X-Git-Url: https://git.njae.me.uk/?a=blobdiff_plain;f=04-08-amidakuji%2Famidakuji-solution-1-slow.ipynb;fp=04-08-amidakuji%2Famidakuji-solution-1-slow.ipynb;h=0000000000000000000000000000000000000000;hb=55f602f3ca4d1297233e471706caaad9c7a99b5e;hp=345321daa12de45880fa71827fb01305186f3017;hpb=c1f001553a729b73032babaeb7b900a63704c436;p=ou-summer-of-code-2017.git

diff --git a/04-08-amidakuji/amidakuji-solution-1-slow.ipynb b/04-08-amidakuji/amidakuji-solution-1-slow.ipynb
deleted file mode 100644
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
-}