{
 "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": {
    "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": 7,
   "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": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "small_net = read_net('04-small.txt')\n",
    "small_net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10135"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net = read_net('04-lines.txt')\n",
    "len(net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permnet = read_net('permutations.txt')\n",
    "len(permnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rpermnet = read_net('permutations.txt', rev=True)\n",
    "len(rpermnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def link_ends(link):\n",
    "    return set((link.left, link.right))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": 14,
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(l.height for l in small_net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(l.height for l in pack(small_net))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10134"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(l.height for l in net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2286"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(l.height for l in pack(net))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": 20,
   "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'acfbedghij'"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many('abcdefghij', small_net))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 loops, best of 3: 41.3 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "follow_many('abcdefghij', small_net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'doqzmbishkwunvltpcexyjgfra'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, net))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'zfrasxwigvjoembqcyhplnktud'"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, permnet))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'doqzmbishkwunvltpcexyjgfra'"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, rpermnet))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 20.8 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "follow_many(string.ascii_lowercase, net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pnet = pack(net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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": 29,
   "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": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eliminable_pairs(pnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 24.7 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "eliminable_pairs(pnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "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": 32,
   "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": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "enet = eliminate_pairs(pnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 2.41 s per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "eliminate_pairs(pnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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": 37,
   "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": 38,
   "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": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hgs = height_groups(enet)\n",
    "triple_pair(hgs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "etnet = eliminate_a_triple_pair(enet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "assert follow_many(string.ascii_lowercase, etnet) == follow_many(string.ascii_lowercase, enet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": 42,
   "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": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9937"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(setnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "assert follow_many(string.ascii_lowercase, etnet) == follow_many(string.ascii_lowercase, enet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'doqzmbishkwunvltpcexyjgfra'"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, etnet))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'doqzmbishkwunvltpcexyjgfra'"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, setnet))"
   ]
  },
  {
   "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, enet))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'doqzmbishkwunvltpcexyjgfra'"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, net))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eliminable_pairs(etnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10135, 10031)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(net), len(etnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "simple_net = simplify(pnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "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": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'doqzmbishkwunvltpcexyjgfra'"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, simple_net))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'doqzmbishkwunvltpcexyjgfra'"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(follow_many(string.ascii_lowercase, net))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9931"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(simple_net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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": 58,
   "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": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 59,
     "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": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9931"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(spnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2205"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(height_groups(spnet).keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9931"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(simple_net)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2205"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(height_groups(simple_net).keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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