height=320, left=2, right=8),\n",
-       " Link(height=320, left=17, right=21)]"
-      ]
-     },
-     "execution_count": 136,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[l for l in elnet if l.height >= 315 if l.height <= 320 if link_ends(l) & set((8, 17, 21))] "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 137,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=17, right=20),\n",
-       " Link(height=1, left=8, right=17),\n",
-       " Link(height=2, left=8, right=21),\n",
-       " Link(height=3, left=8, right=17),\n",
-       " Link(height=4, left=8, right=21),\n",
-       " Link(height=4, left=14, right=17),\n",
-       " Link(height=5, left=2, right=8),\n",
-       " Link(height=5, left=17, right=21)]"
-      ]
-     },
-     "execution_count": 137,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "nf = [l for l in elnet if l.height >= 315 if l.height <= 320 if link_ends(l) & set((8, 17, 21))]\n",
-    "pnf = pack(nf)\n",
-    "pnf"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 138,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "d: Link(height=3, left=8, right=17)\n",
-      "cs: [Link(height=2, left=8, right=21)]\n",
-      "c: ; lines: {8, 17, 21}\n",
-      "b: Link(height=1, left=8, right=17) ; bs: [Link(height=1, left=8, right=17)]\n",
-      "ah: 0 ; als: []\n",
-      "a: Link(height=0, left=8, right=21)\n",
-      "d: Link(height=4, left=8, right=21)\n",
-      "cs: [Link(height=3, left=8, right=17)]\n",
-      "c: ; lines: {8, 17, 21}\n",
-      "b: Link(height=2, left=8, right=21) ; bs: [Link(height=2, left=8, right=21)]\n",
-      "ah: 1 ; als: [Link(height=1, left=8, right=17)]\n",
-      "a: Link(height=1, left=8, right=17)\n",
-      "adding: Link(height=1, left=8, right=17) Link(height=2, left=8, right=21) Link(height=3, left=8, right=17) Link(height=4, left=8, right=21)\n",
-      "d: Link(height=4, left=14, right=17)\n",
-      "cs: [Link(height=3, left=8, right=17)]\n",
-      "c: ; lines: {8, 17, 14}\n",
-      "b: Link(height=2, left=14, right=17) ; bs: [Link(height=2, left=8, right=21)]\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=1, left=8, right=17),\n",
-       "  Link(height=2, left=8, right=21),\n",
-       "  Link(height=3, left=8, right=17),\n",
-       "  Link(height=4, left=8, right=21))]"
-      ]
-     },
-     "execution_count": 138,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(pnf), lambda l: l.height)}\n",
-    "triple_pair_hg(height_groups, debug=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 139,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "9811\n",
-      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
-      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=316, left=8, right=21) Link(height=317, left=8, right=17)\n",
-      "9811\n",
-      "eatp [(Link(height=866, left=4, right=11), Link(height=867, left=5, right=11), Link(height=868, left=4, right=11), Link(height=869, left=5, right=11))]\n",
-      "removing Link(height=866, left=4, right=11) Link(height=867, left=5, right=11) Link(height=868, left=4, right=11) Link(height=869, left=5, right=11) ; adding Link(height=866, left=5, right=11) Link(height=867, left=4, right=11)\n",
-      "9809\n",
-      "eatp []\n"
-     ]
-    }
-   ],
-   "source": [
-    "setlnet = eliminate_triple_pairs_slow(elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 140,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9807"
-      ]
-     },
-     "execution_count": 140,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(setlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 141,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 142,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'zdunvslcfiqywjmkobhxtraegp'"
-      ]
-     },
-     "execution_count": 142,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, etlnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 143,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'zdunvslcfiqywjmkobhxtraegp'"
-      ]
-     },
-     "execution_count": 143,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, setlnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 144,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'zdunvslcfiqywjmkobhxtraegp'"
-      ]
-     },
-     "execution_count": 144,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, elnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 145,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'zdunvslcfiqywjmkobhxtraegp'"
-      ]
-     },
-     "execution_count": 145,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 146,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 146,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "eliminable_pairs(etlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 147,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(10207, 9807)"
-      ]
-     },
-     "execution_count": 147,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(lnet), len(etlnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 148,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def simplify(net0):\n",
-    "    netp = eliminate_pairs(net0)\n",
-    "    new_net = eliminate_a_triple_pair(netp)\n",
-    "    while new_net:\n",
-    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
-    "        netp = eliminate_pairs(new_net)\n",
-    "        new_net = eliminate_a_triple_pair(netp)\n",
-    "    return netp"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 149,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
-      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=316, left=8, right=21) Link(height=317, left=8, right=17)\n",
-      "eatp [(Link(height=866, left=4, right=11), Link(height=867, left=5, right=11), Link(height=868, left=4, right=11), Link(height=869, left=5, right=11))]\n",
-      "removing Link(height=866, left=4, right=11) Link(height=867, left=5, right=11) Link(height=868, left=4, right=11) Link(height=869, left=5, right=11) ; adding Link(height=866, left=5, right=11) Link(height=867, left=4, right=11)\n",
-      "eatp []\n"
-     ]
-    }
-   ],
-   "source": [
-    "simple_lnet = simplify(plnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 150,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 150,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, simple_lnet)) == ''.join(follow_many(string.ascii_lowercase, lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 151,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'zdunvslcfiqywjmkobhxtraegp'"
-      ]
-     },
-     "execution_count": 151,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, simple_lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 152,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'zdunvslcfiqywjmkobhxtraegp'"
-      ]
-     },
-     "execution_count": 152,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, lnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 153,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9807"
-      ]
-     },
-     "execution_count": 153,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(simple_lnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def add_triple_pair(net, max_lines=None):\n",
-    "    if not max_lines:\n",
-    "        max_lines = max(l.right for l in net)\n",
-    "    a, b, c = 0, 0, 0\n",
-    "    while len(set((a, b, c))) != 3:\n",
-    "        a = random.randrange(max_lines)\n",
-    "        b = random.randrange(max_lines)\n",
-    "        c = random.randrange(max_lines)\n",
-    "    tp = [(min(a, b), max(a, b)), (min(b, c), max(b, c))] * 2\n",
-    "    \n",
-    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
-    "    i = random.randrange(len(pairs))\n",
-    "    print(i, tp)\n",
-    "    new_pairs = pairs[:i] + tp + pairs[i:]\n",
-    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def add_pair(net, max_lines=None):\n",
-    "    if not max_lines:\n",
-    "        max_lines = max(l.right for l in net)\n",
-    "\n",
-    "    a, b = 0, 0\n",
-    "    while a == b:\n",
-    "        a = random.randrange(max_lines)\n",
-    "        b = random.randrange(max_lines)\n",
-    "    p = [(min(a, b), max(a, b))] * 2\n",
-    "    \n",
-    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
-    "    i = random.randrange(len(pairs))\n",
-    "    \n",
-    "    print(i, p)\n",
-    "    new_pairs = pairs[:i] + p + pairs[i:]\n",
-    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true,
-    "scrolled": true
-   },
-   "outputs": [],
-   "source": [
-    "lnettp = simple_lnet\n",
-    "for _ in range(10):\n",
-    "    lnettp = add_pair(lnettp)\n",
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true,
-    "scrolled": true
-   },
-   "outputs": [],
-   "source": [
-    "lnettp = simple_lnet\n",
-    "for _ in range(10):\n",
-    "    lnettp = add_triple_pair(lnettp)\n",
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true,
-    "scrolled": true
-   },
-   "outputs": [],
-   "source": [
-    "lnettp = simple_lnet\n",
-    "for _ in range(10):\n",
-    "    lnettp = add_pair(lnettp)\n",
-    "for _ in range(10):\n",
-    "    lnettp = add_triple_pair(lnettp)\n",
-    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
-    "tps = triple_pair_hg(height_groups)\n",
-    "tps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "lnettp == pack(lnettp)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "lnettps = simplify(lnettp)\n",
-    "len(lnettps)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "len(simple_lnet), len(lnettp), len(lnettps)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

diff --git a/04-08-amidakuji/amidakuji-solution-1.ipynb b/04-08-amidakuji/amidakuji-solution-1.ipynb
deleted file mode 100644 (file)
index 7f149b4..0000000
--- a/04-08-amidakuji/amidakuji-solution-1.ipynb
+++ /dev/null
@@ -1,431 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import collections\n",
-    "import string\n",
-    "import itertools\n",
-    "import re"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "Link = collections.namedtuple('Link', 'height left right')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def extract_pairs(net_string):\n",
-    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def read_net_string(net_string):\n",
-    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def read_net(filename):\n",
-    "    with open(filename) as f:\n",
-    "        pairs = [re.split('\\D+', p.strip()) for p in f.readlines()]\n",
-    "        lrs = [(int(lr[1]), int(lr[2])) for lr in pairs]\n",
-    "        return [Link(h, l, r) \n",
-    "                for h, (l, r) in enumerate(lrs)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=2, right=5),\n",
-       " Link(height=1, left=1, right=4),\n",
-       " Link(height=2, left=0, right=3),\n",
-       " Link(height=3, left=0, right=3),\n",
-       " Link(height=4, left=0, right=5),\n",
-       " Link(height=5, left=3, right=5),\n",
-       " Link(height=6, left=0, right=2),\n",
-       " Link(height=7, left=3, right=4),\n",
-       " Link(height=8, left=2, right=4),\n",
-       " Link(height=9, left=1, right=2),\n",
-       " Link(height=10, left=0, right=4),\n",
-       " Link(height=11, left=1, right=2),\n",
-       " Link(height=12, left=2, right=4),\n",
-       " Link(height=13, left=0, right=4),\n",
-       " Link(height=14, left=1, right=4)]"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "small_net = read_net('04-small.txt')\n",
-    "small_net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10135"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "net = read_net('04-lines.txt')\n",
-    "len(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def show_net(links, pair_sep=', '):\n",
-    "    return pair_sep.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def link_ends(link):\n",
-    "    return set((link.left, link.right))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow(initial_line, links):\n",
-    "    line = initial_line\n",
-    "    heights = sorted(set(l.height for l in links))\n",
-    "    for h in heights:\n",
-    "        for l in [l for l in links if l.height == h]:\n",
-    "            if line in link_ends(l):\n",
-    "                line = [e for e in link_ends(l) if e != line][0]\n",
-    "#                 print(l, line)\n",
-    "    return line"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def pack(net):\n",
-    "    packed_links = []\n",
-    "    line_heights = collections.defaultdict(lambda: -1)\n",
-    "    for link in sorted(net):\n",
-    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
-    "        line_heights[link.left] = link_height\n",
-    "        line_heights[link.right] = link_height\n",
-    "        packed_links += [Link(link_height, link.left, link.right)]\n",
-    "    return sorted(packed_links)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "14"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in small_net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in pack(small_net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10134"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "pnet = pack(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2286"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def height_groups(net):\n",
-    "    return {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow_many(in_sequence, net):\n",
-    "    hgs = height_groups(net)\n",
-    "    seq = list(in_sequence)\n",
-    "    for h in hgs:\n",
-    "        for link in hgs[h]:\n",
-    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
-    "    return seq"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'acfbed'"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many('abcdef', small_net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10000 loops, best of 3: 39.5 µs per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many('abcdefghij', small_net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 19.7 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many(string.ascii_lowercase, net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "100 loops, best of 3: 18.6 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many(string.ascii_lowercase, pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

diff --git a/04-08-amidakuji/amidakuji-solution-2.ipynb b/04-08-amidakuji/amidakuji-solution-2.ipynb
deleted file mode 100644 (file)
index 3bc37db..0000000
--- a/04-08-amidakuji/amidakuji-solution-2.ipynb
+++ /dev/null
@@ -1,1452 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import collections\n",
-    "import string\n",
-    "import itertools\n",
-    "import re"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "Link = collections.namedtuple('Link', 'height left right')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def extract_pairs(net_string):\n",
-    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def read_net_string(net_string):\n",
-    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def read_net(filename):\n",
-    "    with open(filename) as f:\n",
-    "        pairs = [re.split('\\D+', p.strip()) for p in f.readlines()]\n",
-    "        lrs = [(int(lr[1]), int(lr[2])) for lr in pairs]\n",
-    "        return [Link(h, l, r) \n",
-    "                for h, (l, r) in enumerate(lrs)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Link(height=0, left=2, right=5),\n",
-       " Link(height=1, left=1, right=4),\n",
-       " Link(height=2, left=0, right=3),\n",
-       " Link(height=3, left=0, right=3),\n",
-       " Link(height=4, left=0, right=5),\n",
-       " Link(height=5, left=3, right=5),\n",
-       " Link(height=6, left=0, right=2),\n",
-       " Link(height=7, left=3, right=4),\n",
-       " Link(height=8, left=2, right=4),\n",
-       " Link(height=9, left=1, right=2),\n",
-       " Link(height=10, left=0, right=4),\n",
-       " Link(height=11, left=1, right=2),\n",
-       " Link(height=12, left=2, right=4),\n",
-       " Link(height=13, left=0, right=4),\n",
-       " Link(height=14, left=1, right=4)]"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "small_net = read_net('04-small.txt')\n",
-    "small_net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10135"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "net = read_net('04-lines.txt')\n",
-    "len(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def show_net(links, pair_sep=', '):\n",
-    "    return pair_sep.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def link_ends(link):\n",
-    "    return set((link.left, link.right))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow(initial_line, links):\n",
-    "    line = initial_line\n",
-    "    heights = sorted(set(l.height for l in links))\n",
-    "    for h in heights:\n",
-    "        for l in [l for l in links if l.height == h]:\n",
-    "            if line in link_ends(l):\n",
-    "                line = [e for e in link_ends(l) if e != line][0]\n",
-    "#                 print(l, line)\n",
-    "    return line"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def pack(net):\n",
-    "    packed_links = []\n",
-    "    line_heights = collections.defaultdict(lambda: -1)\n",
-    "    for link in sorted(net):\n",
-    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
-    "        line_heights[link.left] = link_height\n",
-    "        line_heights[link.right] = link_height\n",
-    "        packed_links += [Link(link_height, link.left, link.right)]\n",
-    "    return sorted(packed_links)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "14"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in small_net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in pack(small_net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10134"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2286"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "max(l.height for l in pack(net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def height_groups(net):\n",
-    "    return {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def follow_many(in_sequence, net):\n",
-    "    hgs = height_groups(net)\n",
-    "    seq = list(in_sequence)\n",
-    "    for h in hgs:\n",
-    "        for link in hgs[h]:\n",
-    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
-    "    return seq"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'acfbedghij'"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many('abcdefghij', small_net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10000 loops, best of 3: 38.1 µs per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many('abcdefghij', small_net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "100 loops, best of 3: 19 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "follow_many(string.ascii_lowercase, net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "pnet = pack(net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pairs(net):\n",
-    "    hgs = height_groups(net)\n",
-    "    eps = []\n",
-    "    for h in range(1, max(hgs.keys())):\n",
-    "        for l in hgs[h]:\n",
-    "            o = Link(l.height - 1, l.left, l.right)\n",
-    "            if o in hgs[h-1]:\n",
-    "                eps += [(l, o)]\n",
-    "    return eps"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=115, left=2, right=23), Link(height=114, left=2, right=23)),\n",
-       " (Link(height=149, left=15, right=23), Link(height=148, left=15, right=23)),\n",
-       " (Link(height=201, left=0, right=7), Link(height=200, left=0, right=7)),\n",
-       " (Link(height=207, left=22, right=23), Link(height=206, left=22, right=23)),\n",
-       " (Link(height=210, left=17, right=23), Link(height=209, left=17, right=23)),\n",
-       " (Link(height=247, left=16, right=20), Link(height=246, left=16, right=20)),\n",
-       " (Link(height=418, left=19, right=24), Link(height=417, left=19, right=24)),\n",
-       " (Link(height=424, left=9, right=21), Link(height=423, left=9, right=21)),\n",
-       " (Link(height=453, left=3, right=16), Link(height=452, left=3, right=16)),\n",
-       " (Link(height=456, left=2, right=22), Link(height=455, left=2, right=22)),\n",
-       " (Link(height=465, left=18, right=20), Link(height=464, left=18, right=20)),\n",
-       " (Link(height=491, left=14, right=18), Link(height=490, left=14, right=18)),\n",
-       " (Link(height=552, left=16, right=17), Link(height=551, left=16, right=17)),\n",
-       " (Link(height=772, left=0, right=7), Link(height=771, left=0, right=7)),\n",
-       " (Link(height=848, left=1, right=2), Link(height=847, left=1, right=2)),\n",
-       " (Link(height=895, left=6, right=21), Link(height=894, left=6, right=21)),\n",
-       " (Link(height=930, left=11, right=13), Link(height=929, left=11, right=13)),\n",
-       " (Link(height=987, left=8, right=17), Link(height=986, left=8, right=17)),\n",
-       " (Link(height=988, left=8, right=17), Link(height=987, left=8, right=17)),\n",
-       " (Link(height=1030, left=9, right=24), Link(height=1029, left=9, right=24)),\n",
-       " (Link(height=1134, left=4, right=23), Link(height=1133, left=4, right=23)),\n",
-       " (Link(height=1163, left=14, right=15), Link(height=1162, left=14, right=15)),\n",
-       " (Link(height=1164, left=14, right=15), Link(height=1163, left=14, right=15)),\n",
-       " (Link(height=1170, left=2, right=21), Link(height=1169, left=2, right=21)),\n",
-       " (Link(height=1232, left=6, right=22), Link(height=1231, left=6, right=22)),\n",
-       " (Link(height=1254, left=13, right=15), Link(height=1253, left=13, right=15)),\n",
-       " (Link(height=1255, left=1, right=24), Link(height=1254, left=1, right=24)),\n",
-       " (Link(height=1324, left=3, right=22), Link(height=1323, left=3, right=22)),\n",
-       " (Link(height=1370, left=15, right=19), Link(height=1369, left=15, right=19)),\n",
-       " (Link(height=1441, left=0, right=14), Link(height=1440, left=0, right=14)),\n",
-       " (Link(height=1441, left=11, right=24), Link(height=1440, left=11, right=24)),\n",
-       " (Link(height=1547, left=11, right=13), Link(height=1546, left=11, right=13)),\n",
-       " (Link(height=1578, left=14, right=23), Link(height=1577, left=14, right=23)),\n",
-       " (Link(height=1616, left=7, right=14), Link(height=1615, left=7, right=14)),\n",
-       " (Link(height=1671, left=8, right=20), Link(height=1670, left=8, right=20)),\n",
-       " (Link(height=1684, left=14, right=18), Link(height=1683, left=14, right=18)),\n",
-       " (Link(height=1717, left=0, right=17), Link(height=1716, left=0, right=17)),\n",
-       " (Link(height=1727, left=7, right=8), Link(height=1726, left=7, right=8)),\n",
-       " (Link(height=1866, left=8, right=16), Link(height=1865, left=8, right=16)),\n",
-       " (Link(height=1911, left=1, right=12), Link(height=1910, left=1, right=12)),\n",
-       " (Link(height=1966, left=20, right=23), Link(height=1965, left=20, right=23)),\n",
-       " (Link(height=1974, left=5, right=23), Link(height=1973, left=5, right=23)),\n",
-       " (Link(height=1994, left=18, right=19), Link(height=1993, left=18, right=19)),\n",
-       " (Link(height=2005, left=2, right=19), Link(height=2004, left=2, right=19)),\n",
-       " (Link(height=2031, left=12, right=17), Link(height=2030, left=12, right=17)),\n",
-       " (Link(height=2108, left=7, right=12), Link(height=2107, left=7, right=12)),\n",
-       " (Link(height=2137, left=7, right=16), Link(height=2136, left=7, right=16)),\n",
-       " (Link(height=2138, left=7, right=16), Link(height=2137, left=7, right=16)),\n",
-       " (Link(height=2229, left=10, right=11), Link(height=2228, left=10, right=11)),\n",
-       " (Link(height=2239, left=16, right=24), Link(height=2238, left=16, right=24)),\n",
-       " (Link(height=2240, left=16, right=24), Link(height=2239, left=16, right=24)),\n",
-       " (Link(height=2246, left=4, right=13), Link(height=2245, left=4, right=13)),\n",
-       " (Link(height=2247, left=4, right=13), Link(height=2246, left=4, right=13)),\n",
-       " (Link(height=2276, left=19, right=24), Link(height=2275, left=19, right=24)),\n",
-       " (Link(height=2277, left=4, right=18), Link(height=2276, left=4, right=18))]"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "eliminable_pairs(pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 23.5 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "eliminable_pairs(pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminable_pair(hgs):\n",
-    "    for h in range(1, max(hgs.keys())):\n",
-    "        for l in hgs[h]:\n",
-    "            o = Link(l.height - 1, l.left, l.right)\n",
-    "            if o in hgs[h-1]:\n",
-    "                return l, o\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_pairs(net):\n",
-    "    hgs = height_groups(pack(net))\n",
-    "    eliminable_links = eliminable_pair(hgs)\n",
-    "    while eliminable_links:\n",
-    "        net = pack(l for l in net if l not in eliminable_links)\n",
-    "        hgs = height_groups(pack(net))\n",
-    "        eliminable_links = eliminable_pair(hgs)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "enet = eliminate_pairs(pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase,  net) == follow_many(string.ascii_lowercase, enet)\n",
-    "assert follow_many(string.ascii_lowercase, pnet) == follow_many(string.ascii_lowercase, enet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 2.35 s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "eliminate_pairs(pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def triple_pair(height_groups, debug=False):\n",
-    "    ts = []\n",
-    "    for h in range(3, max(height_groups.keys())):\n",
-    "        for d in height_groups[h]:\n",
-    "            if debug: print('d:', d)\n",
-    "            ch = h - 1\n",
-    "            cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
-    "            if debug: print('cs:', cs)\n",
-    "            while ch > 2 and not cs:\n",
-    "                ch -= 1\n",
-    "                cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
-    "                if debug: print('cs:', cs)\n",
-    "            if len(cs) == 1:\n",
-    "                c = cs[0]\n",
-    "                lines = set((d.left, d.right, c.left, c.right))\n",
-    "                if debug: print('c:', '; lines:', lines)\n",
-    "                bs = [l for l in height_groups[ch-1] if link_ends(l) & lines]\n",
-    "                b = Link(ch - 1, d.left, d.right)\n",
-    "                if debug: print('b:', b, '; bs:', bs)\n",
-    "                if len(bs) == 1 and b in bs:\n",
-    "                    ah = b.height - 1\n",
-    "                    als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
-    "                    if debug: print('ah:', ah, '; als:', als)\n",
-    "                    while ah > 0 and not als:\n",
-    "                        ah -= 1\n",
-    "                        als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
-    "                        if debug: print('ah:', ah, '; als:', als)\n",
-    "                    a = Link(ah, c.left, c.right)\n",
-    "                    if debug: print('a:', a)\n",
-    "                    if a in als:\n",
-    "                        if debug: print('adding:', a, b, c, d)\n",
-    "                        ts += [(a, b, c, d)]\n",
-    "    return ts"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_a_triple_pair(net, debug=False):\n",
-    "    hgs = height_groups(net)\n",
-    "\n",
-    "    tps = triple_pair(hgs)\n",
-    "    if debug: print('eatp', tps)\n",
-    "    if tps:\n",
-    "        a, b, c, d = tps[0]\n",
-    "        x = Link(b.height - 0.5, b.left, b.right)\n",
-    "        y = Link(b.height, a.left, a.right)\n",
-    "        if debug: print('removing', a, b, c, d, '; adding', x, y)\n",
-    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
-    "    return None"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(Link(height=8, left=1, right=5),\n",
-       "  Link(height=9, left=1, right=21),\n",
-       "  Link(height=10, left=1, right=5),\n",
-       "  Link(height=11, left=1, right=21)),\n",
-       " (Link(height=40, left=16, right=23),\n",
-       "  Link(height=41, left=16, right=19),\n",
-       "  Link(height=42, left=16, right=23),\n",
-       "  Link(height=43, left=16, right=19)),\n",
-       " (Link(height=62, left=0, right=10),\n",
-       "  Link(height=63, left=10, right=13),\n",
-       "  Link(height=64, left=0, right=10),\n",
-       "  Link(height=65, left=10, right=13)),\n",
-       " (Link(height=137, left=23, right=24),\n",
-       "  Link(height=139, left=0, right=24),\n",
-       "  Link(height=140, left=23, right=24),\n",
-       "  Link(height=141, left=0, right=24)),\n",
-       " (Link(height=138, left=10, right=21),\n",
-       "  Link(height=139, left=2, right=10),\n",
-       "  Link(height=140, left=10, right=21),\n",
-       "  Link(height=141, left=2, right=10)),\n",
-       " (Link(height=139, left=2, right=10),\n",
-       "  Link(height=140, left=10, right=21),\n",
-       "  Link(height=141, left=2, right=10),\n",
-       "  Link(height=142, left=10, right=21)),\n",
-       " (Link(height=156, left=6, right=11),\n",
-       "  Link(height=157, left=3, right=6),\n",
-       "  Link(height=158, left=6, right=11),\n",
-       "  Link(height=159, left=3, right=6)),\n",
-       " (Link(height=184, left=2, right=21),\n",
-       "  Link(height=185, left=5, right=21),\n",
-       "  Link(height=186, left=2, right=21),\n",
-       "  Link(height=187, left=5, right=21)),\n",
-       " (Link(height=272, left=7, right=13),\n",
-       "  Link(height=273, left=7, right=11),\n",
-       "  Link(height=274, left=7, right=13),\n",
-       "  Link(height=275, left=7, right=11)),\n",
-       " (Link(height=290, left=14, right=15),\n",
-       "  Link(height=291, left=5, right=15),\n",
-       "  Link(height=292, left=14, right=15),\n",
-       "  Link(height=293, left=5, right=15)),\n",
-       " (Link(height=387, left=1, right=8),\n",
-       "  Link(height=389, left=8, right=15),\n",
-       "  Link(height=390, left=1, right=8),\n",
-       "  Link(height=391, left=8, right=15)),\n",
-       " (Link(height=420, left=14, right=22),\n",
-       "  Link(height=422, left=14, right=18),\n",
-       "  Link(height=423, left=14, right=22),\n",
-       "  Link(height=424, left=14, right=18)),\n",
-       " (Link(height=432, left=5, right=19),\n",
-       "  Link(height=433, left=1, right=19),\n",
-       "  Link(height=434, left=5, right=19),\n",
-       "  Link(height=435, left=1, right=19)),\n",
-       " (Link(height=454, left=0, right=15),\n",
-       "  Link(height=455, left=14, right=15),\n",
-       "  Link(height=456, left=0, right=15),\n",
-       "  Link(height=457, left=14, right=15)),\n",
-       " (Link(height=546, left=13, right=21),\n",
-       "  Link(height=547, left=6, right=21),\n",
-       "  Link(height=548, left=13, right=21),\n",
-       "  Link(height=549, left=6, right=21)),\n",
-       " (Link(height=620, left=17, right=23),\n",
-       "  Link(height=621, left=1, right=23),\n",
-       "  Link(height=622, left=17, right=23),\n",
-       "  Link(height=623, left=1, right=23)),\n",
-       " (Link(height=699, left=8, right=15),\n",
-       "  Link(height=700, left=3, right=15),\n",
-       "  Link(height=701, left=8, right=15),\n",
-       "  Link(height=702, left=3, right=15)),\n",
-       " (Link(height=789, left=7, right=24),\n",
-       "  Link(height=790, left=8, right=24),\n",
-       "  Link(height=791, left=7, right=24),\n",
-       "  Link(height=792, left=8, right=24)),\n",
-       " (Link(height=795, left=8, right=13),\n",
-       "  Link(height=796, left=4, right=8),\n",
-       "  Link(height=797, left=8, right=13),\n",
-       "  Link(height=798, left=4, right=8)),\n",
-       " (Link(height=809, left=16, right=17),\n",
-       "  Link(height=810, left=3, right=16),\n",
-       "  Link(height=811, left=16, right=17),\n",
-       "  Link(height=812, left=3, right=16)),\n",
-       " (Link(height=900, left=2, right=15),\n",
-       "  Link(height=901, left=13, right=15),\n",
-       "  Link(height=902, left=2, right=15),\n",
-       "  Link(height=903, left=13, right=15)),\n",
-       " (Link(height=921, left=2, right=15),\n",
-       "  Link(height=922, left=15, right=16),\n",
-       "  Link(height=923, left=2, right=15),\n",
-       "  Link(height=924, left=15, right=16)),\n",
-       " (Link(height=961, left=2, right=15),\n",
-       "  Link(height=962, left=2, right=14),\n",
-       "  Link(height=963, left=2, right=15),\n",
-       "  Link(height=964, left=2, right=14)),\n",
-       " (Link(height=976, left=13, right=18),\n",
-       "  Link(height=979, left=18, right=19),\n",
-       "  Link(height=980, left=13, right=18),\n",
-       "  Link(height=981, left=18, right=19)),\n",
-       " (Link(height=985, left=5, right=16),\n",
-       "  Link(height=986, left=2, right=5),\n",
-       "  Link(height=987, left=5, right=16),\n",
-       "  Link(height=988, left=2, right=5)),\n",
-       " (Link(height=1050, left=9, right=24),\n",
-       "  Link(height=1054, left=9, right=18),\n",
-       "  Link(height=1055, left=9, right=24),\n",
-       "  Link(height=1056, left=9, right=18)),\n",
-       " (Link(height=1159, left=11, right=21),\n",
-       "  Link(height=1160, left=11, right=14),\n",
-       "  Link(height=1161, left=11, right=21),\n",
-       "  Link(height=1162, left=11, right=14)),\n",
-       " (Link(height=1284, left=0, right=11),\n",
-       "  Link(height=1285, left=0, right=14),\n",
-       "  Link(height=1286, left=0, right=11),\n",
-       "  Link(height=1287, left=0, right=14)),\n",
-       " (Link(height=1331, left=4, right=9),\n",
-       "  Link(height=1333, left=4, right=10),\n",
-       "  Link(height=1334, left=4, right=9),\n",
-       "  Link(height=1335, left=4, right=10)),\n",
-       " (Link(height=1332, left=12, right=18),\n",
-       "  Link(height=1333, left=12, right=24),\n",
-       "  Link(height=1334, left=12, right=18),\n",
-       "  Link(height=1335, left=12, right=24)),\n",
-       " (Link(height=1343, left=0, right=17),\n",
-       "  Link(height=1344, left=0, right=23),\n",
-       "  Link(height=1345, left=0, right=17),\n",
-       "  Link(height=1346, left=0, right=23)),\n",
-       " (Link(height=1357, left=4, right=16),\n",
-       "  Link(height=1358, left=16, right=17),\n",
-       "  Link(height=1359, left=4, right=16),\n",
-       "  Link(height=1360, left=16, right=17)),\n",
-       " (Link(height=1441, left=6, right=20),\n",
-       "  Link(height=1443, left=16, right=20),\n",
-       "  Link(height=1444, left=6, right=20),\n",
-       "  Link(height=1445, left=16, right=20)),\n",
-       " (Link(height=1464, left=17, right=23),\n",
-       "  Link(height=1465, left=3, right=17),\n",
-       "  Link(height=1466, left=17, right=23),\n",
-       "  Link(height=1467, left=3, right=17)),\n",
-       " (Link(height=1540, left=8, right=23),\n",
-       "  Link(height=1541, left=7, right=23),\n",
-       "  Link(height=1542, left=8, right=23),\n",
-       "  Link(height=1543, left=7, right=23)),\n",
-       " (Link(height=1570, left=0, right=1),\n",
-       "  Link(height=1571, left=1, right=21),\n",
-       "  Link(height=1572, left=0, right=1),\n",
-       "  Link(height=1573, left=1, right=21)),\n",
-       " (Link(height=1600, left=15, right=22),\n",
-       "  Link(height=1603, left=7, right=15),\n",
-       "  Link(height=1604, left=15, right=22),\n",
-       "  Link(height=1605, left=7, right=15)),\n",
-       " (Link(height=1632, left=12, right=18),\n",
-       "  Link(height=1634, left=12, right=20),\n",
-       "  Link(height=1635, left=12, right=18),\n",
-       "  Link(height=1636, left=12, right=20)),\n",
-       " (Link(height=1702, left=13, right=24),\n",
-       "  Link(height=1705, left=14, right=24),\n",
-       "  Link(height=1706, left=13, right=24),\n",
-       "  Link(height=1707, left=14, right=24)),\n",
-       " (Link(height=1721, left=3, right=24),\n",
-       "  Link(height=1722, left=3, right=21),\n",
-       "  Link(height=1723, left=3, right=24),\n",
-       "  Link(height=1724, left=3, right=21)),\n",
-       " (Link(height=1722, left=3, right=21),\n",
-       "  Link(height=1723, left=3, right=24),\n",
-       "  Link(height=1724, left=3, right=21),\n",
-       "  Link(height=1725, left=3, right=24)),\n",
-       " (Link(height=1762, left=0, right=21),\n",
-       "  Link(height=1763, left=13, right=21),\n",
-       "  Link(height=1764, left=0, right=21),\n",
-       "  Link(height=1765, left=13, right=21)),\n",
-       " (Link(height=1769, left=7, right=9),\n",
-       "  Link(height=1770, left=7, right=12),\n",
-       "  Link(height=1771, left=7, right=9),\n",
-       "  Link(height=1772, left=7, right=12)),\n",
-       " (Link(height=1914, left=10, right=24),\n",
-       "  Link(height=1915, left=8, right=24),\n",
-       "  Link(height=1916, left=10, right=24),\n",
-       "  Link(height=1917, left=8, right=24)),\n",
-       " (Link(height=1920, left=4, right=23),\n",
-       "  Link(height=1921, left=3, right=4),\n",
-       "  Link(height=1922, left=4, right=23),\n",
-       "  Link(height=1923, left=3, right=4)),\n",
-       " (Link(height=2023, left=4, right=7),\n",
-       "  Link(height=2024, left=7, right=15),\n",
-       "  Link(height=2025, left=4, right=7),\n",
-       "  Link(height=2026, left=7, right=15)),\n",
-       " (Link(height=2025, left=8, right=19),\n",
-       "  Link(height=2031, left=8, right=15),\n",
-       "  Link(height=2032, left=8, right=19),\n",
-       "  Link(height=2033, left=8, right=15)),\n",
-       " (Link(height=2152, left=10, right=15),\n",
-       "  Link(height=2153, left=10, right=16),\n",
-       "  Link(height=2154, left=10, right=15),\n",
-       "  Link(height=2155, left=10, right=16)),\n",
-       " (Link(height=2194, left=22, right=24),\n",
-       "  Link(height=2195, left=7, right=22),\n",
-       "  Link(height=2196, left=22, right=24),\n",
-       "  Link(height=2197, left=7, right=22)),\n",
-       " (Link(height=2211, left=5, right=6),\n",
-       "  Link(height=2212, left=6, right=14),\n",
-       "  Link(height=2213, left=5, right=6),\n",
-       "  Link(height=2214, left=6, right=14))]"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "hgs = height_groups(enet)\n",
-    "triple_pair(hgs)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "etnet = eliminate_a_triple_pair(enet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, etnet) == follow_many(string.ascii_lowercase, enet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def eliminate_triple_pairs(net):\n",
-    "    print(len(net))\n",
-    "    new_net = eliminate_a_triple_pair(net)\n",
-    "    while new_net:\n",
-    "        print(len(net))\n",
-    "        net = new_net\n",
-    "        new_net = eliminate_a_triple_pair(net)\n",
-    "    return net"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10033\n",
-      "10033\n",
-      "10031\n",
-      "10029\n",
-      "10027\n",
-      "10025\n",
-      "10023\n",
-      "10021\n",
-      "10019\n",
-      "10017\n",
-      "10015\n",
-      "10013\n",
-      "10011\n",
-      "10009\n",
-      "10007\n",
-      "10005\n",
-      "10003\n",
-      "10001\n",
-      "9999\n",
-      "9997\n",
-      "9995\n",
-      "9993\n",
-      "9991\n",
-      "9989\n",
-      "9987\n",
-      "9985\n",
-      "9983\n",
-      "9981\n",
-      "9979\n",
-      "9977\n",
-      "9975\n",
-      "9973\n",
-      "9971\n",
-      "9969\n",
-      "9967\n",
-      "9965\n",
-      "9963\n",
-      "9961\n",
-      "9959\n",
-      "9957\n",
-      "9955\n",
-      "9953\n",
-      "9951\n",
-      "9949\n",
-      "9947\n",
-      "9945\n",
-      "9943\n",
-      "9941\n",
-      "9939\n"
-     ]
-    }
-   ],
-   "source": [
-    "setnet = eliminate_triple_pairs(enet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9937"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(setnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "assert follow_many(string.ascii_lowercase, etnet) == follow_many(string.ascii_lowercase, enet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, etnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, setnet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, enet))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[]"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "eliminable_pairs(etnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(10135, 10031)"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(net), len(etnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def simplify(net0):\n",
-    "    netp = eliminate_pairs(net0)\n",
-    "    new_net = eliminate_a_triple_pair(netp)\n",
-    "    while new_net:\n",
-    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
-    "        netp = eliminate_pairs(new_net)\n",
-    "        new_net = eliminate_a_triple_pair(netp)\n",
-    "    return netp"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "simple_net = simplify(pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, simple_net)) == ''.join(follow_many(string.ascii_lowercase, net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 49,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, simple_net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'doqzmbishkwunvltpcexyjgfra'"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9931"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(simple_net)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def simplify_with_checks(net0):\n",
-    "    netp = eliminate_pairs(net0)\n",
-    "    if follow_many(string.ascii_lowercase, net0) != follow_many(string.ascii_lowercase, netp):\n",
-    "        print('pairs', eliminable_pairs(net0))\n",
-    "        return net0\n",
-    "    else:\n",
-    "        print('pairs ok')\n",
-    "    new_net = eliminate_a_triple_pair(netp)\n",
-    "    if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
-    "        hg = find_height_groups(netp)\n",
-    "        print('triple', triple_pair_hg(hg))\n",
-    "        return netp\n",
-    "    else:\n",
-    "        print('triple ok')\n",
-    "    while new_net:\n",
-    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
-    "        netp = eliminate_pairs(new_net)\n",
-    "        if follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
-    "            print('pairs', eliminable_pairs(new_net))\n",
-    "            return new_net\n",
-    "        else:\n",
-    "            print('pairs ok')\n",
-    "        new_net = eliminate_a_triple_pair(netp)\n",
-    "        if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
-    "            hg = find_height_groups(netp)\n",
-    "            print('triple', triple_pair_hg(hg))\n",
-    "            return netp\n",
-    "        else:\n",
-    "            print('triple ok')\n",
-    "    print('** done')\n",
-    "    return netp"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "pairs ok\n",
-      "triple ok\n",
-      "** done\n"
-     ]
-    }
-   ],
-   "source": [
-    "spnet = simplify_with_checks(pnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "''.join(follow_many(string.ascii_lowercase, spnet)) == ''.join(follow_many(string.ascii_lowercase, net))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9931"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(spnet)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
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-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

diff --git a/04-08-amidakuji/day4.clj b/04-08-amidakuji/day4.clj
deleted file mode 100644 (file)
index 3c5d494..0000000
--- a/04-08-amidakuji/day4.clj
+++ /dev/null
@@ -1,70 +0,0 @@
-(ns day4
-    (:require [clojure.string :as str]))
-
-(defstruct link :height :left :right)
-
-; (def network (str/split-lines (slurp "../04-small.txt")))
-(def network (str/split-lines (slurp "../04-lines.txt")))
-
-(defn parse-link [l, h]
-    (let [endss (rest (str/split l #"\D+"))
-          ends (map #(Integer/parseInt %) endss)]
-        (struct-map link
-            :height h
-            :left (first ends)
-            :right (second ends))))
-
-(defn parse-network [links]
-    (map-indexed 
-        (fn [i l] (parse-link l i)) 
-        links))
-
-(def parsed-network
-    (parse-network network))
-
-
-(def initial
-    (str/split "abcdefghijklmnopqrstuvwxyz" #""))
-
-(defn apply-link [items link]
-    (let [li (get link :left)
-          ri (get link :right)
-          le (nth items li)
-          re (nth items ri)
-          pre (subvec items 0 li)
-          mid (subvec items (inc li) ri)
-          suf (subvec items (inc ri))]
-    (into [] (concat pre (vector re) mid (vector le) suf))))
-
-(defn follow [items links]
-    (reduce apply-link items links))
-
-
-(defn lane-count [links]
-    (inc (apply max (map (fn [l] (get l :right)) links))))
-
-(defn initial-heights [links]
-    (vec (replicate (lane-count links) -1)))
-
-(defn pack-one [lane-heights link]
-    (let 
-        [li (get link :left)
-         ri (get link :right)
-         new-height (inc (max (nth lane-heights li)
-                              (nth lane-heights ri)))]
-        (assoc lane-heights li new-height ri new-height)))
-
-(defn pack [lane-heights links]
-    (reduce pack-one lane-heights links))
-
-
-(spit "day4.out" (prn-str 
-    (str/join (follow initial parsed-network))))
-
-(spit "day4.out" (prn-str 
-    (apply max 
-        (pack
-            (initial-heights parsed-network)
-            parsed-network)))
-    :append true)
-

diff --git a/04-08-amidakuji/small-expanded-trace.svg b/04-08-amidakuji/small-expanded-trace.svg
deleted file mode 100644 (file)
index 3bed4a4..0000000
--- a/04-08-amidakuji/small-expanded-trace.svg
+++ /dev/null
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+(15, 21)
+(3, 19)
\ No newline at end of file

diff --git a/04-amidakuji/04-small.txt b/04-amidakuji/04-small.txt
new file mode 100644 (file)
index 0000000..75e0d3d
--- /dev/null
+++ b/04-amidakuji/04-small.txt
@@ -0,0 +1,15 @@
+(2, 5)
+(1, 4)
+(0, 3)
+(0, 3)
+(0, 5)
+(3, 5)
+(0, 2)
+(3, 4)
+(2, 4)
+(1, 2)
+(0, 4)
+(1, 2)
+(2, 4)
+(0, 4)
+(1, 4)
\ No newline at end of file

diff --git a/04-amidakuji/amidakuji-creation.ipynb b/04-amidakuji/amidakuji-creation.ipynb
new file mode 100644 (file)
index 0000000..65d9751
--- /dev/null
+++ b/04-amidakuji/amidakuji-creation.ipynb
@@ -0,0 +1,2514 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import collections\n",
+    "import random\n",
+    "import string\n",
+    "import itertools"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Link = collections.namedtuple('Link', 'height left right')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def link_ends(link):\n",
+    "    return set((link.left, link.right))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def can_add(link, links):\n",
+    "    ends = link_ends(link)\n",
+    "    same_height_links = [l for l in links if l.height == link.height]\n",
+    "    return all(ends.isdisjoint(link_ends(l)) for l in same_height_links)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def make_net(num_links, lines=10, height=50):\n",
+    "    links = set()\n",
+    "    while len(links) < num_links:\n",
+    "        a = random.randrange(lines)\n",
+    "        b = random.randrange(lines)\n",
+    "        if a != b:\n",
+    "            l = min(a, b)\n",
+    "            r = max(a, b)\n",
+    "            h = random.randrange(height)\n",
+    "            link = Link(h, l, r)\n",
+    "            if can_add(link, links):\n",
+    "                links.add(link)\n",
+    "    return links"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{Link(height=4, left=0, right=3),\n",
+       " Link(height=8, left=1, right=5),\n",
+       " Link(height=16, left=0, right=4),\n",
+       " Link(height=17, left=1, right=5),\n",
+       " Link(height=18, left=3, right=5),\n",
+       " Link(height=20, left=0, right=1),\n",
+       " Link(height=25, left=0, right=3),\n",
+       " Link(height=30, left=1, right=4),\n",
+       " Link(height=33, left=0, right=4),\n",
+       " Link(height=34, left=4, right=5),\n",
+       " Link(height=35, left=0, right=3),\n",
+       " Link(height=36, left=1, right=4),\n",
+       " Link(height=37, left=2, right=5),\n",
+       " Link(height=45, left=4, right=5),\n",
+       " Link(height=46, left=2, right=5)}"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "net = make_net(15, lines=6)\n",
+    "net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow(initial_line, links):\n",
+    "    line = initial_line\n",
+    "    heights = sorted(set(l.height for l in links))\n",
+    "    for h in heights:\n",
+    "        for l in [l for l in links if l.height == h]:\n",
+    "            if line in link_ends(l):\n",
+    "                line = [e for e in link_ends(l) if e != line][0]\n",
+    "#                 print(l, line)\n",
+    "    return line"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "follow(4, net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def pack(net):\n",
+    "    packed_links = []\n",
+    "    line_heights = collections.defaultdict(lambda: -1)\n",
+    "    for link in sorted(net):\n",
+    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
+    "        line_heights[link.left] = link_height\n",
+    "        line_heights[link.right] = link_height\n",
+    "        packed_links += [Link(link_height, link.left, link.right)]\n",
+    "    return sorted(packed_links)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow_many_slow(in_sequence, links):\n",
+    "    out_sequence = [(follow(i, links), term) \n",
+    "                    for i, term in enumerate(in_sequence)]\n",
+    "    return [term for i, term in sorted(out_sequence)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow_many(in_sequence, net):\n",
+    "    height_groups = [list(g) for _, g in itertools.groupby(pack(net), lambda l: l.height)]\n",
+    "    seq = list(in_sequence)\n",
+    "    for links in height_groups:\n",
+    "        for link in links:\n",
+    "#             l = seq[link.left]\n",
+    "#             r = seq[link.right]\n",
+    "#             seq[link.right] = l\n",
+    "#             seq[link.left] = r\n",
+    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
+    "    return seq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10000 loops, best of 3: 39.2 µs per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many('abcdef', net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# %%timeit\n",
+    "# follow_many_slow('abcdefghij', net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def show_net(links, randomise=False, pair_sep=', '):\n",
+    "    if randomise:\n",
+    "        output = []\n",
+    "        heights = sorted(set(l.height for l in links))\n",
+    "        for h in heights:\n",
+    "            ls = [l for l in links if l.height == h]\n",
+    "            random.shuffle(ls)\n",
+    "            output += ['({}, {})'.format(l.left, l.right) for l in ls]\n",
+    "        return pair_sep.join(output)\n",
+    "    return pair_sep.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'(0, 3), (1, 5), (0, 4), (1, 5), (3, 5), (0, 1), (0, 3), (1, 4), (0, 4), (4, 5), (0, 3), (1, 4), (2, 5), (4, 5), (2, 5)'"
+      ]
+     },
+     "execution_count": 50,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "show_net(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'(0, 3), (1, 5), (0, 4), (1, 5), (3, 5), (0, 1), (0, 3), (1, 4), (0, 4), (4, 5), (0, 3), (1, 4), (2, 5), (4, 5), (2, 5)'"
+      ]
+     },
+     "execution_count": 51,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "show_net(net, randomise=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'(0, 3) : (1, 5) : (0, 4) : (1, 5) : (3, 5) : (0, 1) : (0, 3) : (1, 4) : (0, 4) : (4, 5) : (0, 3) : (1, 4) : (2, 5) : (4, 5) : (2, 5)'"
+      ]
+     },
+     "execution_count": 52,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "show_net(net, pair_sep=' : ')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'(0, 3)\\n(1, 5)\\n(0, 4)\\n(1, 5)\\n(3, 5)\\n(0, 1)\\n(0, 3)\\n(1, 4)\\n(0, 4)\\n(4, 5)\\n(0, 3)\\n(1, 4)\\n(2, 5)\\n(4, 5)\\n(2, 5)'"
+      ]
+     },
+     "execution_count": 53,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "show_net(net, pair_sep='\\n')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(0, 3)\n",
+      "(1, 5)\n",
+      "(0, 4)\n",
+      "(1, 5)\n",
+      "(3, 5)\n",
+      "(0, 1)\n",
+      "(0, 3)\n",
+      "(1, 4)\n",
+      "(0, 4)\n",
+      "(4, 5)\n",
+      "(0, 3)\n",
+      "(1, 4)\n",
+      "(2, 5)\n",
+      "(4, 5)\n",
+      "(2, 5)\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(show_net(net, pair_sep='\\n'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# open('04-small.txt', 'w').write(show_net(net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'(0, 3), (1, 5), (0, 4), (1, 5), (3, 5), (0, 1), (0, 3), (1, 4), (0, 4), (4, 5), (0, 3), (1, 4), (2, 5), (4, 5), (2, 5)'"
+      ]
+     },
+     "execution_count": 56,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "show_net(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 57,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ls = [l for l in net if l.height == 1]\n",
+    "ls"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "random.shuffle(ls)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def read_net(net_string):\n",
+    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extract_pairs(net_string):\n",
+    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "net = read_net('(1, 5), (2, 4), (0, 2), (0, 4), (0, 1), (0, 2), (1, 5), (0, 3), (1, 2), (4, 5), (0, 5), (3, 5), (1, 4), (0, 1), (2, 3)')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=1, right=5),\n",
+       " Link(height=1, left=2, right=4),\n",
+       " Link(height=2, left=0, right=2),\n",
+       " Link(height=3, left=0, right=4),\n",
+       " Link(height=4, left=0, right=1),\n",
+       " Link(height=5, left=0, right=2),\n",
+       " Link(height=6, left=1, right=5),\n",
+       " Link(height=7, left=0, right=3),\n",
+       " Link(height=8, left=1, right=2),\n",
+       " Link(height=9, left=4, right=5),\n",
+       " Link(height=10, left=0, right=5),\n",
+       " Link(height=11, left=3, right=5),\n",
+       " Link(height=12, left=1, right=4),\n",
+       " Link(height=13, left=0, right=1),\n",
+       " Link(height=14, left=2, right=3)]"
+      ]
+     },
+     "execution_count": 62,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "read_net(show_net(net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=1, right=5),\n",
+       " Link(height=0, left=2, right=4),\n",
+       " Link(height=1, left=0, right=2),\n",
+       " Link(height=2, left=0, right=4),\n",
+       " Link(height=3, left=0, right=1),\n",
+       " Link(height=4, left=0, right=2),\n",
+       " Link(height=4, left=1, right=5),\n",
+       " Link(height=5, left=0, right=3),\n",
+       " Link(height=5, left=1, right=2),\n",
+       " Link(height=5, left=4, right=5),\n",
+       " Link(height=6, left=0, right=5),\n",
+       " Link(height=6, left=1, right=4),\n",
+       " Link(height=7, left=0, right=1),\n",
+       " Link(height=7, left=3, right=5),\n",
+       " Link(height=8, left=2, right=3)]"
+      ]
+     },
+     "execution_count": 63,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pack(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=1, right=5),\n",
+       " Link(height=0, left=2, right=4),\n",
+       " Link(height=1, left=0, right=2),\n",
+       " Link(height=2, left=0, right=4),\n",
+       " Link(height=3, left=0, right=1),\n",
+       " Link(height=4, left=0, right=2),\n",
+       " Link(height=4, left=1, right=5),\n",
+       " Link(height=5, left=0, right=3),\n",
+       " Link(height=5, left=1, right=2),\n",
+       " Link(height=5, left=4, right=5),\n",
+       " Link(height=6, left=0, right=5),\n",
+       " Link(height=6, left=1, right=4),\n",
+       " Link(height=7, left=0, right=1),\n",
+       " Link(height=7, left=3, right=5),\n",
+       " Link(height=8, left=2, right=3)]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pack(read_net(show_net(net)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(True, True)"
+      ]
+     },
+     "execution_count": 65,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pnet = pack(net)\n",
+    "rrnet = read_net(show_net(net, randomise=True))\n",
+    "rnet = read_net(show_net(net))\n",
+    "rnet == rrnet, pack(rrnet) == pnet"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "lnet = make_net(10207, 26, 100000)\n",
+    "plnet = pack(lnet)\n",
+    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, plnet)\n",
+    "# for i in range(204):\n",
+    "#     assert follow(i, lnet) == follow(i, plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "rlnet = read_net(show_net(lnet))\n",
+    "prlnet = pack(rlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2239"
+      ]
+     },
+     "execution_count": 68,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "99989"
+      ]
+     },
+     "execution_count": 69,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10206"
+      ]
+     },
+     "execution_count": 70,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in rlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 71,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2239"
+      ]
+     },
+     "execution_count": 71,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in prlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, prlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 73,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 25.9 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many(string.ascii_lowercase, lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 74,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# %%timeit\n",
+    "# follow_many_slow(string.ascii_lowercase, lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 75,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pairs_slow(net):\n",
+    "    eps = []\n",
+    "    for l in net:\n",
+    "        o = Link(l.height + 1, l.left, l.right)\n",
+    "        if o in net:\n",
+    "            eps += [(l, o)]\n",
+    "    return eps    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 76,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pairs(net):\n",
+    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "    eps = []\n",
+    "    for h in range(1, max(height_groups.keys())):\n",
+    "        for l in height_groups[h]:\n",
+    "            o = Link(l.height - 1, l.left, l.right)\n",
+    "            if o in height_groups[h-1]:\n",
+    "                eps += [(l, o)]\n",
+    "    return eps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 24.1 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "eliminable_pairs(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pair(net):\n",
+    "    for l in net:\n",
+    "        o = Link(l.height + 1, l.left, l.right)\n",
+    "        if o in net:\n",
+    "            return l, o\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pair_hg(height_groups):\n",
+    "    for h in range(1, max(height_groups.keys())):\n",
+    "        for l in height_groups[h]:\n",
+    "            o = Link(l.height - 1, l.left, l.right)\n",
+    "            if o in height_groups[h-1]:\n",
+    "                return l, o\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_pairs_slow(net):\n",
+    "    eliminable_links = eliminable_pair(net)\n",
+    "    while eliminable_links:\n",
+    "        net = pack(l for l in net if l not in eliminable_links)\n",
+    "        eliminable_links = eliminable_pair(net)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_pairs(net):\n",
+    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "    eliminable_links = eliminable_pair_hg(height_groups)\n",
+    "    while eliminable_links:\n",
+    "        net = pack(l for l in net if l not in eliminable_links)\n",
+    "        height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "        eliminable_links = eliminable_pair_hg(height_groups)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10207\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(10207, 9813)"
+      ]
+     },
+     "execution_count": 82,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "print(len(plnet))\n",
+    "elnet = eliminate_pairs(plnet)\n",
+    "len(plnet), len(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 83,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eliminable_pairs(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 84,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase,  lnet) == follow_many(string.ascii_lowercase, elnet)\n",
+    "assert follow_many(string.ascii_lowercase, plnet) == follow_many(string.ascii_lowercase, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 6.08 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "elnet = eliminate_pairs(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# for i in range(26):\n",
+    "#     assert follow(i, plnet) == follow(i, elnet)\n",
+    "#     assert follow(i,  lnet) == follow(i, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# follow(0, plnet), follow(0, elnet), follow(0, lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def triple_slow(net):\n",
+    "    x = None\n",
+    "    y = None\n",
+    "    ts = []\n",
+    "    for a in net:\n",
+    "        bs = [l for l in net if l.height == a.height + 1 \n",
+    "              if l.left == a.right or l.right == a.left]\n",
+    "        for b in bs:\n",
+    "            c = Link(a.height + 2, a.left, a.right)\n",
+    "            if c in net:\n",
+    "                ts += [(a, b, c)]\n",
+    "    return ts"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def triple_pair_slow(net):\n",
+    "    ts = []\n",
+    "    for a in net:\n",
+    "        a_ends = link_ends(a)\n",
+    "        bs = [l for l in net if l.height == a.height + 1 \n",
+    "              if link_ends(l) & a_ends]\n",
+    "        if len(bs) == 1:\n",
+    "            b = bs[0]\n",
+    "            lines = set((a.left, a.right, b.left, b.right))\n",
+    "            cs = [l for l in net \n",
+    "                  if l.height == a.height + 2\n",
+    "                  if link_ends(l) & lines]\n",
+    "            if len(cs) == 1:\n",
+    "                c = Link(a.height + 2, a.left, a.right)\n",
+    "                if c in cs:\n",
+    "                    ds = [l for l in net \n",
+    "                          if l.height == a.height + 3\n",
+    "                          if link_ends(l) & lines]\n",
+    "                    d = Link(a.height + 3, b.left, b.right)\n",
+    "                    if d in ds:\n",
+    "                        ts += [(a, b, c, d)]\n",
+    "    return ts"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 90,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def find_height_groups(net):\n",
+    "    return {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def triple_pair_hg(height_groups, debug=False):\n",
+    "    ts = []\n",
+    "    for h in range(3, max(height_groups.keys())):\n",
+    "        for d in height_groups[h]:\n",
+    "            if debug: print('d:', d)\n",
+    "            ch = h - 1\n",
+    "            cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
+    "            if debug: print('cs:', cs)\n",
+    "            while ch > 2 and not cs:\n",
+    "                ch -= 1\n",
+    "                cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
+    "                if debug: print('cs:', cs)\n",
+    "            if len(cs) == 1:\n",
+    "                c = cs[0]\n",
+    "                lines = set((d.left, d.right, c.left, c.right))\n",
+    "                if debug: print('c:', '; lines:', lines)\n",
+    "                bs = [l for l in height_groups[ch-1] if link_ends(l) & lines]\n",
+    "                b = Link(ch - 1, d.left, d.right)\n",
+    "                if debug: print('b:', b, '; bs:', bs)\n",
+    "                if len(bs) == 1 and b in bs:\n",
+    "                    ah = b.height - 1\n",
+    "                    als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
+    "                    if debug: print('ah:', ah, '; als:', als)\n",
+    "                    while ah > 0 and not als:\n",
+    "                        ah -= 1\n",
+    "                        als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
+    "                        if debug: print('ah:', ah, '; als:', als)\n",
+    "                    a = Link(ah, c.left, c.right)\n",
+    "                    if debug: print('a:', a)\n",
+    "                    if a in als:\n",
+    "                        if debug: print('adding:', a, b, c, d)\n",
+    "                        ts += [(a, b, c, d)]\n",
+    "    return ts"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_a_triple_pair_slow(net, debug=False):\n",
+    "    tps = triple_pair_slow(net)\n",
+    "    if debug: print('eatp', tps)\n",
+    "\n",
+    "    if tps:\n",
+    "        a, b, c, d = tps[0]\n",
+    "#         x = Link(a.height, b.left, b.right)\n",
+    "#         y = Link(b.height, a.left, a.right)\n",
+    "        x = Link(b.height - 0.5, b.left, b.right)\n",
+    "        y = Link(b.height, a.left, a.right)\n",
+    "        if debug: print('removing', a, b, c, d, '; adding', x, y)\n",
+    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_a_triple_pair(net, debug=False):\n",
+    "    height_groups = find_height_groups(net)\n",
+    "\n",
+    "    tps = triple_pair_hg(height_groups)\n",
+    "    if debug: print('eatp', tps)\n",
+    "    if tps:\n",
+    "        a, b, c, d = tps[0]\n",
+    "        x = Link(b.height - 0.5, b.left, b.right)\n",
+    "        y = Link(b.height, a.left, a.right)\n",
+    "        if debug: print('removing', a, b, c, d, '; adding', x, y)\n",
+    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=1126, left=8, right=17),\n",
+       "  Link(height=1127, left=1, right=8),\n",
+       "  Link(height=1128, left=8, right=17),\n",
+       "  Link(height=1129, left=1, right=8)),\n",
+       " (Link(height=1952, left=12, right=25),\n",
+       "  Link(height=1953, left=10, right=12),\n",
+       "  Link(height=1954, left=12, right=25),\n",
+       "  Link(height=1955, left=10, right=12))]"
+      ]
+     },
+     "execution_count": 94,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "height_groups = find_height_groups(elnet)\n",
+    "triple_pair_hg(height_groups)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 98.7 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "height_groups = find_height_groups(elnet)\n",
+    "triple_pair_hg(height_groups)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_triple_pairs_slow(net):\n",
+    "    print(len(net))\n",
+    "    new_net = eliminate_a_triple_pair_slow(net)\n",
+    "    while new_net:\n",
+    "        print(len(net))\n",
+    "        net = new_net\n",
+    "        new_net = eliminate_a_triple_pair_slow(net)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_triple_pairs(net):\n",
+    "    print(len(net))\n",
+    "    new_net = eliminate_a_triple_pair(net)\n",
+    "    while new_net:\n",
+    "        print(len(net))\n",
+    "        net = new_net\n",
+    "        new_net = eliminate_a_triple_pair(net)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "etlnet = eliminate_a_triple_pair(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 99,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "9813\n",
+      "9813\n",
+      "9811\n"
+     ]
+    }
+   ],
+   "source": [
+    "setlnet = eliminate_triple_pairs(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 101,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9809"
+      ]
+     },
+     "execution_count": 101,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(setlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 103,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'ypetfugkzdsacbvwjohqlnirmx'"
+      ]
+     },
+     "execution_count": 103,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, etlnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 104,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'ypetfugkzdsacbvwjohqlnirmx'"
+      ]
+     },
+     "execution_count": 104,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, setlnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'ypetfugkzdsacbvwjohqlnirmx'"
+      ]
+     },
+     "execution_count": 105,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, elnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'ypetfugkzdsacbvwjohqlnirmx'"
+      ]
+     },
+     "execution_count": 106,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 107,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 107,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eliminable_pairs(etlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(10207, 9811)"
+      ]
+     },
+     "execution_count": 108,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(lnet), len(etlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 109,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def simplify(net0):\n",
+    "    netp = eliminate_pairs(net0)\n",
+    "    new_net = eliminate_a_triple_pair(netp)\n",
+    "    while new_net:\n",
+    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
+    "        netp = eliminate_pairs(new_net)\n",
+    "        new_net = eliminate_a_triple_pair(netp)\n",
+    "    return netp"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "simple_lnet = simplify(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 111,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, simple_lnet)) == ''.join(follow_many(string.ascii_lowercase, lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'ypetfugkzdsacbvwjohqlnirmx'"
+      ]
+     },
+     "execution_count": 112,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, simple_lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 113,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'ypetfugkzdsacbvwjohqlnirmx'"
+      ]
+     },
+     "execution_count": 113,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 114,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9809"
+      ]
+     },
+     "execution_count": 114,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(simple_lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 115,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def add_triple_pair(net, max_lines=None, trace=False):\n",
+    "    if not max_lines:\n",
+    "        max_lines = max(l.right for l in net)\n",
+    "    a, b, c = 0, 0, 0\n",
+    "    while len(set((a, b, c))) != 3:\n",
+    "        a = random.randrange(max_lines)\n",
+    "        b = random.randrange(max_lines)\n",
+    "        c = random.randrange(max_lines)\n",
+    "    tp = [(min(a, b), max(a, b)), (min(b, c), max(b, c))] * 2\n",
+    "    \n",
+    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
+    "    i = random.randrange(len(pairs))\n",
+    "    if trace: print(i, tp)\n",
+    "    new_pairs = pairs[:i] + tp + pairs[i:]\n",
+    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def add_pair(net, max_lines=None, trace=False):\n",
+    "    if not max_lines:\n",
+    "        max_lines = max(l.right for l in net)\n",
+    "\n",
+    "    a, b = 0, 0\n",
+    "    while a == b:\n",
+    "        a = random.randrange(max_lines)\n",
+    "        b = random.randrange(max_lines)\n",
+    "    p = [(min(a, b), max(a, b))] * 2\n",
+    "    \n",
+    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
+    "    i = random.randrange(len(pairs))\n",
+    "    \n",
+    "    if trace: print(i, p)\n",
+    "    new_pairs = pairs[:i] + p + pairs[i:]\n",
+    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 117,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 117,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 118,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 118,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "lnettp = simple_lnet\n",
+    "for _ in range(10):\n",
+    "    lnettp = add_pair(lnettp)\n",
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 119,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=301, left=7, right=23),\n",
+       "  Link(height=302, left=16, right=23),\n",
+       "  Link(height=303, left=7, right=23),\n",
+       "  Link(height=304, left=16, right=23)),\n",
+       " (Link(height=362, left=11, right=23),\n",
+       "  Link(height=363, left=3, right=23),\n",
+       "  Link(height=364, left=11, right=23),\n",
+       "  Link(height=365, left=3, right=23)),\n",
+       " (Link(height=363, left=3, right=23),\n",
+       "  Link(height=364, left=11, right=23),\n",
+       "  Link(height=365, left=3, right=23),\n",
+       "  Link(height=366, left=11, right=23)),\n",
+       " (Link(height=595, left=12, right=15),\n",
+       "  Link(height=596, left=10, right=15),\n",
+       "  Link(height=597, left=12, right=15),\n",
+       "  Link(height=598, left=10, right=15)),\n",
+       " (Link(height=796, left=12, right=21),\n",
+       "  Link(height=797, left=4, right=12),\n",
+       "  Link(height=798, left=12, right=21),\n",
+       "  Link(height=799, left=4, right=12)),\n",
+       " (Link(height=879, left=0, right=18),\n",
+       "  Link(height=880, left=0, right=8),\n",
+       "  Link(height=881, left=0, right=18),\n",
+       "  Link(height=882, left=0, right=8)),\n",
+       " (Link(height=930, left=3, right=17),\n",
+       "  Link(height=931, left=3, right=21),\n",
+       "  Link(height=932, left=3, right=17),\n",
+       "  Link(height=933, left=3, right=21)),\n",
+       " (Link(height=1120, left=5, right=19),\n",
+       "  Link(height=1121, left=18, right=19),\n",
+       "  Link(height=1122, left=5, right=19),\n",
+       "  Link(height=1123, left=18, right=19)),\n",
+       " (Link(height=2040, left=9, right=21),\n",
+       "  Link(height=2041, left=9, right=15),\n",
+       "  Link(height=2042, left=9, right=21),\n",
+       "  Link(height=2043, left=9, right=15)),\n",
+       " (Link(height=2110, left=13, right=21),\n",
+       "  Link(height=2111, left=13, right=24),\n",
+       "  Link(height=2112, left=13, right=21),\n",
+       "  Link(height=2113, left=13, right=24))]"
+      ]
+     },
+     "execution_count": 119,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "lnettp = simple_lnet\n",
+    "for _ in range(10):\n",
+    "    lnettp = add_triple_pair(lnettp)\n",
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 120,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=49, left=10, right=20),\n",
+       "  Link(height=50, left=2, right=20),\n",
+       "  Link(height=51, left=10, right=20),\n",
+       "  Link(height=52, left=2, right=20)),\n",
+       " (Link(height=54, left=2, right=24),\n",
+       "  Link(height=55, left=3, right=24),\n",
+       "  Link(height=56, left=2, right=24),\n",
+       "  Link(height=57, left=3, right=24)),\n",
+       " (Link(height=62, left=2, right=15),\n",
+       "  Link(height=63, left=0, right=15),\n",
+       "  Link(height=64, left=2, right=15),\n",
+       "  Link(height=65, left=0, right=15)),\n",
+       " (Link(height=114, left=14, right=18),\n",
+       "  Link(height=115, left=3, right=18),\n",
+       "  Link(height=116, left=14, right=18),\n",
+       "  Link(height=117, left=3, right=18)),\n",
+       " (Link(height=138, left=13, right=19),\n",
+       "  Link(height=139, left=8, right=19),\n",
+       "  Link(height=140, left=13, right=19),\n",
+       "  Link(height=141, left=8, right=19)),\n",
+       " (Link(height=160, left=12, right=13),\n",
+       "  Link(height=161, left=4, right=12),\n",
+       "  Link(height=162, left=12, right=13),\n",
+       "  Link(height=163, left=4, right=12)),\n",
+       " (Link(height=315, left=23, right=24),\n",
+       "  Link(height=320, left=20, right=23),\n",
+       "  Link(height=321, left=23, right=24),\n",
+       "  Link(height=322, left=20, right=23)),\n",
+       " (Link(height=324, left=3, right=18),\n",
+       "  Link(height=325, left=16, right=18),\n",
+       "  Link(height=326, left=3, right=18),\n",
+       "  Link(height=327, left=16, right=18)),\n",
+       " (Link(height=342, left=21, right=22),\n",
+       "  Link(height=345, left=1, right=22),\n",
+       "  Link(height=346, left=21, right=22),\n",
+       "  Link(height=347, left=1, right=22)),\n",
+       " (Link(height=405, left=8, right=19),\n",
+       "  Link(height=406, left=4, right=8),\n",
+       "  Link(height=407, left=8, right=19),\n",
+       "  Link(height=408, left=4, right=8)),\n",
+       " (Link(height=468, left=11, right=22),\n",
+       "  Link(height=469, left=15, right=22),\n",
+       "  Link(height=470, left=11, right=22),\n",
+       "  Link(height=471, left=15, right=22)),\n",
+       " (Link(height=549, left=1, right=2),\n",
+       "  Link(height=550, left=1, right=6),\n",
+       "  Link(height=551, left=1, right=2),\n",
+       "  Link(height=552, left=1, right=6)),\n",
+       " (Link(height=568, left=16, right=21),\n",
+       "  Link(height=569, left=11, right=21),\n",
+       "  Link(height=570, left=16, right=21),\n",
+       "  Link(height=571, left=11, right=21)),\n",
+       " (Link(height=608, left=17, right=20),\n",
+       "  Link(height=609, left=2, right=17),\n",
+       "  Link(height=610, left=17, right=20),\n",
+       "  Link(height=611, left=2, right=17)),\n",
+       " (Link(height=613, left=18, right=21),\n",
+       "  Link(height=618, left=18, right=19),\n",
+       "  Link(height=619, left=18, right=21),\n",
+       "  Link(height=620, left=18, right=19)),\n",
+       " (Link(height=635, left=2, right=4),\n",
+       "  Link(height=636, left=4, right=20),\n",
+       "  Link(height=637, left=2, right=4),\n",
+       "  Link(height=638, left=4, right=20)),\n",
+       " (Link(height=681, left=7, right=20),\n",
+       "  Link(height=682, left=20, right=22),\n",
+       "  Link(height=683, left=7, right=20),\n",
+       "  Link(height=684, left=20, right=22)),\n",
+       " (Link(height=750, left=23, right=24),\n",
+       "  Link(height=751, left=18, right=24),\n",
+       "  Link(height=752, left=23, right=24),\n",
+       "  Link(height=753, left=18, right=24)),\n",
+       " (Link(height=760, left=12, right=18),\n",
+       "  Link(height=761, left=17, right=18),\n",
+       "  Link(height=762, left=12, right=18),\n",
+       "  Link(height=763, left=17, right=18)),\n",
+       " (Link(height=765, left=0, right=9),\n",
+       "  Link(height=766, left=0, right=14),\n",
+       "  Link(height=767, left=0, right=9),\n",
+       "  Link(height=768, left=0, right=14)),\n",
+       " (Link(height=805, left=16, right=22),\n",
+       "  Link(height=806, left=0, right=16),\n",
+       "  Link(height=807, left=16, right=22),\n",
+       "  Link(height=808, left=0, right=16)),\n",
+       " (Link(height=834, left=1, right=6),\n",
+       "  Link(height=835, left=3, right=6),\n",
+       "  Link(height=836, left=1, right=6),\n",
+       "  Link(height=837, left=3, right=6)),\n",
+       " (Link(height=881, left=2, right=12),\n",
+       "  Link(height=882, left=2, right=23),\n",
+       "  Link(height=883, left=2, right=12),\n",
+       "  Link(height=884, left=2, right=23)),\n",
+       " (Link(height=904, left=12, right=23),\n",
+       "  Link(height=905, left=12, right=14),\n",
+       "  Link(height=906, left=12, right=23),\n",
+       "  Link(height=907, left=12, right=14)),\n",
+       " (Link(height=936, left=7, right=17),\n",
+       "  Link(height=937, left=15, right=17),\n",
+       "  Link(height=938, left=7, right=17),\n",
+       "  Link(height=939, left=15, right=17)),\n",
+       " (Link(height=1010, left=4, right=6),\n",
+       "  Link(height=1011, left=6, right=17),\n",
+       "  Link(height=1012, left=4, right=6),\n",
+       "  Link(height=1013, left=6, right=17)),\n",
+       " (Link(height=1030, left=1, right=12),\n",
+       "  Link(height=1031, left=1, right=20),\n",
+       "  Link(height=1032, left=1, right=12),\n",
+       "  Link(height=1033, left=1, right=20)),\n",
+       " (Link(height=1197, left=2, right=9),\n",
+       "  Link(height=1198, left=9, right=22),\n",
+       "  Link(height=1199, left=2, right=9),\n",
+       "  Link(height=1200, left=9, right=22)),\n",
+       " (Link(height=1222, left=2, right=3),\n",
+       "  Link(height=1223, left=2, right=5),\n",
+       "  Link(height=1224, left=2, right=3),\n",
+       "  Link(height=1225, left=2, right=5)),\n",
+       " (Link(height=1318, left=12, right=23),\n",
+       "  Link(height=1319, left=4, right=12),\n",
+       "  Link(height=1320, left=12, right=23),\n",
+       "  Link(height=1321, left=4, right=12)),\n",
+       " (Link(height=1341, left=17, right=22),\n",
+       "  Link(height=1342, left=11, right=17),\n",
+       "  Link(height=1343, left=17, right=22),\n",
+       "  Link(height=1344, left=11, right=17)),\n",
+       " (Link(height=1396, left=4, right=9),\n",
+       "  Link(height=1397, left=3, right=9),\n",
+       "  Link(height=1398, left=4, right=9),\n",
+       "  Link(height=1399, left=3, right=9)),\n",
+       " (Link(height=1426, left=18, right=24),\n",
+       "  Link(height=1427, left=17, right=18),\n",
+       "  Link(height=1428, left=18, right=24),\n",
+       "  Link(height=1429, left=17, right=18)),\n",
+       " (Link(height=1456, left=2, right=15),\n",
+       "  Link(height=1457, left=3, right=15),\n",
+       "  Link(height=1458, left=2, right=15),\n",
+       "  Link(height=1459, left=3, right=15)),\n",
+       " (Link(height=1505, left=13, right=18),\n",
+       "  Link(height=1506, left=13, right=21),\n",
+       "  Link(height=1507, left=13, right=18),\n",
+       "  Link(height=1508, left=13, right=21)),\n",
+       " (Link(height=1551, left=10, right=12),\n",
+       "  Link(height=1552, left=4, right=12),\n",
+       "  Link(height=1553, left=10, right=12),\n",
+       "  Link(height=1554, left=4, right=12)),\n",
+       " (Link(height=1622, left=4, right=11),\n",
+       "  Link(height=1623, left=11, right=16),\n",
+       "  Link(height=1624, left=4, right=11),\n",
+       "  Link(height=1625, left=11, right=16)),\n",
+       " (Link(height=1653, left=8, right=24),\n",
+       "  Link(height=1654, left=4, right=8),\n",
+       "  Link(height=1655, left=8, right=24),\n",
+       "  Link(height=1656, left=4, right=8)),\n",
+       " (Link(height=1688, left=0, right=5),\n",
+       "  Link(height=1689, left=0, right=23),\n",
+       "  Link(height=1690, left=0, right=5),\n",
+       "  Link(height=1691, left=0, right=23)),\n",
+       " (Link(height=1724, left=10, right=23),\n",
+       "  Link(height=1725, left=10, right=11),\n",
+       "  Link(height=1726, left=10, right=23),\n",
+       "  Link(height=1727, left=10, right=11)),\n",
+       " (Link(height=1863, left=1, right=12),\n",
+       "  Link(height=1864, left=1, right=13),\n",
+       "  Link(height=1865, left=1, right=12),\n",
+       "  Link(height=1866, left=1, right=13)),\n",
+       " (Link(height=1873, left=10, right=22),\n",
+       "  Link(height=1874, left=10, right=15),\n",
+       "  Link(height=1875, left=10, right=22),\n",
+       "  Link(height=1876, left=10, right=15)),\n",
+       " (Link(height=1879, left=18, right=20),\n",
+       "  Link(height=1880, left=17, right=20),\n",
+       "  Link(height=1881, left=18, right=20),\n",
+       "  Link(height=1882, left=17, right=20)),\n",
+       " (Link(height=1916, left=18, right=19),\n",
+       "  Link(height=1917, left=7, right=18),\n",
+       "  Link(height=1918, left=18, right=19),\n",
+       "  Link(height=1919, left=7, right=18)),\n",
+       " (Link(height=1961, left=11, right=20),\n",
+       "  Link(height=1962, left=7, right=20),\n",
+       "  Link(height=1963, left=11, right=20),\n",
+       "  Link(height=1964, left=7, right=20)),\n",
+       " (Link(height=1962, left=9, right=18),\n",
+       "  Link(height=1963, left=18, right=19),\n",
+       "  Link(height=1964, left=9, right=18),\n",
+       "  Link(height=1965, left=18, right=19)),\n",
+       " (Link(height=2031, left=3, right=6),\n",
+       "  Link(height=2032, left=3, right=4),\n",
+       "  Link(height=2033, left=3, right=6),\n",
+       "  Link(height=2034, left=3, right=4)),\n",
+       " (Link(height=2077, left=2, right=9),\n",
+       "  Link(height=2078, left=2, right=23),\n",
+       "  Link(height=2079, left=2, right=9),\n",
+       "  Link(height=2080, left=2, right=23)),\n",
+       " (Link(height=2165, left=1, right=8),\n",
+       "  Link(height=2166, left=4, right=8),\n",
+       "  Link(height=2167, left=1, right=8),\n",
+       "  Link(height=2168, left=4, right=8)),\n",
+       " (Link(height=2185, left=6, right=21),\n",
+       "  Link(height=2186, left=11, right=21),\n",
+       "  Link(height=2187, left=6, right=21),\n",
+       "  Link(height=2188, left=11, right=21))]"
+      ]
+     },
+     "execution_count": 120,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "lnettp = simple_lnet\n",
+    "for _ in range(50):\n",
+    "    lnettp = add_pair(lnettp)\n",
+    "for _ in range(50):\n",
+    "    lnettp = add_triple_pair(lnettp)\n",
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 121,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 121,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "lnettp == pack(lnettp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 122,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9909"
+      ]
+     },
+     "execution_count": 122,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "lnettps = simplify(lnettp)\n",
+    "len(lnettps)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 123,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(9809, 10109, 9909)"
+      ]
+     },
+     "execution_count": 123,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(simple_lnet), len(lnettp), len(lnettps)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 124,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 124,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, lnet)) == ''.join(follow_many(string.ascii_lowercase, simple_lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 125,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 125,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, lnettps)) == ''.join(follow_many(string.ascii_lowercase, lnettp))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 126,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2285"
+      ]
+     },
+     "execution_count": 126,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in lnettp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 127,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def simplify_with_checks(net0):\n",
+    "    netp = eliminate_pairs(net0)\n",
+    "    if follow_many(string.ascii_lowercase, net0) != follow_many(string.ascii_lowercase, netp):\n",
+    "        print('pairs', eliminable_pairs(net0))\n",
+    "        return net0\n",
+    "    else:\n",
+    "        print('pairs ok')\n",
+    "    new_net = eliminate_a_triple_pair(netp)\n",
+    "    if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
+    "        hg = find_height_groups(netp)\n",
+    "        print('triple', triple_pair_hg(hg))\n",
+    "        return netp\n",
+    "    else:\n",
+    "        print('triple ok')\n",
+    "    while new_net:\n",
+    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
+    "        netp = eliminate_pairs(new_net)\n",
+    "        if follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
+    "            print('pairs', eliminable_pairs(new_net))\n",
+    "            return new_net\n",
+    "        else:\n",
+    "            print('pairs ok')\n",
+    "        new_net = eliminate_a_triple_pair(netp)\n",
+    "        if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
+    "            hg = find_height_groups(netp)\n",
+    "            print('triple', triple_pair_hg(hg))\n",
+    "            return netp\n",
+    "        else:\n",
+    "            print('triple ok')\n",
+    "    print('** done')\n",
+    "    return netp"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 128,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "** done\n"
+     ]
+    }
+   ],
+   "source": [
+    "lnettps = simplify_with_checks(lnettp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 129,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 129,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, lnettps)) == ''.join(follow_many(string.ascii_lowercase, lnettp))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 130,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10109"
+      ]
+     },
+     "execution_count": 130,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(lnettp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 131,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# open('04-lines.txt', 'w').write(show_net(lnettp, randomise=True, pair_sep='\\n'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 114,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "139"
+      ]
+     },
+     "execution_count": 114,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# open('04-small.txt', 'w').write(show_net(make_net(20), randomise=True, pair_sep='\\n'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 143,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "8 [(2, 4), (0, 4), (2, 4), (0, 4)]\n",
+      "10 [(1, 2), (1, 2)]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=1, right=4),\n",
+       " Link(height=2, left=0, right=3),\n",
+       " Link(height=3, left=0, right=3),\n",
+       " Link(height=4, left=0, right=5),\n",
+       " Link(height=5, left=3, right=5),\n",
+       " Link(height=6, left=0, right=2),\n",
+       " Link(height=7, left=3, right=4),\n",
+       " Link(height=8, left=2, right=4),\n",
+       " Link(height=9, left=1, right=2),\n",
+       " Link(height=10, left=0, right=4),\n",
+       " Link(height=11, left=1, right=2),\n",
+       " Link(height=12, left=2, right=4),\n",
+       " Link(height=13, left=1, right=2),\n",
+       " Link(height=14, left=0, right=4),\n",
+       " Link(height=15, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 143,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "net = make_net(10, lines=6)\n",
+    "net = add_triple_pair(net, trace=True)\n",
+    "net = add_pair(net, trace=True)\n",
+    "net = read_net(show_net(net, randomise=True))\n",
+    "net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 147,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'(2, 5), (1, 4), (0, 3), (0, 3), (0, 5), (3, 5), (0, 2), (3, 4), (2, 4), (1, 2), (0, 4), (1, 2), (2, 4), (1, 2), (0, 4), (1, 4)'"
+      ]
+     },
+     "execution_count": 147,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "show_net(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 149,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=1, right=4),\n",
+       " Link(height=2, left=0, right=3),\n",
+       " Link(height=3, left=0, right=3),\n",
+       " Link(height=4, left=0, right=5),\n",
+       " Link(height=5, left=3, right=5),\n",
+       " Link(height=6, left=0, right=2),\n",
+       " Link(height=7, left=3, right=4),\n",
+       " Link(height=8, left=2, right=4),\n",
+       " Link(height=9, left=1, right=2),\n",
+       " Link(height=10, left=0, right=4),\n",
+       " Link(height=11, left=1, right=2),\n",
+       " Link(height=12, left=2, right=4),\n",
+       " Link(height=13, left=0, right=4),\n",
+       " Link(height=14, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 149,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "net = read_net('(2, 5), (1, 4), (0, 3), (0, 3), (0, 5), (3, 5), (0, 2), (3, 4), (2, 4), (1, 2), (0, 4), (1, 2), (2, 4), (0, 4), (1, 4)')\n",
+    "net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 150,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=0, right=3),\n",
+       " Link(height=0, left=1, right=4),\n",
+       " Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=0, right=3),\n",
+       " Link(height=2, left=0, right=5),\n",
+       " Link(height=3, left=0, right=2),\n",
+       " Link(height=3, left=3, right=5),\n",
+       " Link(height=4, left=3, right=4),\n",
+       " Link(height=5, left=2, right=4),\n",
+       " Link(height=6, left=0, right=4),\n",
+       " Link(height=6, left=1, right=2),\n",
+       " Link(height=7, left=1, right=2),\n",
+       " Link(height=8, left=2, right=4),\n",
+       " Link(height=9, left=0, right=4),\n",
+       " Link(height=10, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 150,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pack(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 151,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=1, right=4),\n",
+       " Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=0, right=5),\n",
+       " Link(height=2, left=0, right=2),\n",
+       " Link(height=2, left=3, right=5),\n",
+       " Link(height=3, left=3, right=4),\n",
+       " Link(height=4, left=2, right=4),\n",
+       " Link(height=5, left=0, right=4),\n",
+       " Link(height=6, left=2, right=4),\n",
+       " Link(height=7, left=0, right=4),\n",
+       " Link(height=8, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 151,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "epnet = eliminate_pairs(net)\n",
+    "pack(epnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 152,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "11\n",
+      "11\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=1, right=4),\n",
+       " Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=0, right=5),\n",
+       " Link(height=2, left=0, right=2),\n",
+       " Link(height=2, left=3, right=5),\n",
+       " Link(height=3, left=3, right=4),\n",
+       " Link(height=4, left=0, right=4),\n",
+       " Link(height=5, left=2, right=4),\n",
+       " Link(height=6, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 152,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eptnet = eliminate_triple_pairs(epnet)\n",
+    "pack(eptnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 153,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 153,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, net)) == ''.join(follow_many(string.ascii_lowercase, eptnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 155,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "104"
+      ]
+     },
+     "execution_count": 155,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "open('04-small.txt', 'w').write(show_net(net, pair_sep='\\n'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/04-amidakuji/amidakuji-solution-1-slow.ipynb b/04-amidakuji/amidakuji-solution-1-slow.ipynb
new file mode 100644 (file)
index 0000000..345321d
--- /dev/null
+++ b/04-amidakuji/amidakuji-solution-1-slow.ipynb
@@ -0,0 +1,1881 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import collections\n",
+    "import string\n",
+    "import itertools"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Link = collections.namedtuple('Link', 'height left right')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def link_ends(link):\n",
+    "    return set((link.left, link.right))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def read_net(net_string):\n",
+    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow(initial_line, links):\n",
+    "    line = initial_line\n",
+    "    heights = sorted(set(l.height for l in links))\n",
+    "    for h in heights:\n",
+    "        for l in [l for l in links if l.height == h]:\n",
+    "            if line in link_ends(l):\n",
+    "                line = [e for e in link_ends(l) if e != line][0]\n",
+    "#                 print(l, line)\n",
+    "    return line"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def pack(net):\n",
+    "    packed_links = []\n",
+    "    line_heights = collections.defaultdict(lambda: -1)\n",
+    "    for link in sorted(net):\n",
+    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
+    "        line_heights[link.left] = link_height\n",
+    "        line_heights[link.right] = link_height\n",
+    "        packed_links += [Link(link_height, link.left, link.right)]\n",
+    "    return sorted(packed_links)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow_many_slow(in_sequence, links):\n",
+    "    out_sequence = [(follow(i, links), term) \n",
+    "                    for i, term in enumerate(in_sequence)]\n",
+    "    return [term for i, term in sorted(out_sequence)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow_many(in_sequence, net):\n",
+    "    height_groups = [list(g) for _, g in itertools.groupby(pack(net), lambda l: l.height)]\n",
+    "    seq = list(in_sequence)\n",
+    "    for links in height_groups:\n",
+    "        for link in links:\n",
+    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
+    "    return seq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10000 loops, best of 3: 47.5 µs per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many('abcdefghij', net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# %%timeit\n",
+    "# follow_many_slow('abcdefghij', net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def show_net(links, randomise=False):\n",
+    "    if randomise:\n",
+    "        output = []\n",
+    "        heights = sorted(set(l.height for l in links))\n",
+    "        for h in heights:\n",
+    "            ls = [l for l in links if l.height == h]\n",
+    "            random.shuffle(ls)\n",
+    "            output += ['({}, {})'.format(l.left, l.right) for l in ls]\n",
+    "        return ', '.join(output)\n",
+    "    return ', '.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extract_pairs(net_string):\n",
+    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(True, True)"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rrnet = read_net(show_net(net, randomise=True))\n",
+    "rnet = read_net(show_net(net))\n",
+    "rnet == rrnet, pack(rrnet) == pnet"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "lnet = make_net(10207, 26, 100000)\n",
+    "plnet = pack(lnet)\n",
+    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, plnet)\n",
+    "# for i in range(204):\n",
+    "#     assert follow(i, lnet) == follow(i, plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "rlnet = read_net(show_net(lnet))\n",
+    "prlnet = pack(rlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2251"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "99998"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10206"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in rlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2251"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(link.height for link in prlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, lnet) == follow_many(string.ascii_lowercase, prlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 24.5 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many(string.ascii_lowercase, lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# %%timeit\n",
+    "# follow_many_slow(string.ascii_lowercase, lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pairs_slow(net):\n",
+    "    eps = []\n",
+    "    for l in net:\n",
+    "        o = Link(l.height + 1, l.left, l.right)\n",
+    "        if o in net:\n",
+    "            eps += [(l, o)]\n",
+    "    return eps    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pairs(net):\n",
+    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "    eps = []\n",
+    "    for h in range(1, max(height_groups.keys())):\n",
+    "        for l in height_groups[h]:\n",
+    "            o = Link(l.height - 1, l.left, l.right)\n",
+    "            if o in height_groups[h-1]:\n",
+    "                eps += [(l, o)]\n",
+    "    return eps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 23.5 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "eliminable_pairs(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 2.33 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "eliminable_pairs_slow(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert sorted(sorted(p) for p in eliminable_pairs(plnet)) == sorted(sorted(p) for p in eliminable_pairs_slow(plnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pair(net):\n",
+    "    for l in net:\n",
+    "        o = Link(l.height + 1, l.left, l.right)\n",
+    "        if o in net:\n",
+    "            return l, o\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pair_hg(height_groups):\n",
+    "    for h in range(1, max(height_groups.keys())):\n",
+    "        for l in height_groups[h]:\n",
+    "            o = Link(l.height - 1, l.left, l.right)\n",
+    "            if o in height_groups[h-1]:\n",
+    "                return l, o\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_pairs_slow(net):\n",
+    "    eliminable_links = eliminable_pair(net)\n",
+    "    while eliminable_links:\n",
+    "        net = pack(l for l in net if l not in eliminable_links)\n",
+    "        eliminable_links = eliminable_pair(net)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_pairs(net):\n",
+    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "    eliminable_links = eliminable_pair_hg(height_groups)\n",
+    "    while eliminable_links:\n",
+    "        net = pack(l for l in net if l not in eliminable_links)\n",
+    "        height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "        eliminable_links = eliminable_pair_hg(height_groups)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10207\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(10207, 9811)"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "print(len(plnet))\n",
+    "elnet = eliminate_pairs_slow(plnet)\n",
+    "len(plnet), len(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10207\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(10207, 9811)"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "print(len(plnet))\n",
+    "elnet = eliminate_pairs(plnet)\n",
+    "len(plnet), len(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eliminable_pairs(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert eliminate_pairs_slow(plnet) == eliminate_pairs(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase,  lnet) == follow_many(string.ascii_lowercase, elnet)\n",
+    "assert follow_many(string.ascii_lowercase, plnet) == follow_many(string.ascii_lowercase, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 3min 30s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "elnet = eliminate_pairs_slow(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 6.27 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "elnet = eliminate_pairs(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# for i in range(26):\n",
+    "#     assert follow(i, plnet) == follow(i, elnet)\n",
+    "#     assert follow(i,  lnet) == follow(i, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# follow(0, plnet), follow(0, elnet), follow(0, lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def triple(net):\n",
+    "    x = None\n",
+    "    y = None\n",
+    "    ts = []\n",
+    "    for a in net:\n",
+    "        bs = [l for l in net if l.height == a.height + 1 \n",
+    "              if l.left == a.right or l.right == a.left]\n",
+    "        for b in bs:\n",
+    "            c = Link(a.height + 2, a.left, a.right)\n",
+    "            if c in net:\n",
+    "                ts += [(a, b, c)]\n",
+    "    return ts"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def triple_pair(net):\n",
+    "    ts = []\n",
+    "    for a in net:\n",
+    "        a_ends = link_ends(a)\n",
+    "        bs = [l for l in net if l.height == a.height + 1 \n",
+    "              if link_ends(l) & a_ends]\n",
+    "        if len(bs) == 1:\n",
+    "            b = bs[0]\n",
+    "            lines = set((a.left, a.right, b.left, b.right))\n",
+    "            cs = [l for l in net \n",
+    "                  if l.height == a.height + 2\n",
+    "                  if link_ends(l) & lines]\n",
+    "            if len(cs) == 1:\n",
+    "                c = Link(a.height + 2, a.left, a.right)\n",
+    "                if c in cs:\n",
+    "                    ds = [l for l in net \n",
+    "                          if l.height == a.height + 3\n",
+    "                          if link_ends(l) & lines]\n",
+    "                    d = Link(a.height + 3, b.left, b.right)\n",
+    "                    if d in ds:\n",
+    "                        ts += [(a, b, c, d)]\n",
+    "    return ts"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 129,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def triple_pair_hg(height_groups, debug=False):\n",
+    "    ts = []\n",
+    "    for h in range(3, max(height_groups.keys())):\n",
+    "        for d in height_groups[h]:\n",
+    "            if debug: print('d:', d)\n",
+    "            ch = h - 1\n",
+    "            cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
+    "            if debug: print('cs:', cs)\n",
+    "            while ch > 2 and not cs:\n",
+    "                ch -= 1\n",
+    "                cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
+    "                if debug: print('cs:', cs)\n",
+    "            if len(cs) == 1:\n",
+    "                c = cs[0]\n",
+    "                lines = set((d.left, d.right, c.left, c.right))\n",
+    "                if debug: print('c:', '; lines:', lines)\n",
+    "                bs = [l for l in height_groups[ch-1] if link_ends(l) & lines]\n",
+    "                b = Link(ch - 1, d.left, d.right)\n",
+    "                if debug: print('b:', b, '; bs:', bs)\n",
+    "                if len(bs) == 1 and b in bs:\n",
+    "                    ah = b.height - 1\n",
+    "                    als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
+    "                    if debug: print('ah:', ah, '; als:', als)\n",
+    "                    while ah > 0 and not als:\n",
+    "                        ah -= 1\n",
+    "                        als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
+    "                        if debug: print('ah:', ah, '; als:', als)\n",
+    "                    a = Link(ah, c.left, c.right)\n",
+    "                    if debug: print('a:', a)\n",
+    "                    if a in als:\n",
+    "                        if debug: print('adding:', a, b, c, d)\n",
+    "                        ts += [(a, b, c, d)]\n",
+    "    return ts"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 132,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_a_triple_pair_slow(net):\n",
+    "    tps = triple_pair(net)\n",
+    "    print('eatp', tps)\n",
+    "\n",
+    "    if tps:\n",
+    "        a, b, c, d = tps[0]\n",
+    "#         x = Link(a.height, b.left, b.right)\n",
+    "#         y = Link(b.height, a.left, a.right)\n",
+    "        x = Link(a.height, b.left, b.right)\n",
+    "        y = Link(b.height, a.left, a.right)\n",
+    "        print('removing', a, b, c, d, '; adding', x, y)\n",
+    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 133,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_a_triple_pair(net):\n",
+    "    height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "\n",
+    "    tps = triple_pair_hg(height_groups)\n",
+    "    print('eatp', tps)\n",
+    "    if tps:\n",
+    "        a, b, c, d = tps[0]\n",
+    "        x = Link(a.height, b.left, b.right)\n",
+    "        y = Link(b.height, a.left, a.right)\n",
+    "        print('removing', a, b, c, d, '; adding', x, y)\n",
+    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=12, left=0, right=5),\n",
+       "  Link(height=13, left=5, right=11),\n",
+       "  Link(height=14, left=0, right=5)),\n",
+       " (Link(height=29, left=2, right=18),\n",
+       "  Link(height=30, left=1, right=2),\n",
+       "  Link(height=31, left=2, right=18)),\n",
+       " (Link(height=40, left=2, right=3),\n",
+       "  Link(height=41, left=3, right=18),\n",
+       "  Link(height=42, left=2, right=3)),\n",
+       " (Link(height=43, left=1, right=10),\n",
+       "  Link(height=44, left=10, right=20),\n",
+       "  Link(height=45, left=1, right=10)),\n",
+       " (Link(height=91, left=5, right=8),\n",
+       "  Link(height=92, left=3, right=5),\n",
+       "  Link(height=93, left=5, right=8)),\n",
+       " (Link(height=91, left=5, right=8),\n",
+       "  Link(height=92, left=8, right=18),\n",
+       "  Link(height=93, left=5, right=8)),\n",
+       " (Link(height=99, left=13, right=17),\n",
+       "  Link(height=100, left=4, right=13),\n",
+       "  Link(height=101, left=13, right=17)),\n",
+       " (Link(height=120, left=18, right=20),\n",
+       "  Link(height=121, left=9, right=18),\n",
+       "  Link(height=122, left=18, right=20)),\n",
+       " (Link(height=147, left=19, right=21),\n",
+       "  Link(height=148, left=7, right=19),\n",
+       "  Link(height=149, left=19, right=21)),\n",
+       " (Link(height=147, left=19, right=21),\n",
+       "  Link(height=148, left=21, right=23),\n",
+       "  Link(height=149, left=19, right=21)),\n",
+       " (Link(height=179, left=13, right=25),\n",
+       "  Link(height=180, left=12, right=13),\n",
+       "  Link(height=181, left=13, right=25)),\n",
+       " (Link(height=265, left=3, right=20),\n",
+       "  Link(height=266, left=20, right=23),\n",
+       "  Link(height=267, left=3, right=20)),\n",
+       " (Link(height=291, left=5, right=23),\n",
+       "  Link(height=292, left=2, right=5),\n",
+       "  Link(height=293, left=5, right=23)),\n",
+       " (Link(height=292, left=18, right=25),\n",
+       "  Link(height=293, left=0, right=18),\n",
+       "  Link(height=294, left=18, right=25)),\n",
+       " (Link(height=302, left=11, right=19),\n",
+       "  Link(height=303, left=6, right=11),\n",
+       "  Link(height=304, left=11, right=19)),\n",
+       " (Link(height=309, left=15, right=20),\n",
+       "  Link(height=310, left=20, right=25),\n",
+       "  Link(height=311, left=15, right=20)),\n",
+       " (Link(height=325, left=13, right=18),\n",
+       "  Link(height=326, left=11, right=13),\n",
+       "  Link(height=327, left=13, right=18)),\n",
+       " (Link(height=362, left=11, right=22),\n",
+       "  Link(height=363, left=22, right=24),\n",
+       "  Link(height=364, left=11, right=22)),\n",
+       " (Link(height=372, left=22, right=23),\n",
+       "  Link(height=373, left=1, right=22),\n",
+       "  Link(height=374, left=22, right=23)),\n",
+       " (Link(height=386, left=4, right=17),\n",
+       "  Link(height=387, left=17, right=21),\n",
+       "  Link(height=388, left=4, right=17)),\n",
+       " (Link(height=393, left=4, right=16),\n",
+       "  Link(height=394, left=0, right=4),\n",
+       "  Link(height=395, left=4, right=16)),\n",
+       " (Link(height=531, left=0, right=4),\n",
+       "  Link(height=532, left=4, right=15),\n",
+       "  Link(height=533, left=0, right=4)),\n",
+       " (Link(height=575, left=5, right=21),\n",
+       "  Link(height=576, left=1, right=5),\n",
+       "  Link(height=577, left=5, right=21)),\n",
+       " (Link(height=639, left=7, right=11),\n",
+       "  Link(height=640, left=11, right=17),\n",
+       "  Link(height=641, left=7, right=11)),\n",
+       " (Link(height=687, left=2, right=4),\n",
+       "  Link(height=688, left=4, right=15),\n",
+       "  Link(height=689, left=2, right=4)),\n",
+       " (Link(height=706, left=8, right=11),\n",
+       "  Link(height=707, left=11, right=22),\n",
+       "  Link(height=708, left=8, right=11)),\n",
+       " (Link(height=722, left=22, right=23),\n",
+       "  Link(height=723, left=21, right=22),\n",
+       "  Link(height=724, left=22, right=23)),\n",
+       " (Link(height=768, left=9, right=11),\n",
+       "  Link(height=769, left=11, right=17),\n",
+       "  Link(height=770, left=9, right=11)),\n",
+       " (Link(height=792, left=5, right=12),\n",
+       "  Link(height=793, left=12, right=17),\n",
+       "  Link(height=794, left=5, right=12)),\n",
+       " (Link(height=805, left=20, right=22),\n",
+       "  Link(height=806, left=19, right=20),\n",
+       "  Link(height=807, left=20, right=22)),\n",
+       " (Link(height=806, left=19, right=20),\n",
+       "  Link(height=807, left=18, right=19),\n",
+       "  Link(height=808, left=19, right=20)),\n",
+       " (Link(height=806, left=19, right=20),\n",
+       "  Link(height=807, left=20, right=22),\n",
+       "  Link(height=808, left=19, right=20)),\n",
+       " (Link(height=882, left=7, right=14),\n",
+       "  Link(height=883, left=14, right=22),\n",
+       "  Link(height=884, left=7, right=14)),\n",
+       " (Link(height=884, left=6, right=11),\n",
+       "  Link(height=885, left=11, right=19),\n",
+       "  Link(height=886, left=6, right=11)),\n",
+       " (Link(height=892, left=12, right=17),\n",
+       "  Link(height=893, left=10, right=12),\n",
+       "  Link(height=894, left=12, right=17)),\n",
+       " (Link(height=916, left=18, right=24),\n",
+       "  Link(height=917, left=16, right=18),\n",
+       "  Link(height=918, left=18, right=24)),\n",
+       " (Link(height=919, left=14, right=17),\n",
+       "  Link(height=920, left=6, right=14),\n",
+       "  Link(height=921, left=14, right=17)),\n",
+       " (Link(height=994, left=0, right=3),\n",
+       "  Link(height=995, left=3, right=24),\n",
+       "  Link(height=996, left=0, right=3)),\n",
+       " (Link(height=1012, left=9, right=12),\n",
+       "  Link(height=1013, left=12, right=24),\n",
+       "  Link(height=1014, left=9, right=12)),\n",
+       " (Link(height=1034, left=1, right=6),\n",
+       "  Link(height=1035, left=6, right=12),\n",
+       "  Link(height=1036, left=1, right=6)),\n",
+       " (Link(height=1035, left=7, right=21),\n",
+       "  Link(height=1036, left=4, right=7),\n",
+       "  Link(height=1037, left=7, right=21)),\n",
+       " (Link(height=1047, left=3, right=10),\n",
+       "  Link(height=1048, left=10, right=11),\n",
+       "  Link(height=1049, left=3, right=10)),\n",
+       " (Link(height=1088, left=7, right=8),\n",
+       "  Link(height=1089, left=8, right=14),\n",
+       "  Link(height=1090, left=7, right=8)),\n",
+       " (Link(height=1104, left=3, right=10),\n",
+       "  Link(height=1105, left=10, right=11),\n",
+       "  Link(height=1106, left=3, right=10)),\n",
+       " (Link(height=1135, left=5, right=8),\n",
+       "  Link(height=1136, left=8, right=19),\n",
+       "  Link(height=1137, left=5, right=8)),\n",
+       " (Link(height=1138, left=1, right=3),\n",
+       "  Link(height=1139, left=3, right=23),\n",
+       "  Link(height=1140, left=1, right=3)),\n",
+       " (Link(height=1146, left=5, right=7),\n",
+       "  Link(height=1147, left=7, right=24),\n",
+       "  Link(height=1148, left=5, right=7)),\n",
+       " (Link(height=1197, left=5, right=14),\n",
+       "  Link(height=1198, left=14, right=15),\n",
+       "  Link(height=1199, left=5, right=14)),\n",
+       " (Link(height=1205, left=7, right=23),\n",
+       "  Link(height=1206, left=3, right=7),\n",
+       "  Link(height=1207, left=7, right=23)),\n",
+       " (Link(height=1276, left=18, right=25),\n",
+       "  Link(height=1277, left=17, right=18),\n",
+       "  Link(height=1278, left=18, right=25)),\n",
+       " (Link(height=1319, left=14, right=20),\n",
+       "  Link(height=1320, left=20, right=24),\n",
+       "  Link(height=1321, left=14, right=20)),\n",
+       " (Link(height=1328, left=8, right=21),\n",
+       "  Link(height=1329, left=1, right=8),\n",
+       "  Link(height=1330, left=8, right=21)),\n",
+       " (Link(height=1329, left=2, right=14),\n",
+       "  Link(height=1330, left=14, right=25),\n",
+       "  Link(height=1331, left=2, right=14)),\n",
+       " (Link(height=1385, left=10, right=14),\n",
+       "  Link(height=1386, left=14, right=15),\n",
+       "  Link(height=1387, left=10, right=14)),\n",
+       " (Link(height=1419, left=2, right=8),\n",
+       "  Link(height=1420, left=8, right=15),\n",
+       "  Link(height=1421, left=2, right=8)),\n",
+       " (Link(height=1465, left=13, right=21),\n",
+       "  Link(height=1466, left=21, right=24),\n",
+       "  Link(height=1467, left=13, right=21)),\n",
+       " (Link(height=1514, left=11, right=15),\n",
+       "  Link(height=1515, left=15, right=21),\n",
+       "  Link(height=1516, left=11, right=15)),\n",
+       " (Link(height=1545, left=3, right=11),\n",
+       "  Link(height=1546, left=11, right=25),\n",
+       "  Link(height=1547, left=3, right=11)),\n",
+       " (Link(height=1561, left=7, right=18),\n",
+       "  Link(height=1562, left=0, right=7),\n",
+       "  Link(height=1563, left=7, right=18)),\n",
+       " (Link(height=1671, left=9, right=15),\n",
+       "  Link(height=1672, left=15, right=23),\n",
+       "  Link(height=1673, left=9, right=15)),\n",
+       " (Link(height=1701, left=13, right=21),\n",
+       "  Link(height=1702, left=4, right=13),\n",
+       "  Link(height=1703, left=13, right=21)),\n",
+       " (Link(height=1706, left=5, right=13),\n",
+       "  Link(height=1707, left=13, right=23),\n",
+       "  Link(height=1708, left=5, right=13)),\n",
+       " (Link(height=1730, left=7, right=16),\n",
+       "  Link(height=1731, left=1, right=7),\n",
+       "  Link(height=1732, left=7, right=16)),\n",
+       " (Link(height=1781, left=0, right=8),\n",
+       "  Link(height=1782, left=8, right=17),\n",
+       "  Link(height=1783, left=0, right=8)),\n",
+       " (Link(height=1784, left=8, right=18),\n",
+       "  Link(height=1785, left=1, right=8),\n",
+       "  Link(height=1786, left=8, right=18)),\n",
+       " (Link(height=1804, left=19, right=24),\n",
+       "  Link(height=1805, left=7, right=19),\n",
+       "  Link(height=1806, left=19, right=24)),\n",
+       " (Link(height=1827, left=3, right=23),\n",
+       "  Link(height=1828, left=23, right=25),\n",
+       "  Link(height=1829, left=3, right=23)),\n",
+       " (Link(height=1837, left=1, right=16),\n",
+       "  Link(height=1838, left=16, right=17),\n",
+       "  Link(height=1839, left=1, right=16)),\n",
+       " (Link(height=1849, left=18, right=25),\n",
+       "  Link(height=1850, left=4, right=18),\n",
+       "  Link(height=1851, left=18, right=25)),\n",
+       " (Link(height=1856, left=6, right=13),\n",
+       "  Link(height=1857, left=13, right=17),\n",
+       "  Link(height=1858, left=6, right=13)),\n",
+       " (Link(height=1875, left=2, right=11),\n",
+       "  Link(height=1876, left=11, right=15),\n",
+       "  Link(height=1877, left=2, right=11)),\n",
+       " (Link(height=1970, left=6, right=24),\n",
+       "  Link(height=1971, left=1, right=6),\n",
+       "  Link(height=1972, left=6, right=24)),\n",
+       " (Link(height=2075, left=20, right=25),\n",
+       "  Link(height=2076, left=5, right=20),\n",
+       "  Link(height=2077, left=20, right=25)),\n",
+       " (Link(height=2081, left=4, right=19),\n",
+       "  Link(height=2082, left=1, right=4),\n",
+       "  Link(height=2083, left=4, right=19)),\n",
+       " (Link(height=2111, left=3, right=25),\n",
+       "  Link(height=2112, left=1, right=3),\n",
+       "  Link(height=2113, left=3, right=25)),\n",
+       " (Link(height=2225, left=3, right=12),\n",
+       "  Link(height=2226, left=12, right=24),\n",
+       "  Link(height=2227, left=3, right=12)),\n",
+       " (Link(height=2242, left=3, right=18),\n",
+       "  Link(height=2243, left=18, right=23),\n",
+       "  Link(height=2244, left=3, right=18))]"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "triple(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=316, left=8, right=17),\n",
+       "  Link(height=317, left=8, right=21),\n",
+       "  Link(height=318, left=8, right=17),\n",
+       "  Link(height=319, left=8, right=21)),\n",
+       " (Link(height=867, left=4, right=11),\n",
+       "  Link(height=868, left=5, right=11),\n",
+       "  Link(height=869, left=4, right=11),\n",
+       "  Link(height=870, left=5, right=11))]"
+      ]
+     },
+     "execution_count": 59,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "triple_pair(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=316, left=8, right=17),\n",
+       "  Link(height=317, left=8, right=21),\n",
+       "  Link(height=318, left=8, right=17),\n",
+       "  Link(height=319, left=8, right=21)),\n",
+       " (Link(height=867, left=4, right=11),\n",
+       "  Link(height=868, left=5, right=11),\n",
+       "  Link(height=869, left=4, right=11),\n",
+       "  Link(height=870, left=5, right=11))]"
+      ]
+     },
+     "execution_count": 60,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(elnet), lambda l: l.height)}\n",
+    "triple_pair_hg(height_groups)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=1368, left=13, right=19),\n",
+       " Link(height=1368, left=14, right=16),\n",
+       " Link(height=1369, left=3, right=6)]"
+      ]
+     },
+     "execution_count": 61,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[l for l in elnet if l.height >= 1367 if l.height <= 1370 if link_ends(l) & set((6, 16, 19))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 21.3 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "triple_pair(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 105 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(elnet), lambda l: l.height)}\n",
+    "triple_pair_hg(height_groups)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(elnet), lambda l: l.height)}\n",
+    "assert triple_pair_hg(height_groups) == triple_pair(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=242, left=8, right=9),\n",
+       " Link(height=242, left=15, right=21),\n",
+       " Link(height=243, left=1, right=9),\n",
+       " Link(height=243, left=8, right=14),\n",
+       " Link(height=243, left=11, right=15),\n",
+       " Link(height=244, left=1, right=18),\n",
+       " Link(height=244, left=6, right=8),\n",
+       " Link(height=244, left=9, right=20),\n",
+       " Link(height=244, left=15, right=25),\n",
+       " Link(height=245, left=0, right=15),\n",
+       " Link(height=245, left=1, right=16),\n",
+       " Link(height=245, left=9, right=12),\n",
+       " Link(height=245, left=18, right=21)]"
+      ]
+     },
+     "execution_count": 65,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[l for l in elnet if l.height >= 242 if l.height <= 245 ] #if l.left in [13, 17, 20] or l.right in [13, 17, 20]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_triple_pairs_slow(net):\n",
+    "    print(len(net))\n",
+    "    new_net = eliminate_a_triple_pair_slow(net)\n",
+    "    while new_net:\n",
+    "        print(len(net))\n",
+    "        net = new_net\n",
+    "        new_net = eliminate_a_triple_pair_slow(net)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 118,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_triple_pairs(net):\n",
+    "    print(len(net))\n",
+    "    new_net = eliminate_a_triple_pair(net)\n",
+    "    while new_net:\n",
+    "        print(len(net))\n",
+    "        net = new_net\n",
+    "        new_net = eliminate_a_triple_pair(net)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 134,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "9811\n",
+      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
+      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=316, left=8, right=21) Link(height=317, left=8, right=17)\n",
+      "9811\n",
+      "eatp [(Link(height=866, left=4, right=11), Link(height=867, left=5, right=11), Link(height=868, left=4, right=11), Link(height=869, left=5, right=11))]\n",
+      "removing Link(height=866, left=4, right=11) Link(height=867, left=5, right=11) Link(height=868, left=4, right=11) Link(height=869, left=5, right=11) ; adding Link(height=866, left=5, right=11) Link(height=867, left=4, right=11)\n",
+      "9809\n",
+      "eatp []\n"
+     ]
+    }
+   ],
+   "source": [
+    "etlnet = eliminate_triple_pairs(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
+      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=317, left=8, right=17) Link(height=318, left=8, right=21)\n"
+     ]
+    }
+   ],
+   "source": [
+    "etlnet = eliminate_a_triple_pair(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 135,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 136,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=315, left=17, right=20),\n",
+       " Link(height=316, left=8, right=17),\n",
+       " Link(height=317, left=8, right=21),\n",
+       " Link(height=318, left=8, right=17),\n",
+       " Link(height=319, left=8, right=21),\n",
+       " Link(height=319, left=14, right=17),\n",
+       " Link(height=320, left=2, right=8),\n",
+       " Link(height=320, left=17, right=21)]"
+      ]
+     },
+     "execution_count": 136,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[l for l in elnet if l.height >= 315 if l.height <= 320 if link_ends(l) & set((8, 17, 21))] "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 137,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=17, right=20),\n",
+       " Link(height=1, left=8, right=17),\n",
+       " Link(height=2, left=8, right=21),\n",
+       " Link(height=3, left=8, right=17),\n",
+       " Link(height=4, left=8, right=21),\n",
+       " Link(height=4, left=14, right=17),\n",
+       " Link(height=5, left=2, right=8),\n",
+       " Link(height=5, left=17, right=21)]"
+      ]
+     },
+     "execution_count": 137,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "nf = [l for l in elnet if l.height >= 315 if l.height <= 320 if link_ends(l) & set((8, 17, 21))]\n",
+    "pnf = pack(nf)\n",
+    "pnf"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 138,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "d: Link(height=3, left=8, right=17)\n",
+      "cs: [Link(height=2, left=8, right=21)]\n",
+      "c: ; lines: {8, 17, 21}\n",
+      "b: Link(height=1, left=8, right=17) ; bs: [Link(height=1, left=8, right=17)]\n",
+      "ah: 0 ; als: []\n",
+      "a: Link(height=0, left=8, right=21)\n",
+      "d: Link(height=4, left=8, right=21)\n",
+      "cs: [Link(height=3, left=8, right=17)]\n",
+      "c: ; lines: {8, 17, 21}\n",
+      "b: Link(height=2, left=8, right=21) ; bs: [Link(height=2, left=8, right=21)]\n",
+      "ah: 1 ; als: [Link(height=1, left=8, right=17)]\n",
+      "a: Link(height=1, left=8, right=17)\n",
+      "adding: Link(height=1, left=8, right=17) Link(height=2, left=8, right=21) Link(height=3, left=8, right=17) Link(height=4, left=8, right=21)\n",
+      "d: Link(height=4, left=14, right=17)\n",
+      "cs: [Link(height=3, left=8, right=17)]\n",
+      "c: ; lines: {8, 17, 14}\n",
+      "b: Link(height=2, left=14, right=17) ; bs: [Link(height=2, left=8, right=21)]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=1, left=8, right=17),\n",
+       "  Link(height=2, left=8, right=21),\n",
+       "  Link(height=3, left=8, right=17),\n",
+       "  Link(height=4, left=8, right=21))]"
+      ]
+     },
+     "execution_count": 138,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(pnf), lambda l: l.height)}\n",
+    "triple_pair_hg(height_groups, debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 139,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "9811\n",
+      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
+      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=316, left=8, right=21) Link(height=317, left=8, right=17)\n",
+      "9811\n",
+      "eatp [(Link(height=866, left=4, right=11), Link(height=867, left=5, right=11), Link(height=868, left=4, right=11), Link(height=869, left=5, right=11))]\n",
+      "removing Link(height=866, left=4, right=11) Link(height=867, left=5, right=11) Link(height=868, left=4, right=11) Link(height=869, left=5, right=11) ; adding Link(height=866, left=5, right=11) Link(height=867, left=4, right=11)\n",
+      "9809\n",
+      "eatp []\n"
+     ]
+    }
+   ],
+   "source": [
+    "setlnet = eliminate_triple_pairs_slow(elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 140,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9807"
+      ]
+     },
+     "execution_count": 140,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(setlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 141,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, etlnet) == follow_many(string.ascii_lowercase, elnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 142,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zdunvslcfiqywjmkobhxtraegp'"
+      ]
+     },
+     "execution_count": 142,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, etlnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 143,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zdunvslcfiqywjmkobhxtraegp'"
+      ]
+     },
+     "execution_count": 143,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, setlnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 144,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zdunvslcfiqywjmkobhxtraegp'"
+      ]
+     },
+     "execution_count": 144,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, elnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 145,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zdunvslcfiqywjmkobhxtraegp'"
+      ]
+     },
+     "execution_count": 145,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 146,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 146,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eliminable_pairs(etlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 147,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(10207, 9807)"
+      ]
+     },
+     "execution_count": 147,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(lnet), len(etlnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 148,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def simplify(net0):\n",
+    "    netp = eliminate_pairs(net0)\n",
+    "    new_net = eliminate_a_triple_pair(netp)\n",
+    "    while new_net:\n",
+    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
+    "        netp = eliminate_pairs(new_net)\n",
+    "        new_net = eliminate_a_triple_pair(netp)\n",
+    "    return netp"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 149,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "eatp [(Link(height=316, left=8, right=17), Link(height=317, left=8, right=21), Link(height=318, left=8, right=17), Link(height=319, left=8, right=21)), (Link(height=867, left=4, right=11), Link(height=868, left=5, right=11), Link(height=869, left=4, right=11), Link(height=870, left=5, right=11))]\n",
+      "removing Link(height=316, left=8, right=17) Link(height=317, left=8, right=21) Link(height=318, left=8, right=17) Link(height=319, left=8, right=21) ; adding Link(height=316, left=8, right=21) Link(height=317, left=8, right=17)\n",
+      "eatp [(Link(height=866, left=4, right=11), Link(height=867, left=5, right=11), Link(height=868, left=4, right=11), Link(height=869, left=5, right=11))]\n",
+      "removing Link(height=866, left=4, right=11) Link(height=867, left=5, right=11) Link(height=868, left=4, right=11) Link(height=869, left=5, right=11) ; adding Link(height=866, left=5, right=11) Link(height=867, left=4, right=11)\n",
+      "eatp []\n"
+     ]
+    }
+   ],
+   "source": [
+    "simple_lnet = simplify(plnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 150,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 150,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, simple_lnet)) == ''.join(follow_many(string.ascii_lowercase, lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 151,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zdunvslcfiqywjmkobhxtraegp'"
+      ]
+     },
+     "execution_count": 151,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, simple_lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 152,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zdunvslcfiqywjmkobhxtraegp'"
+      ]
+     },
+     "execution_count": 152,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, lnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 153,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9807"
+      ]
+     },
+     "execution_count": 153,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(simple_lnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def add_triple_pair(net, max_lines=None):\n",
+    "    if not max_lines:\n",
+    "        max_lines = max(l.right for l in net)\n",
+    "    a, b, c = 0, 0, 0\n",
+    "    while len(set((a, b, c))) != 3:\n",
+    "        a = random.randrange(max_lines)\n",
+    "        b = random.randrange(max_lines)\n",
+    "        c = random.randrange(max_lines)\n",
+    "    tp = [(min(a, b), max(a, b)), (min(b, c), max(b, c))] * 2\n",
+    "    \n",
+    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
+    "    i = random.randrange(len(pairs))\n",
+    "    print(i, tp)\n",
+    "    new_pairs = pairs[:i] + tp + pairs[i:]\n",
+    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def add_pair(net, max_lines=None):\n",
+    "    if not max_lines:\n",
+    "        max_lines = max(l.right for l in net)\n",
+    "\n",
+    "    a, b = 0, 0\n",
+    "    while a == b:\n",
+    "        a = random.randrange(max_lines)\n",
+    "        b = random.randrange(max_lines)\n",
+    "    p = [(min(a, b), max(a, b))] * 2\n",
+    "    \n",
+    "    pairs = [(l.left, l.right) for l in sorted(net)]\n",
+    "    i = random.randrange(len(pairs))\n",
+    "    \n",
+    "    print(i, p)\n",
+    "    new_pairs = pairs[:i] + p + pairs[i:]\n",
+    "    return pack([Link(h, l, r) for h, (l, r) in enumerate(new_pairs)])   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true,
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "lnettp = simple_lnet\n",
+    "for _ in range(10):\n",
+    "    lnettp = add_pair(lnettp)\n",
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true,
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "lnettp = simple_lnet\n",
+    "for _ in range(10):\n",
+    "    lnettp = add_triple_pair(lnettp)\n",
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true,
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "lnettp = simple_lnet\n",
+    "for _ in range(10):\n",
+    "    lnettp = add_pair(lnettp)\n",
+    "for _ in range(10):\n",
+    "    lnettp = add_triple_pair(lnettp)\n",
+    "height_groups = {h: list(g) for h, g in itertools.groupby(pack(lnettp), lambda l: l.height)}\n",
+    "tps = triple_pair_hg(height_groups)\n",
+    "tps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "lnettp == pack(lnettp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "lnettps = simplify(lnettp)\n",
+    "len(lnettps)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "len(simple_lnet), len(lnettp), len(lnettps)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/04-amidakuji/amidakuji-solution-1.ipynb b/04-amidakuji/amidakuji-solution-1.ipynb
new file mode 100644 (file)
index 0000000..df69a1f
--- /dev/null
+++ b/04-amidakuji/amidakuji-solution-1.ipynb
@@ -0,0 +1,613 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import collections\n",
+    "import string\n",
+    "import itertools\n",
+    "import re"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Link = collections.namedtuple('Link', 'height left right')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extract_pairs(net_string):\n",
+    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def read_net_string(net_string):\n",
+    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def read_net(filename, rev=False):\n",
+    "    with open(filename) as f:\n",
+    "        pairs = [re.split('\\D+', p.strip()) for p in f.readlines()]\n",
+    "        if rev:\n",
+    "            lrs = [(int(lr[1]), int(lr[2])) for lr in reversed(pairs)]\n",
+    "        else:\n",
+    "            lrs = [(int(lr[1]), int(lr[2])) for lr in pairs]\n",
+    "        return [Link(h, l, r) \n",
+    "                for h, (l, r) in enumerate(lrs)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=1, right=4),\n",
+       " Link(height=2, left=0, right=3),\n",
+       " Link(height=3, left=0, right=3),\n",
+       " Link(height=4, left=0, right=5),\n",
+       " Link(height=5, left=3, right=5),\n",
+       " Link(height=6, left=0, right=2),\n",
+       " Link(height=7, left=3, right=4),\n",
+       " Link(height=8, left=2, right=4),\n",
+       " Link(height=9, left=1, right=2),\n",
+       " Link(height=10, left=0, right=4),\n",
+       " Link(height=11, left=1, right=2),\n",
+       " Link(height=12, left=2, right=4),\n",
+       " Link(height=13, left=0, right=4),\n",
+       " Link(height=14, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "small_net = read_net('04-small.txt')\n",
+    "small_net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10135"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "net = read_net('04-lines.txt')\n",
+    "len(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "23"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "permnet = read_net('permutations.txt')\n",
+    "len(permnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "23"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rpermnet = read_net('permutations.txt', rev=True)\n",
+    "len(rpermnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def show_net(links, pair_sep=', '):\n",
+    "    return pair_sep.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def link_ends(link):\n",
+    "    return set((link.left, link.right))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow(initial_line, links):\n",
+    "    line = initial_line\n",
+    "    heights = sorted(set(l.height for l in links))\n",
+    "    for h in heights:\n",
+    "        for l in [l for l in links if l.height == h]:\n",
+    "            if line in link_ends(l):\n",
+    "                line = [e for e in link_ends(l) if e != line][0]\n",
+    "#                 print(l, line)\n",
+    "    return line"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def pack(net):\n",
+    "    packed_links = []\n",
+    "    line_heights = collections.defaultdict(lambda: -1)\n",
+    "    for link in sorted(net):\n",
+    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
+    "        line_heights[link.left] = link_height\n",
+    "        line_heights[link.right] = link_height\n",
+    "        packed_links += [Link(link_height, link.left, link.right)]\n",
+    "    return sorted(packed_links)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in small_net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in pack(small_net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10134"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "pnet = pack(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2286"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def height_groups(net):\n",
+    "    return {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow_many(in_sequence, net):\n",
+    "    hgs = height_groups(net)\n",
+    "    seq = list(in_sequence)\n",
+    "    for h in hgs:\n",
+    "        for link in hgs[h]:\n",
+    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
+    "    return seq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'acfbed'"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many('abcdef', small_net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      " 0        ['0', '1', '2', '3', '4', '5']\n",
+      " 1 (2, 5) ['0', '1', '5', '3', '4', '2']\n",
+      " 2 (1, 4) ['0', '4', '5', '3', '1', '2']\n",
+      " 3 (0, 3) ['3', '4', '5', '0', '1', '2']\n",
+      " 4 (0, 3) ['0', '4', '5', '3', '1', '2']\n",
+      " 5 (0, 5) ['2', '4', '5', '3', '1', '0']\n",
+      " 6 (3, 5) ['2', '4', '5', '0', '1', '3']\n",
+      " 7 (0, 2) ['5', '4', '2', '0', '1', '3']\n",
+      " 8 (3, 4) ['5', '4', '2', '1', '0', '3']\n",
+      " 9 (2, 4) ['5', '4', '0', '1', '2', '3']\n",
+      "10 (1, 2) ['5', '0', '4', '1', '2', '3']\n",
+      "11 (0, 4) ['2', '0', '4', '1', '5', '3']\n",
+      "12 (1, 2) ['2', '4', '0', '1', '5', '3']\n",
+      "13 (2, 4) ['2', '4', '5', '1', '0', '3']\n",
+      "14 (0, 4) ['0', '4', '5', '1', '2', '3']\n",
+      "15 (1, 4) ['0', '2', '5', '1', '4', '3']\n"
+     ]
+    }
+   ],
+   "source": [
+    "for i in range(len(small_net)+1):\n",
+    "    pre_net = small_net[:i]\n",
+    "    if i == 0:\n",
+    "        print('{:2}'.format(i), \n",
+    "          \"      \".format(small_net[i-1].left, small_net[i-1].right),\n",
+    "          follow_many(\"012345\", pre_net))\n",
+    "    else:\n",
+    "        print('{:2}'.format(i), \n",
+    "          \"({}, {})\".format(small_net[i-1].left, small_net[i-1].right),\n",
+    "          follow_many(\"012345\", pre_net))\n",
+    "\n",
+    "        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=1, right=4),\n",
+       " Link(height=2, left=0, right=3),\n",
+       " Link(height=3, left=0, right=3),\n",
+       " Link(height=4, left=0, right=5),\n",
+       " Link(height=5, left=3, right=5),\n",
+       " Link(height=6, left=0, right=2),\n",
+       " Link(height=7, left=3, right=4),\n",
+       " Link(height=8, left=2, right=4),\n",
+       " Link(height=9, left=1, right=2),\n",
+       " Link(height=10, left=0, right=4),\n",
+       " Link(height=11, left=1, right=2),\n",
+       " Link(height=12, left=2, right=4),\n",
+       " Link(height=13, left=0, right=4),\n",
+       " Link(height=14, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 66,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "small_net[:15]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10000 loops, best of 3: 42 µs per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many('abcdefghij', small_net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zfrasxwigvjoembqcyhplnktud'"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, permnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, rpermnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "follow_many(string.ascii_lowercase, net) == follow_many(string.ascii_lowercase, rpermnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 19.3 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many(string.ascii_lowercase, net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "100 loops, best of 3: 18.7 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many(string.ascii_lowercase, pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/04-amidakuji/amidakuji-solution-2.ipynb b/04-amidakuji/amidakuji-solution-2.ipynb
new file mode 100644 (file)
index 0000000..3745c3c
--- /dev/null
+++ b/04-amidakuji/amidakuji-solution-2.ipynb
@@ -0,0 +1,1553 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import collections\n",
+    "import string\n",
+    "import itertools\n",
+    "import re"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Link = collections.namedtuple('Link', 'height left right')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extract_pairs(net_string):\n",
+    "    return [[int(pi) for pi in p.split(', ')] for p in net_string[1:-1].split('), (')]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def read_net_string(net_string):\n",
+    "    return [Link(h, l, r) for h, (l, r) in enumerate(extract_pairs(net_string))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# def read_net(filename):\n",
+    "#     with open(filename) as f:\n",
+    "#         pairs = [re.split('\\D+', p.strip()) for p in f.readlines()]\n",
+    "#         lrs = [(int(lr[1]), int(lr[2])) for lr in pairs]\n",
+    "#         return [Link(h, l, r) \n",
+    "#                 for h, (l, r) in enumerate(lrs)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def read_net(filename, rev=False):\n",
+    "    with open(filename) as f:\n",
+    "        pairs = [re.split('\\D+', p.strip()) for p in f.readlines()]\n",
+    "        if rev:\n",
+    "            lrs = [(int(lr[1]), int(lr[2])) for lr in reversed(pairs)]\n",
+    "        else:\n",
+    "            lrs = [(int(lr[1]), int(lr[2])) for lr in pairs]\n",
+    "        return [Link(h, l, r) \n",
+    "                for h, (l, r) in enumerate(lrs)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Link(height=0, left=2, right=5),\n",
+       " Link(height=1, left=1, right=4),\n",
+       " Link(height=2, left=0, right=3),\n",
+       " Link(height=3, left=0, right=3),\n",
+       " Link(height=4, left=0, right=5),\n",
+       " Link(height=5, left=3, right=5),\n",
+       " Link(height=6, left=0, right=2),\n",
+       " Link(height=7, left=3, right=4),\n",
+       " Link(height=8, left=2, right=4),\n",
+       " Link(height=9, left=1, right=2),\n",
+       " Link(height=10, left=0, right=4),\n",
+       " Link(height=11, left=1, right=2),\n",
+       " Link(height=12, left=2, right=4),\n",
+       " Link(height=13, left=0, right=4),\n",
+       " Link(height=14, left=1, right=4)]"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "small_net = read_net('04-small.txt')\n",
+    "small_net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10135"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "net = read_net('04-lines.txt')\n",
+    "len(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "23"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "permnet = read_net('permutations.txt')\n",
+    "len(permnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "23"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rpermnet = read_net('permutations.txt', rev=True)\n",
+    "len(rpermnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def show_net(links, pair_sep=', '):\n",
+    "    return pair_sep.join('({}, {})'.format(l.left, l.right) for l in sorted(links))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def link_ends(link):\n",
+    "    return set((link.left, link.right))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow(initial_line, links):\n",
+    "    line = initial_line\n",
+    "    heights = sorted(set(l.height for l in links))\n",
+    "    for h in heights:\n",
+    "        for l in [l for l in links if l.height == h]:\n",
+    "            if line in link_ends(l):\n",
+    "                line = [e for e in link_ends(l) if e != line][0]\n",
+    "#                 print(l, line)\n",
+    "    return line"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def pack(net):\n",
+    "    packed_links = []\n",
+    "    line_heights = collections.defaultdict(lambda: -1)\n",
+    "    for link in sorted(net):\n",
+    "        link_height = max(line_heights[link.left], line_heights[link.right]) + 1\n",
+    "        line_heights[link.left] = link_height\n",
+    "        line_heights[link.right] = link_height\n",
+    "        packed_links += [Link(link_height, link.left, link.right)]\n",
+    "    return sorted(packed_links)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in small_net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in pack(small_net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10134"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2286"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(l.height for l in pack(net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def height_groups(net):\n",
+    "    return {h: list(g) for h, g in itertools.groupby(pack(net), lambda l: l.height)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def follow_many(in_sequence, net):\n",
+    "    hgs = height_groups(net)\n",
+    "    seq = list(in_sequence)\n",
+    "    for h in hgs:\n",
+    "        for link in hgs[h]:\n",
+    "            seq[link.right], seq[link.left] = seq[link.left], seq[link.right]\n",
+    "    return seq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'acfbedghij'"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many('abcdefghij', small_net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10000 loops, best of 3: 40.1 µs per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many('abcdefghij', small_net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'zfrasxwigvjoembqcyhplnktud'"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, permnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, rpermnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "100 loops, best of 3: 19 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "follow_many(string.ascii_lowercase, net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "pnet = pack(net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pairs(net):\n",
+    "    hgs = height_groups(net)\n",
+    "    eps = []\n",
+    "    for h in range(1, max(hgs.keys())):\n",
+    "        for l in hgs[h]:\n",
+    "            o = Link(l.height - 1, l.left, l.right)\n",
+    "            if o in hgs[h-1]:\n",
+    "                eps += [(l, o)]\n",
+    "    return eps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=115, left=2, right=23), Link(height=114, left=2, right=23)),\n",
+       " (Link(height=149, left=15, right=23), Link(height=148, left=15, right=23)),\n",
+       " (Link(height=201, left=0, right=7), Link(height=200, left=0, right=7)),\n",
+       " (Link(height=207, left=22, right=23), Link(height=206, left=22, right=23)),\n",
+       " (Link(height=210, left=17, right=23), Link(height=209, left=17, right=23)),\n",
+       " (Link(height=247, left=16, right=20), Link(height=246, left=16, right=20)),\n",
+       " (Link(height=418, left=19, right=24), Link(height=417, left=19, right=24)),\n",
+       " (Link(height=424, left=9, right=21), Link(height=423, left=9, right=21)),\n",
+       " (Link(height=453, left=3, right=16), Link(height=452, left=3, right=16)),\n",
+       " (Link(height=456, left=2, right=22), Link(height=455, left=2, right=22)),\n",
+       " (Link(height=465, left=18, right=20), Link(height=464, left=18, right=20)),\n",
+       " (Link(height=491, left=14, right=18), Link(height=490, left=14, right=18)),\n",
+       " (Link(height=552, left=16, right=17), Link(height=551, left=16, right=17)),\n",
+       " (Link(height=772, left=0, right=7), Link(height=771, left=0, right=7)),\n",
+       " (Link(height=848, left=1, right=2), Link(height=847, left=1, right=2)),\n",
+       " (Link(height=895, left=6, right=21), Link(height=894, left=6, right=21)),\n",
+       " (Link(height=930, left=11, right=13), Link(height=929, left=11, right=13)),\n",
+       " (Link(height=987, left=8, right=17), Link(height=986, left=8, right=17)),\n",
+       " (Link(height=988, left=8, right=17), Link(height=987, left=8, right=17)),\n",
+       " (Link(height=1030, left=9, right=24), Link(height=1029, left=9, right=24)),\n",
+       " (Link(height=1134, left=4, right=23), Link(height=1133, left=4, right=23)),\n",
+       " (Link(height=1163, left=14, right=15), Link(height=1162, left=14, right=15)),\n",
+       " (Link(height=1164, left=14, right=15), Link(height=1163, left=14, right=15)),\n",
+       " (Link(height=1170, left=2, right=21), Link(height=1169, left=2, right=21)),\n",
+       " (Link(height=1232, left=6, right=22), Link(height=1231, left=6, right=22)),\n",
+       " (Link(height=1254, left=13, right=15), Link(height=1253, left=13, right=15)),\n",
+       " (Link(height=1255, left=1, right=24), Link(height=1254, left=1, right=24)),\n",
+       " (Link(height=1324, left=3, right=22), Link(height=1323, left=3, right=22)),\n",
+       " (Link(height=1370, left=15, right=19), Link(height=1369, left=15, right=19)),\n",
+       " (Link(height=1441, left=0, right=14), Link(height=1440, left=0, right=14)),\n",
+       " (Link(height=1441, left=11, right=24), Link(height=1440, left=11, right=24)),\n",
+       " (Link(height=1547, left=11, right=13), Link(height=1546, left=11, right=13)),\n",
+       " (Link(height=1578, left=14, right=23), Link(height=1577, left=14, right=23)),\n",
+       " (Link(height=1616, left=7, right=14), Link(height=1615, left=7, right=14)),\n",
+       " (Link(height=1671, left=8, right=20), Link(height=1670, left=8, right=20)),\n",
+       " (Link(height=1684, left=14, right=18), Link(height=1683, left=14, right=18)),\n",
+       " (Link(height=1717, left=0, right=17), Link(height=1716, left=0, right=17)),\n",
+       " (Link(height=1727, left=7, right=8), Link(height=1726, left=7, right=8)),\n",
+       " (Link(height=1866, left=8, right=16), Link(height=1865, left=8, right=16)),\n",
+       " (Link(height=1911, left=1, right=12), Link(height=1910, left=1, right=12)),\n",
+       " (Link(height=1966, left=20, right=23), Link(height=1965, left=20, right=23)),\n",
+       " (Link(height=1974, left=5, right=23), Link(height=1973, left=5, right=23)),\n",
+       " (Link(height=1994, left=18, right=19), Link(height=1993, left=18, right=19)),\n",
+       " (Link(height=2005, left=2, right=19), Link(height=2004, left=2, right=19)),\n",
+       " (Link(height=2031, left=12, right=17), Link(height=2030, left=12, right=17)),\n",
+       " (Link(height=2108, left=7, right=12), Link(height=2107, left=7, right=12)),\n",
+       " (Link(height=2137, left=7, right=16), Link(height=2136, left=7, right=16)),\n",
+       " (Link(height=2138, left=7, right=16), Link(height=2137, left=7, right=16)),\n",
+       " (Link(height=2229, left=10, right=11), Link(height=2228, left=10, right=11)),\n",
+       " (Link(height=2239, left=16, right=24), Link(height=2238, left=16, right=24)),\n",
+       " (Link(height=2240, left=16, right=24), Link(height=2239, left=16, right=24)),\n",
+       " (Link(height=2246, left=4, right=13), Link(height=2245, left=4, right=13)),\n",
+       " (Link(height=2247, left=4, right=13), Link(height=2246, left=4, right=13)),\n",
+       " (Link(height=2276, left=19, right=24), Link(height=2275, left=19, right=24)),\n",
+       " (Link(height=2277, left=4, right=18), Link(height=2276, left=4, right=18))]"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eliminable_pairs(pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 23.5 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "eliminable_pairs(pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminable_pair(hgs):\n",
+    "    for h in range(1, max(hgs.keys())):\n",
+    "        for l in hgs[h]:\n",
+    "            o = Link(l.height - 1, l.left, l.right)\n",
+    "            if o in hgs[h-1]:\n",
+    "                return l, o\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_pairs(net):\n",
+    "    hgs = height_groups(pack(net))\n",
+    "    eliminable_links = eliminable_pair(hgs)\n",
+    "    while eliminable_links:\n",
+    "        net = pack(l for l in net if l not in eliminable_links)\n",
+    "        hgs = height_groups(pack(net))\n",
+    "        eliminable_links = eliminable_pair(hgs)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "enet = eliminate_pairs(pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase,  net) == follow_many(string.ascii_lowercase, enet)\n",
+    "assert follow_many(string.ascii_lowercase, pnet) == follow_many(string.ascii_lowercase, enet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 2.35 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "eliminate_pairs(pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def triple_pair(height_groups, debug=False):\n",
+    "    ts = []\n",
+    "    for h in range(3, max(height_groups.keys())):\n",
+    "        for d in height_groups[h]:\n",
+    "            if debug: print('d:', d)\n",
+    "            ch = h - 1\n",
+    "            cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
+    "            if debug: print('cs:', cs)\n",
+    "            while ch > 2 and not cs:\n",
+    "                ch -= 1\n",
+    "                cs = [l for l in height_groups[ch] if link_ends(l) & link_ends(d)]\n",
+    "                if debug: print('cs:', cs)\n",
+    "            if len(cs) == 1:\n",
+    "                c = cs[0]\n",
+    "                lines = set((d.left, d.right, c.left, c.right))\n",
+    "                if debug: print('c:', '; lines:', lines)\n",
+    "                bs = [l for l in height_groups[ch-1] if link_ends(l) & lines]\n",
+    "                b = Link(ch - 1, d.left, d.right)\n",
+    "                if debug: print('b:', b, '; bs:', bs)\n",
+    "                if len(bs) == 1 and b in bs:\n",
+    "                    ah = b.height - 1\n",
+    "                    als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
+    "                    if debug: print('ah:', ah, '; als:', als)\n",
+    "                    while ah > 0 and not als:\n",
+    "                        ah -= 1\n",
+    "                        als = [l for l in height_groups[ah] if link_ends(l) & link_ends(c)]\n",
+    "                        if debug: print('ah:', ah, '; als:', als)\n",
+    "                    a = Link(ah, c.left, c.right)\n",
+    "                    if debug: print('a:', a)\n",
+    "                    if a in als:\n",
+    "                        if debug: print('adding:', a, b, c, d)\n",
+    "                        ts += [(a, b, c, d)]\n",
+    "    return ts"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_a_triple_pair(net, debug=False):\n",
+    "    hgs = height_groups(net)\n",
+    "\n",
+    "    tps = triple_pair(hgs)\n",
+    "    if debug: print('eatp', tps)\n",
+    "    if tps:\n",
+    "        a, b, c, d = tps[0]\n",
+    "        x = Link(b.height - 0.5, b.left, b.right)\n",
+    "        y = Link(b.height, a.left, a.right)\n",
+    "        if debug: print('removing', a, b, c, d, '; adding', x, y)\n",
+    "        return pack([l for l in net if l not in [a, b, c, d]] + [x, y])\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(Link(height=8, left=1, right=5),\n",
+       "  Link(height=9, left=1, right=21),\n",
+       "  Link(height=10, left=1, right=5),\n",
+       "  Link(height=11, left=1, right=21)),\n",
+       " (Link(height=40, left=16, right=23),\n",
+       "  Link(height=41, left=16, right=19),\n",
+       "  Link(height=42, left=16, right=23),\n",
+       "  Link(height=43, left=16, right=19)),\n",
+       " (Link(height=62, left=0, right=10),\n",
+       "  Link(height=63, left=10, right=13),\n",
+       "  Link(height=64, left=0, right=10),\n",
+       "  Link(height=65, left=10, right=13)),\n",
+       " (Link(height=137, left=23, right=24),\n",
+       "  Link(height=139, left=0, right=24),\n",
+       "  Link(height=140, left=23, right=24),\n",
+       "  Link(height=141, left=0, right=24)),\n",
+       " (Link(height=138, left=10, right=21),\n",
+       "  Link(height=139, left=2, right=10),\n",
+       "  Link(height=140, left=10, right=21),\n",
+       "  Link(height=141, left=2, right=10)),\n",
+       " (Link(height=139, left=2, right=10),\n",
+       "  Link(height=140, left=10, right=21),\n",
+       "  Link(height=141, left=2, right=10),\n",
+       "  Link(height=142, left=10, right=21)),\n",
+       " (Link(height=156, left=6, right=11),\n",
+       "  Link(height=157, left=3, right=6),\n",
+       "  Link(height=158, left=6, right=11),\n",
+       "  Link(height=159, left=3, right=6)),\n",
+       " (Link(height=184, left=2, right=21),\n",
+       "  Link(height=185, left=5, right=21),\n",
+       "  Link(height=186, left=2, right=21),\n",
+       "  Link(height=187, left=5, right=21)),\n",
+       " (Link(height=272, left=7, right=13),\n",
+       "  Link(height=273, left=7, right=11),\n",
+       "  Link(height=274, left=7, right=13),\n",
+       "  Link(height=275, left=7, right=11)),\n",
+       " (Link(height=290, left=14, right=15),\n",
+       "  Link(height=291, left=5, right=15),\n",
+       "  Link(height=292, left=14, right=15),\n",
+       "  Link(height=293, left=5, right=15)),\n",
+       " (Link(height=387, left=1, right=8),\n",
+       "  Link(height=389, left=8, right=15),\n",
+       "  Link(height=390, left=1, right=8),\n",
+       "  Link(height=391, left=8, right=15)),\n",
+       " (Link(height=420, left=14, right=22),\n",
+       "  Link(height=422, left=14, right=18),\n",
+       "  Link(height=423, left=14, right=22),\n",
+       "  Link(height=424, left=14, right=18)),\n",
+       " (Link(height=432, left=5, right=19),\n",
+       "  Link(height=433, left=1, right=19),\n",
+       "  Link(height=434, left=5, right=19),\n",
+       "  Link(height=435, left=1, right=19)),\n",
+       " (Link(height=454, left=0, right=15),\n",
+       "  Link(height=455, left=14, right=15),\n",
+       "  Link(height=456, left=0, right=15),\n",
+       "  Link(height=457, left=14, right=15)),\n",
+       " (Link(height=546, left=13, right=21),\n",
+       "  Link(height=547, left=6, right=21),\n",
+       "  Link(height=548, left=13, right=21),\n",
+       "  Link(height=549, left=6, right=21)),\n",
+       " (Link(height=620, left=17, right=23),\n",
+       "  Link(height=621, left=1, right=23),\n",
+       "  Link(height=622, left=17, right=23),\n",
+       "  Link(height=623, left=1, right=23)),\n",
+       " (Link(height=699, left=8, right=15),\n",
+       "  Link(height=700, left=3, right=15),\n",
+       "  Link(height=701, left=8, right=15),\n",
+       "  Link(height=702, left=3, right=15)),\n",
+       " (Link(height=789, left=7, right=24),\n",
+       "  Link(height=790, left=8, right=24),\n",
+       "  Link(height=791, left=7, right=24),\n",
+       "  Link(height=792, left=8, right=24)),\n",
+       " (Link(height=795, left=8, right=13),\n",
+       "  Link(height=796, left=4, right=8),\n",
+       "  Link(height=797, left=8, right=13),\n",
+       "  Link(height=798, left=4, right=8)),\n",
+       " (Link(height=809, left=16, right=17),\n",
+       "  Link(height=810, left=3, right=16),\n",
+       "  Link(height=811, left=16, right=17),\n",
+       "  Link(height=812, left=3, right=16)),\n",
+       " (Link(height=900, left=2, right=15),\n",
+       "  Link(height=901, left=13, right=15),\n",
+       "  Link(height=902, left=2, right=15),\n",
+       "  Link(height=903, left=13, right=15)),\n",
+       " (Link(height=921, left=2, right=15),\n",
+       "  Link(height=922, left=15, right=16),\n",
+       "  Link(height=923, left=2, right=15),\n",
+       "  Link(height=924, left=15, right=16)),\n",
+       " (Link(height=961, left=2, right=15),\n",
+       "  Link(height=962, left=2, right=14),\n",
+       "  Link(height=963, left=2, right=15),\n",
+       "  Link(height=964, left=2, right=14)),\n",
+       " (Link(height=976, left=13, right=18),\n",
+       "  Link(height=979, left=18, right=19),\n",
+       "  Link(height=980, left=13, right=18),\n",
+       "  Link(height=981, left=18, right=19)),\n",
+       " (Link(height=985, left=5, right=16),\n",
+       "  Link(height=986, left=2, right=5),\n",
+       "  Link(height=987, left=5, right=16),\n",
+       "  Link(height=988, left=2, right=5)),\n",
+       " (Link(height=1050, left=9, right=24),\n",
+       "  Link(height=1054, left=9, right=18),\n",
+       "  Link(height=1055, left=9, right=24),\n",
+       "  Link(height=1056, left=9, right=18)),\n",
+       " (Link(height=1159, left=11, right=21),\n",
+       "  Link(height=1160, left=11, right=14),\n",
+       "  Link(height=1161, left=11, right=21),\n",
+       "  Link(height=1162, left=11, right=14)),\n",
+       " (Link(height=1284, left=0, right=11),\n",
+       "  Link(height=1285, left=0, right=14),\n",
+       "  Link(height=1286, left=0, right=11),\n",
+       "  Link(height=1287, left=0, right=14)),\n",
+       " (Link(height=1331, left=4, right=9),\n",
+       "  Link(height=1333, left=4, right=10),\n",
+       "  Link(height=1334, left=4, right=9),\n",
+       "  Link(height=1335, left=4, right=10)),\n",
+       " (Link(height=1332, left=12, right=18),\n",
+       "  Link(height=1333, left=12, right=24),\n",
+       "  Link(height=1334, left=12, right=18),\n",
+       "  Link(height=1335, left=12, right=24)),\n",
+       " (Link(height=1343, left=0, right=17),\n",
+       "  Link(height=1344, left=0, right=23),\n",
+       "  Link(height=1345, left=0, right=17),\n",
+       "  Link(height=1346, left=0, right=23)),\n",
+       " (Link(height=1357, left=4, right=16),\n",
+       "  Link(height=1358, left=16, right=17),\n",
+       "  Link(height=1359, left=4, right=16),\n",
+       "  Link(height=1360, left=16, right=17)),\n",
+       " (Link(height=1441, left=6, right=20),\n",
+       "  Link(height=1443, left=16, right=20),\n",
+       "  Link(height=1444, left=6, right=20),\n",
+       "  Link(height=1445, left=16, right=20)),\n",
+       " (Link(height=1464, left=17, right=23),\n",
+       "  Link(height=1465, left=3, right=17),\n",
+       "  Link(height=1466, left=17, right=23),\n",
+       "  Link(height=1467, left=3, right=17)),\n",
+       " (Link(height=1540, left=8, right=23),\n",
+       "  Link(height=1541, left=7, right=23),\n",
+       "  Link(height=1542, left=8, right=23),\n",
+       "  Link(height=1543, left=7, right=23)),\n",
+       " (Link(height=1570, left=0, right=1),\n",
+       "  Link(height=1571, left=1, right=21),\n",
+       "  Link(height=1572, left=0, right=1),\n",
+       "  Link(height=1573, left=1, right=21)),\n",
+       " (Link(height=1600, left=15, right=22),\n",
+       "  Link(height=1603, left=7, right=15),\n",
+       "  Link(height=1604, left=15, right=22),\n",
+       "  Link(height=1605, left=7, right=15)),\n",
+       " (Link(height=1632, left=12, right=18),\n",
+       "  Link(height=1634, left=12, right=20),\n",
+       "  Link(height=1635, left=12, right=18),\n",
+       "  Link(height=1636, left=12, right=20)),\n",
+       " (Link(height=1702, left=13, right=24),\n",
+       "  Link(height=1705, left=14, right=24),\n",
+       "  Link(height=1706, left=13, right=24),\n",
+       "  Link(height=1707, left=14, right=24)),\n",
+       " (Link(height=1721, left=3, right=24),\n",
+       "  Link(height=1722, left=3, right=21),\n",
+       "  Link(height=1723, left=3, right=24),\n",
+       "  Link(height=1724, left=3, right=21)),\n",
+       " (Link(height=1722, left=3, right=21),\n",
+       "  Link(height=1723, left=3, right=24),\n",
+       "  Link(height=1724, left=3, right=21),\n",
+       "  Link(height=1725, left=3, right=24)),\n",
+       " (Link(height=1762, left=0, right=21),\n",
+       "  Link(height=1763, left=13, right=21),\n",
+       "  Link(height=1764, left=0, right=21),\n",
+       "  Link(height=1765, left=13, right=21)),\n",
+       " (Link(height=1769, left=7, right=9),\n",
+       "  Link(height=1770, left=7, right=12),\n",
+       "  Link(height=1771, left=7, right=9),\n",
+       "  Link(height=1772, left=7, right=12)),\n",
+       " (Link(height=1914, left=10, right=24),\n",
+       "  Link(height=1915, left=8, right=24),\n",
+       "  Link(height=1916, left=10, right=24),\n",
+       "  Link(height=1917, left=8, right=24)),\n",
+       " (Link(height=1920, left=4, right=23),\n",
+       "  Link(height=1921, left=3, right=4),\n",
+       "  Link(height=1922, left=4, right=23),\n",
+       "  Link(height=1923, left=3, right=4)),\n",
+       " (Link(height=2023, left=4, right=7),\n",
+       "  Link(height=2024, left=7, right=15),\n",
+       "  Link(height=2025, left=4, right=7),\n",
+       "  Link(height=2026, left=7, right=15)),\n",
+       " (Link(height=2025, left=8, right=19),\n",
+       "  Link(height=2031, left=8, right=15),\n",
+       "  Link(height=2032, left=8, right=19),\n",
+       "  Link(height=2033, left=8, right=15)),\n",
+       " (Link(height=2152, left=10, right=15),\n",
+       "  Link(height=2153, left=10, right=16),\n",
+       "  Link(height=2154, left=10, right=15),\n",
+       "  Link(height=2155, left=10, right=16)),\n",
+       " (Link(height=2194, left=22, right=24),\n",
+       "  Link(height=2195, left=7, right=22),\n",
+       "  Link(height=2196, left=22, right=24),\n",
+       "  Link(height=2197, left=7, right=22)),\n",
+       " (Link(height=2211, left=5, right=6),\n",
+       "  Link(height=2212, left=6, right=14),\n",
+       "  Link(height=2213, left=5, right=6),\n",
+       "  Link(height=2214, left=6, right=14))]"
+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "hgs = height_groups(enet)\n",
+    "triple_pair(hgs)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "etnet = eliminate_a_triple_pair(enet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, etnet) == follow_many(string.ascii_lowercase, enet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def eliminate_triple_pairs(net):\n",
+    "    print(len(net))\n",
+    "    new_net = eliminate_a_triple_pair(net)\n",
+    "    while new_net:\n",
+    "        print(len(net))\n",
+    "        net = new_net\n",
+    "        new_net = eliminate_a_triple_pair(net)\n",
+    "    return net"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10033\n",
+      "10033\n",
+      "10031\n",
+      "10029\n",
+      "10027\n",
+      "10025\n",
+      "10023\n",
+      "10021\n",
+      "10019\n",
+      "10017\n",
+      "10015\n",
+      "10013\n",
+      "10011\n",
+      "10009\n",
+      "10007\n",
+      "10005\n",
+      "10003\n",
+      "10001\n",
+      "9999\n",
+      "9997\n",
+      "9995\n",
+      "9993\n",
+      "9991\n",
+      "9989\n",
+      "9987\n",
+      "9985\n",
+      "9983\n",
+      "9981\n",
+      "9979\n",
+      "9977\n",
+      "9975\n",
+      "9973\n",
+      "9971\n",
+      "9969\n",
+      "9967\n",
+      "9965\n",
+      "9963\n",
+      "9961\n",
+      "9959\n",
+      "9957\n",
+      "9955\n",
+      "9953\n",
+      "9951\n",
+      "9949\n",
+      "9947\n",
+      "9945\n",
+      "9943\n",
+      "9941\n",
+      "9939\n"
+     ]
+    }
+   ],
+   "source": [
+    "setnet = eliminate_triple_pairs(enet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9937"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(setnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "assert follow_many(string.ascii_lowercase, etnet) == follow_many(string.ascii_lowercase, enet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, etnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, setnet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, enet))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "eliminable_pairs(etnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(10135, 10031)"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(net), len(etnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def simplify(net0):\n",
+    "    netp = eliminate_pairs(net0)\n",
+    "    new_net = eliminate_a_triple_pair(netp)\n",
+    "    while new_net:\n",
+    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
+    "        netp = eliminate_pairs(new_net)\n",
+    "        new_net = eliminate_a_triple_pair(netp)\n",
+    "    return netp"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "simple_net = simplify(pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, simple_net)) == ''.join(follow_many(string.ascii_lowercase, net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 49,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, simple_net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'doqzmbishkwunvltpcexyjgfra'"
+      ]
+     },
+     "execution_count": 50,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9931"
+      ]
+     },
+     "execution_count": 51,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(simple_net)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def simplify_with_checks(net0):\n",
+    "    netp = eliminate_pairs(net0)\n",
+    "    if follow_many(string.ascii_lowercase, net0) != follow_many(string.ascii_lowercase, netp):\n",
+    "        print('pairs', eliminable_pairs(net0))\n",
+    "        return net0\n",
+    "    else:\n",
+    "        print('pairs ok')\n",
+    "    new_net = eliminate_a_triple_pair(netp)\n",
+    "    if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
+    "        hg = find_height_groups(netp)\n",
+    "        print('triple', triple_pair_hg(hg))\n",
+    "        return netp\n",
+    "    else:\n",
+    "        print('triple ok')\n",
+    "    while new_net:\n",
+    "#         print('sipl', len(net0), len(netp), len(new_net))\n",
+    "        netp = eliminate_pairs(new_net)\n",
+    "        if follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
+    "            print('pairs', eliminable_pairs(new_net))\n",
+    "            return new_net\n",
+    "        else:\n",
+    "            print('pairs ok')\n",
+    "        new_net = eliminate_a_triple_pair(netp)\n",
+    "        if new_net and follow_many(string.ascii_lowercase, new_net) != follow_many(string.ascii_lowercase, netp):\n",
+    "            hg = find_height_groups(netp)\n",
+    "            print('triple', triple_pair_hg(hg))\n",
+    "            return netp\n",
+    "        else:\n",
+    "            print('triple ok')\n",
+    "    print('** done')\n",
+    "    return netp"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "pairs ok\n",
+      "triple ok\n",
+      "** done\n"
+     ]
+    }
+   ],
+   "source": [
+    "spnet = simplify_with_checks(pnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "''.join(follow_many(string.ascii_lowercase, spnet)) == ''.join(follow_many(string.ascii_lowercase, net))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9931"
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(spnet)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/04-amidakuji/day4.clj b/04-amidakuji/day4.clj
new file mode 100644 (file)
index 0000000..3c5d494
--- /dev/null
+++ b/04-amidakuji/day4.clj
@@ -0,0 +1,70 @@
+(ns day4
+    (:require [clojure.string :as str]))
+
+(defstruct link :height :left :right)
+
+; (def network (str/split-lines (slurp "../04-small.txt")))
+(def network (str/split-lines (slurp "../04-lines.txt")))
+
+(defn parse-link [l, h]
+    (let [endss (rest (str/split l #"\D+"))
+          ends (map #(Integer/parseInt %) endss)]
+        (struct-map link
+            :height h
+            :left (first ends)
+            :right (second ends))))
+
+(defn parse-network [links]
+    (map-indexed 
+        (fn [i l] (parse-link l i)) 
+        links))
+
+(def parsed-network
+    (parse-network network))
+
+
+(def initial
+    (str/split "abcdefghijklmnopqrstuvwxyz" #""))
+
+(defn apply-link [items link]
+    (let [li (get link :left)
+          ri (get link :right)
+          le (nth items li)
+          re (nth items ri)
+          pre (subvec items 0 li)
+          mid (subvec items (inc li) ri)
+          suf (subvec items (inc ri))]
+    (into [] (concat pre (vector re) mid (vector le) suf))))
+
+(defn follow [items links]
+    (reduce apply-link items links))
+
+
+(defn lane-count [links]
+    (inc (apply max (map (fn [l] (get l :right)) links))))
+
+(defn initial-heights [links]
+    (vec (replicate (lane-count links) -1)))
+
+(defn pack-one [lane-heights link]
+    (let 
+        [li (get link :left)
+         ri (get link :right)
+         new-height (inc (max (nth lane-heights li)
+                              (nth lane-heights ri)))]
+        (assoc lane-heights li new-height ri new-height)))
+
+(defn pack [lane-heights links]
+    (reduce pack-one lane-heights links))
+
+
+(spit "day4.out" (prn-str 
+    (str/join (follow initial parsed-network))))
+
+(spit "day4.out" (prn-str 
+    (apply max 
+        (pack
+            (initial-heights parsed-network)
+            parsed-network)))
+    :append true)
+

diff --git a/04-amidakuji/packing-variants.svg b/04-amidakuji/packing-variants.svg
new file mode 100644 (file)
index 0000000..07c4963
--- /dev/null
+++ b/04-amidakuji/packing-variants.svg
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diff --git a/04-amidakuji/small-expanded.svg.png b/04-amidakuji/small-expanded.svg.png
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diff --git a/04-amidakuji/small-packed.svg b/04-amidakuji/small-packed.svg
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