Done word chains puzzle

diff --git a/word-chains/build-word-lists.ipynb b/word-chains/build-word-lists.ipynb
new file mode 100644 (file)
index 0000000..d12df78
--- /dev/null
+++ b/word-chains/build-word-lists.ipynb
@@ -0,0 +1,201 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import unicodedata\n",
+    "import string"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "unaccent_specials = ''.maketrans({\"’\": \"'\", '“': '\"', '”': '\"'})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def unaccent(text):\n",
+    "    translated_text = text.translate(unaccent_specials)\n",
+    "    return unicodedata.normalize('NFKD', translated_text).\\\n",
+    "        encode('ascii', 'ignore').\\\n",
+    "        decode('utf-8')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def only_lower(text):\n",
+    "    return all((c in string.ascii_lowercase) for c in text)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "/usr/share/dict/british-english\n",
+      "find: ‘/usr/share/doc/google-chrome-stable’: Permission denied\n",
+      "/usr/share/man/man5/british-english.5.gz\n"
+     ]
+    }
+   ],
+   "source": [
+    "# !find /usr -type f -iname 'british-english*'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "total 2.3M\r\n",
+      "drwxr-xr-x   2 root root 4.0K Dec 29 12:37 .\r\n",
+      "drwxr-xr-x 640 root root  20K Apr 13 17:05 ..\r\n",
+      "-rw-r--r--   1 root root 917K Oct 23  2011 american-english\r\n",
+      "-rw-r--r--   1 root root 917K Oct 23  2011 british-english\r\n",
+      "-rw-r--r--   1 root root 467K Aug 25  2016 cracklib-small\r\n",
+      "-rw-r--r--   1 root root  199 Aug 29  2016 README.select-wordlist\r\n",
+      "lrwxrwxrwx   1 root root   30 Nov 10  2014 words -> /etc/dictionaries-common/words\r\n",
+      "lrwxrwxrwx   1 root root   16 Jun 18  2014 words.pre-dictionaries-common -> american-english\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "# !ls -lah /usr/share/dict"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def rude(word):\n",
+    "    return any(w in word \n",
+    "               for w in 'piss shit cunt fuck arse crap fart jizz whore bitch'.split())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rude('fucks')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def words_with_len(n):\n",
+    "    return [unaccent(w.strip()) for w in open('/usr/share/dict/british-english').readlines()\n",
+    "               if only_lower(unaccent(w.strip()))\n",
+    "               if len(unaccent(w.strip())) == n\n",
+    "               if not rude(unaccent(w.strip()))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2336 4-letter words\n",
+      "4566 5-letter words\n",
+      "7223 6-letter words\n"
+     ]
+    }
+   ],
+   "source": [
+    "dicts = {}\n",
+    "\n",
+    "for n in [4, 5, 6]:\n",
+    "    dicts[n] = words_with_len(n)\n",
+    "    print('{} {}-letter words'.format(len(dicts[n]), n))\n",
+    "    with open('words{}.txt'.format(n), 'w') as f:\n",
+    "        f.write('\\n'.join(sorted(set(dicts[n]))))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/word-chains/explore-word-chain-4.ipynb b/word-chains/explore-word-chain-4.ipynb
new file mode 100644 (file)
index 0000000..6e230ed
--- /dev/null
+++ b/word-chains/explore-word-chain-4.ipynb
@@ -0,0 +1,2761 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import string\n",
+    "import heapq\n",
+    "import collections\n",
+    "import random"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2336"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "words = [w.strip() for w in open('words4.txt').readlines()]\n",
+    "len(words)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['abbe',\n",
+       " 'abed',\n",
+       " 'abet',\n",
+       " 'able',\n",
+       " 'ably',\n",
+       " 'abut',\n",
+       " 'aced',\n",
+       " 'aces',\n",
+       " 'ache',\n",
+       " 'achy']"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "words[:10]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def adjacents_explicit(word):\n",
+    "    neighbours = []\n",
+    "    for i in range(len(word)):\n",
+    "        for l in string.ascii_lowercase:\n",
+    "            if l != word[i]:\n",
+    "                neighbours.append(word[0:i] + l + word[i+1:])\n",
+    "    return neighbours"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def adjacents(word):\n",
+    "    return [word[0:i] + l + word[i+1:]\n",
+    "           for i in range(len(word))\n",
+    "           for l in string.ascii_lowercase\n",
+    "           if l != word[i]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
+    "             for w in words}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['able']"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "neighbours['abbe']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['axle', 'abbe', 'ably']"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "neighbours['able']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def distance(w1, w2):\n",
+    "    return sum(1 for i in range(len(w1))\n",
+    "               if w1[i] != w2[i])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "distance('abbe', 'abbe')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extend(chain):\n",
+    "    return [chain + [s] for s in neighbours[chain[-1]]\n",
+    "           if s not in chain]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[['abbe', 'able']]"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "extend(['abbe'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[['abbe', 'able', 'axle'], ['abbe', 'able', 'ably']]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "extend(['abbe', 'able'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[['abbe', 'able', 'ably', 'ally']]"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "extend(['abbe', 'able', 'ably'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search(start, target, debug=False):\n",
+    "    return bfs([[start]], target, debug=debug)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs(agenda, goal, debug=False):\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['abbe']\n",
+      "['abbe', 'able']\n",
+      "['abbe', 'able', 'axle']\n",
+      "['abbe', 'able', 'ably']\n",
+      "['abbe', 'able', 'ably', 'ally']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['abbe', 'able', 'ably', 'ally']"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bfs_search('abbe', 'ally', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dfs_search(start, target, debug=False):\n",
+    "    return dfs([[start]], target, debug=debug)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dfs(agenda, goal, debug=False):\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = successors + agenda[1:]\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['abbe']\n",
+      "['abbe', 'able']\n",
+      "['abbe', 'able', 'axle']\n",
+      "['abbe', 'able', 'ably']\n",
+      "['abbe', 'able', 'ably', 'ally']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['abbe', 'able', 'ably', 'ally']"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dfs_search('abbe', 'ally', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['cart']\n",
+      "['cart', 'dart']\n",
+      "['cart', 'hart']\n",
+      "['cart', 'mart']\n",
+      "['cart', 'part']\n",
+      "['cart', 'tart']\n",
+      "['cart', 'wart']\n",
+      "['cart', 'curt']\n",
+      "['cart', 'cant']\n",
+      "['cart', 'cast']\n",
+      "['cart', 'card']\n",
+      "['cart', 'care']\n",
+      "['cart', 'carp']\n",
+      "['cart', 'cars']\n",
+      "['cart', 'dart', 'hart']\n",
+      "['cart', 'dart', 'mart']\n",
+      "['cart', 'dart', 'part']\n",
+      "['cart', 'dart', 'tart']\n",
+      "['cart', 'dart', 'wart']\n",
+      "['cart', 'dart', 'dirt']\n",
+      "['cart', 'dart', 'daft']\n",
+      "['cart', 'dart', 'dare']\n",
+      "['cart', 'dart', 'dark']\n",
+      "['cart', 'dart', 'darn']\n",
+      "['cart', 'hart', 'dart']\n",
+      "['cart', 'hart', 'mart']\n",
+      "['cart', 'hart', 'part']\n",
+      "['cart', 'hart', 'tart']\n",
+      "['cart', 'hart', 'wart']\n",
+      "['cart', 'hart', 'hurt']\n",
+      "['cart', 'hart', 'haft']\n",
+      "['cart', 'hart', 'halt']\n",
+      "['cart', 'hart', 'hard']\n",
+      "['cart', 'hart', 'hare']\n",
+      "['cart', 'hart', 'hark']\n",
+      "['cart', 'hart', 'harm']\n",
+      "['cart', 'hart', 'harp']\n",
+      "['cart', 'mart', 'dart']\n",
+      "['cart', 'mart', 'hart']\n",
+      "['cart', 'mart', 'part']\n",
+      "['cart', 'mart', 'tart']\n",
+      "['cart', 'mart', 'wart']\n",
+      "['cart', 'mart', 'malt']\n",
+      "['cart', 'mart', 'mast']\n",
+      "['cart', 'mart', 'matt']\n",
+      "['cart', 'mart', 'mare']\n",
+      "['cart', 'mart', 'mark']\n",
+      "['cart', 'mart', 'mars']\n",
+      "['cart', 'part', 'dart']\n",
+      "['cart', 'part', 'hart']\n",
+      "['cart', 'part', 'mart']\n",
+      "['cart', 'part', 'tart']\n",
+      "['cart', 'part', 'wart']\n",
+      "['cart', 'part', 'pert']\n",
+      "['cart', 'part', 'port']\n",
+      "['cart', 'part', 'pact']\n",
+      "['cart', 'part', 'pant']\n",
+      "['cart', 'part', 'past']\n",
+      "['cart', 'part', 'pare']\n",
+      "['cart', 'part', 'park']\n",
+      "['cart', 'part', 'pars']\n",
+      "['cart', 'tart', 'dart']\n",
+      "['cart', 'tart', 'hart']\n",
+      "['cart', 'tart', 'mart']\n",
+      "['cart', 'tart', 'part']\n",
+      "['cart', 'tart', 'wart']\n",
+      "['cart', 'tart', 'tort']\n",
+      "['cart', 'tart', 'tact']\n",
+      "['cart', 'tart', 'taut']\n",
+      "['cart', 'tart', 'tare']\n",
+      "['cart', 'tart', 'taro']\n",
+      "['cart', 'tart', 'tarp']\n",
+      "['cart', 'tart', 'tars']\n",
+      "['cart', 'wart', 'dart']\n",
+      "['cart', 'wart', 'hart']\n",
+      "['cart', 'wart', 'mart']\n",
+      "['cart', 'wart', 'part']\n",
+      "['cart', 'wart', 'tart']\n",
+      "['cart', 'wart', 'waft']\n",
+      "['cart', 'wart', 'wait']\n",
+      "['cart', 'wart', 'want']\n",
+      "['cart', 'wart', 'watt']\n",
+      "['cart', 'wart', 'ward']\n",
+      "['cart', 'wart', 'ware']\n",
+      "['cart', 'wart', 'warm']\n",
+      "['cart', 'wart', 'warn']\n",
+      "['cart', 'wart', 'warp']\n",
+      "['cart', 'wart', 'wars']\n",
+      "['cart', 'wart', 'wary']\n",
+      "['cart', 'curt', 'hurt']\n",
+      "['cart', 'curt', 'cult']\n",
+      "['cart', 'curt', 'curb']\n",
+      "['cart', 'curt', 'curd']\n",
+      "['cart', 'curt', 'cure']\n",
+      "['cart', 'curt', 'curl']\n",
+      "['cart', 'curt', 'curs']\n",
+      "['cart', 'cant', 'pant']\n",
+      "['cart', 'cant', 'rant']\n",
+      "['cart', 'cant', 'want']\n",
+      "['cart', 'cant', 'cent']\n",
+      "['cart', 'cant', 'cast']\n",
+      "['cart', 'cant', 'cane']\n",
+      "['cart', 'cant', 'cans']\n",
+      "['cart', 'cast', 'bast']\n",
+      "['cart', 'cast', 'east']\n",
+      "['cart', 'cast', 'fast']\n",
+      "['cart', 'cast', 'last']\n",
+      "['cart', 'cast', 'mast']\n",
+      "['cart', 'cast', 'past']\n",
+      "['cart', 'cast', 'vast']\n",
+      "['cart', 'cast', 'cost']\n",
+      "['cart', 'cast', 'cyst']\n",
+      "['cart', 'cast', 'cant']\n",
+      "['cart', 'cast', 'case']\n",
+      "['cart', 'cast', 'cash']\n",
+      "['cart', 'cast', 'cask']\n",
+      "['cart', 'card', 'bard']\n",
+      "['cart', 'card', 'hard']\n",
+      "['cart', 'card', 'lard']\n",
+      "['cart', 'card', 'ward']\n",
+      "['cart', 'card', 'yard']\n",
+      "['cart', 'card', 'cord']\n",
+      "['cart', 'card', 'curd']\n",
+      "['cart', 'card', 'care']\n",
+      "['cart', 'card', 'carp']\n",
+      "['cart', 'card', 'cars']\n",
+      "['cart', 'care', 'bare']\n",
+      "['cart', 'care', 'dare']\n",
+      "['cart', 'care', 'fare']\n",
+      "['cart', 'care', 'hare']\n",
+      "['cart', 'care', 'mare']\n",
+      "['cart', 'care', 'pare']\n",
+      "['cart', 'care', 'rare']\n",
+      "['cart', 'care', 'tare']\n",
+      "['cart', 'care', 'ware']\n",
+      "['cart', 'care', 'core']\n",
+      "['cart', 'care', 'cure']\n",
+      "['cart', 'care', 'cafe']\n",
+      "['cart', 'care', 'cage']\n",
+      "['cart', 'care', 'cake']\n",
+      "['cart', 'care', 'came']\n",
+      "['cart', 'care', 'cane']\n",
+      "['cart', 'care', 'cape']\n",
+      "['cart', 'care', 'case']\n",
+      "['cart', 'care', 'cave']\n",
+      "['cart', 'care', 'card']\n",
+      "['cart', 'care', 'carp']\n",
+      "['cart', 'care', 'cars']\n",
+      "['cart', 'carp', 'harp']\n",
+      "['cart', 'carp', 'tarp']\n",
+      "['cart', 'carp', 'warp']\n",
+      "['cart', 'carp', 'camp']\n",
+      "['cart', 'carp', 'card']\n",
+      "['cart', 'carp', 'care']\n",
+      "['cart', 'carp', 'cars']\n",
+      "['cart', 'cars', 'bars']\n",
+      "['cart', 'cars', 'ears']\n",
+      "['cart', 'cars', 'jars']\n",
+      "['cart', 'cars', 'mars']\n",
+      "['cart', 'cars', 'oars']\n",
+      "['cart', 'cars', 'pars']\n",
+      "['cart', 'cars', 'tars']\n",
+      "['cart', 'cars', 'wars']\n",
+      "['cart', 'cars', 'curs']\n",
+      "['cart', 'cars', 'cabs']\n",
+      "['cart', 'cars', 'cads']\n",
+      "['cart', 'cars', 'cams']\n",
+      "['cart', 'cars', 'cans']\n",
+      "['cart', 'cars', 'caps']\n",
+      "['cart', 'cars', 'cats']\n",
+      "['cart', 'cars', 'caws']\n",
+      "['cart', 'cars', 'card']\n",
+      "['cart', 'cars', 'care']\n",
+      "['cart', 'cars', 'carp']\n",
+      "['cart', 'dart', 'hart', 'mart']\n",
+      "['cart', 'dart', 'hart', 'part']\n",
+      "['cart', 'dart', 'hart', 'tart']\n",
+      "['cart', 'dart', 'hart', 'wart']\n",
+      "['cart', 'dart', 'hart', 'hurt']\n",
+      "['cart', 'dart', 'hart', 'haft']\n",
+      "['cart', 'dart', 'hart', 'halt']\n",
+      "['cart', 'dart', 'hart', 'hard']\n",
+      "['cart', 'dart', 'hart', 'hare']\n",
+      "['cart', 'dart', 'hart', 'hark']\n",
+      "['cart', 'dart', 'hart', 'harm']\n",
+      "['cart', 'dart', 'hart', 'harp']\n",
+      "['cart', 'dart', 'mart', 'hart']\n",
+      "['cart', 'dart', 'mart', 'part']\n",
+      "['cart', 'dart', 'mart', 'tart']\n",
+      "['cart', 'dart', 'mart', 'wart']\n",
+      "['cart', 'dart', 'mart', 'malt']\n",
+      "['cart', 'dart', 'mart', 'mast']\n",
+      "['cart', 'dart', 'mart', 'matt']\n",
+      "['cart', 'dart', 'mart', 'mare']\n",
+      "['cart', 'dart', 'mart', 'mark']\n",
+      "['cart', 'dart', 'mart', 'mars']\n",
+      "['cart', 'dart', 'part', 'hart']\n",
+      "['cart', 'dart', 'part', 'mart']\n",
+      "['cart', 'dart', 'part', 'tart']\n",
+      "['cart', 'dart', 'part', 'wart']\n",
+      "['cart', 'dart', 'part', 'pert']\n",
+      "['cart', 'dart', 'part', 'port']\n",
+      "['cart', 'dart', 'part', 'pact']\n",
+      "['cart', 'dart', 'part', 'pant']\n",
+      "['cart', 'dart', 'part', 'past']\n",
+      "['cart', 'dart', 'part', 'pare']\n",
+      "['cart', 'dart', 'part', 'park']\n",
+      "['cart', 'dart', 'part', 'pars']\n",
+      "['cart', 'dart', 'tart', 'hart']\n",
+      "['cart', 'dart', 'tart', 'mart']\n",
+      "['cart', 'dart', 'tart', 'part']\n",
+      "['cart', 'dart', 'tart', 'wart']\n",
+      "['cart', 'dart', 'tart', 'tort']\n",
+      "['cart', 'dart', 'tart', 'tact']\n",
+      "['cart', 'dart', 'tart', 'taut']\n",
+      "['cart', 'dart', 'tart', 'tare']\n",
+      "['cart', 'dart', 'tart', 'taro']\n",
+      "['cart', 'dart', 'tart', 'tarp']\n",
+      "['cart', 'dart', 'tart', 'tars']\n",
+      "['cart', 'dart', 'wart', 'hart']\n",
+      "['cart', 'dart', 'wart', 'mart']\n",
+      "['cart', 'dart', 'wart', 'part']\n",
+      "['cart', 'dart', 'wart', 'tart']\n",
+      "['cart', 'dart', 'wart', 'waft']\n",
+      "['cart', 'dart', 'wart', 'wait']\n",
+      "['cart', 'dart', 'wart', 'want']\n",
+      "['cart', 'dart', 'wart', 'watt']\n",
+      "['cart', 'dart', 'wart', 'ward']\n",
+      "['cart', 'dart', 'wart', 'ware']\n",
+      "['cart', 'dart', 'wart', 'warm']\n",
+      "['cart', 'dart', 'wart', 'warn']\n",
+      "['cart', 'dart', 'wart', 'warp']\n",
+      "['cart', 'dart', 'wart', 'wars']\n",
+      "['cart', 'dart', 'wart', 'wary']\n",
+      "['cart', 'dart', 'dirt', 'girt']\n",
+      "['cart', 'dart', 'dirt', 'diet']\n",
+      "['cart', 'dart', 'dirt', 'dint']\n",
+      "['cart', 'dart', 'dirt', 'dire']\n",
+      "['cart', 'dart', 'dirt', 'dirk']\n",
+      "['cart', 'dart', 'daft', 'haft']\n",
+      "['cart', 'dart', 'daft', 'raft']\n",
+      "['cart', 'dart', 'daft', 'waft']\n",
+      "['cart', 'dart', 'daft', 'deft']\n",
+      "['cart', 'dart', 'dare', 'bare']\n",
+      "['cart', 'dart', 'dare', 'care']\n",
+      "['cart', 'dart', 'dare', 'fare']\n",
+      "['cart', 'dart', 'dare', 'hare']\n",
+      "['cart', 'dart', 'dare', 'mare']\n",
+      "['cart', 'dart', 'dare', 'pare']\n",
+      "['cart', 'dart', 'dare', 'rare']\n",
+      "['cart', 'dart', 'dare', 'tare']\n",
+      "['cart', 'dart', 'dare', 'ware']\n",
+      "['cart', 'dart', 'dare', 'dire']\n",
+      "['cart', 'dart', 'dare', 'dale']\n",
+      "['cart', 'dart', 'dare', 'dame']\n",
+      "['cart', 'dart', 'dare', 'date']\n",
+      "['cart', 'dart', 'dare', 'daze']\n",
+      "['cart', 'dart', 'dare', 'dark']\n",
+      "['cart', 'dart', 'dare', 'darn']\n",
+      "['cart', 'dart', 'dark', 'bark']\n",
+      "['cart', 'dart', 'dark', 'hark']\n",
+      "['cart', 'dart', 'dark', 'lark']\n",
+      "['cart', 'dart', 'dark', 'mark']\n",
+      "['cart', 'dart', 'dark', 'nark']\n",
+      "['cart', 'dart', 'dark', 'park']\n",
+      "['cart', 'dart', 'dark', 'dirk']\n",
+      "['cart', 'dart', 'dark', 'dork']\n",
+      "['cart', 'dart', 'dark', 'dank']\n",
+      "['cart', 'dart', 'dark', 'dare']\n",
+      "['cart', 'dart', 'dark', 'darn']\n",
+      "['cart', 'dart', 'darn', 'barn']\n",
+      "['cart', 'dart', 'darn', 'earn']\n",
+      "['cart', 'dart', 'darn', 'warn']\n",
+      "['cart', 'dart', 'darn', 'yarn']\n",
+      "['cart', 'dart', 'darn', 'damn']\n",
+      "['cart', 'dart', 'darn', 'dawn']\n",
+      "['cart', 'dart', 'darn', 'dare']\n",
+      "['cart', 'dart', 'darn', 'dark']\n",
+      "['cart', 'hart', 'dart', 'mart']\n",
+      "['cart', 'hart', 'dart', 'part']\n",
+      "['cart', 'hart', 'dart', 'tart']\n",
+      "['cart', 'hart', 'dart', 'wart']\n",
+      "['cart', 'hart', 'dart', 'dirt']\n",
+      "['cart', 'hart', 'dart', 'daft']\n",
+      "['cart', 'hart', 'dart', 'dare']\n",
+      "['cart', 'hart', 'dart', 'dark']\n",
+      "['cart', 'hart', 'dart', 'darn']\n",
+      "['cart', 'hart', 'mart', 'dart']\n",
+      "['cart', 'hart', 'mart', 'part']\n",
+      "['cart', 'hart', 'mart', 'tart']\n",
+      "['cart', 'hart', 'mart', 'wart']\n",
+      "['cart', 'hart', 'mart', 'malt']\n",
+      "['cart', 'hart', 'mart', 'mast']\n",
+      "['cart', 'hart', 'mart', 'matt']\n",
+      "['cart', 'hart', 'mart', 'mare']\n",
+      "['cart', 'hart', 'mart', 'mark']\n",
+      "['cart', 'hart', 'mart', 'mars']\n",
+      "['cart', 'hart', 'part', 'dart']\n",
+      "['cart', 'hart', 'part', 'mart']\n",
+      "['cart', 'hart', 'part', 'tart']\n",
+      "['cart', 'hart', 'part', 'wart']\n",
+      "['cart', 'hart', 'part', 'pert']\n",
+      "['cart', 'hart', 'part', 'port']\n",
+      "['cart', 'hart', 'part', 'pact']\n",
+      "['cart', 'hart', 'part', 'pant']\n",
+      "['cart', 'hart', 'part', 'past']\n",
+      "['cart', 'hart', 'part', 'pare']\n",
+      "['cart', 'hart', 'part', 'park']\n",
+      "['cart', 'hart', 'part', 'pars']\n",
+      "['cart', 'hart', 'tart', 'dart']\n",
+      "['cart', 'hart', 'tart', 'mart']\n",
+      "['cart', 'hart', 'tart', 'part']\n",
+      "['cart', 'hart', 'tart', 'wart']\n",
+      "['cart', 'hart', 'tart', 'tort']\n",
+      "['cart', 'hart', 'tart', 'tact']\n",
+      "['cart', 'hart', 'tart', 'taut']\n",
+      "['cart', 'hart', 'tart', 'tare']\n",
+      "['cart', 'hart', 'tart', 'taro']\n",
+      "['cart', 'hart', 'tart', 'tarp']\n",
+      "['cart', 'hart', 'tart', 'tars']\n",
+      "['cart', 'hart', 'wart', 'dart']\n",
+      "['cart', 'hart', 'wart', 'mart']\n",
+      "['cart', 'hart', 'wart', 'part']\n",
+      "['cart', 'hart', 'wart', 'tart']\n",
+      "['cart', 'hart', 'wart', 'waft']\n",
+      "['cart', 'hart', 'wart', 'wait']\n",
+      "['cart', 'hart', 'wart', 'want']\n",
+      "['cart', 'hart', 'wart', 'watt']\n",
+      "['cart', 'hart', 'wart', 'ward']\n",
+      "['cart', 'hart', 'wart', 'ware']\n",
+      "['cart', 'hart', 'wart', 'warm']\n",
+      "['cart', 'hart', 'wart', 'warn']\n",
+      "['cart', 'hart', 'wart', 'warp']\n",
+      "['cart', 'hart', 'wart', 'wars']\n",
+      "['cart', 'hart', 'wart', 'wary']\n",
+      "['cart', 'hart', 'hurt', 'curt']\n",
+      "['cart', 'hart', 'hurt', 'hunt']\n",
+      "['cart', 'hart', 'hurt', 'hurl']\n",
+      "['cart', 'hart', 'haft', 'daft']\n",
+      "['cart', 'hart', 'haft', 'raft']\n",
+      "['cart', 'hart', 'haft', 'waft']\n",
+      "['cart', 'hart', 'haft', 'heft']\n",
+      "['cart', 'hart', 'haft', 'halt']\n",
+      "['cart', 'hart', 'halt', 'malt']\n",
+      "['cart', 'hart', 'halt', 'salt']\n",
+      "['cart', 'hart', 'halt', 'hilt']\n",
+      "['cart', 'hart', 'halt', 'haft']\n",
+      "['cart', 'hart', 'halt', 'hale']\n",
+      "['cart', 'hart', 'halt', 'half']\n",
+      "['cart', 'hart', 'halt', 'hall']\n",
+      "['cart', 'hart', 'halt', 'halo']\n",
+      "['cart', 'hart', 'hard', 'bard']\n",
+      "['cart', 'hart', 'hard', 'card']\n",
+      "['cart', 'hart', 'hard', 'lard']\n",
+      "['cart', 'hart', 'hard', 'ward']\n",
+      "['cart', 'hart', 'hard', 'yard']\n",
+      "['cart', 'hart', 'hard', 'herd']\n",
+      "['cart', 'hart', 'hard', 'hand']\n",
+      "['cart', 'hart', 'hard', 'hare']\n",
+      "['cart', 'hart', 'hard', 'hark']\n",
+      "['cart', 'hart', 'hard', 'harm']\n",
+      "['cart', 'hart', 'hard', 'harp']\n",
+      "['cart', 'hart', 'hare', 'bare']\n",
+      "['cart', 'hart', 'hare', 'care']\n",
+      "['cart', 'hart', 'hare', 'dare']\n",
+      "['cart', 'hart', 'hare', 'fare']\n",
+      "['cart', 'hart', 'hare', 'mare']\n",
+      "['cart', 'hart', 'hare', 'pare']\n",
+      "['cart', 'hart', 'hare', 'rare']\n",
+      "['cart', 'hart', 'hare', 'tare']\n",
+      "['cart', 'hart', 'hare', 'ware']\n",
+      "['cart', 'hart', 'hare', 'here']\n",
+      "['cart', 'hart', 'hare', 'hire']\n",
+      "['cart', 'hart', 'hare', 'hake']\n",
+      "['cart', 'hart', 'hare', 'hale']\n",
+      "['cart', 'hart', 'hare', 'hate']\n",
+      "['cart', 'hart', 'hare', 'have']\n",
+      "['cart', 'hart', 'hare', 'haze']\n",
+      "['cart', 'hart', 'hare', 'hard']\n",
+      "['cart', 'hart', 'hare', 'hark']\n",
+      "['cart', 'hart', 'hare', 'harm']\n",
+      "['cart', 'hart', 'hare', 'harp']\n",
+      "['cart', 'hart', 'hark', 'bark']\n",
+      "['cart', 'hart', 'hark', 'dark']\n",
+      "['cart', 'hart', 'hark', 'lark']\n",
+      "['cart', 'hart', 'hark', 'mark']\n",
+      "['cart', 'hart', 'hark', 'nark']\n",
+      "['cart', 'hart', 'hark', 'park']\n",
+      "['cart', 'hart', 'hark', 'hack']\n",
+      "['cart', 'hart', 'hark', 'hank']\n",
+      "['cart', 'hart', 'hark', 'hawk']\n",
+      "['cart', 'hart', 'hark', 'hard']\n",
+      "['cart', 'hart', 'hark', 'hare']\n",
+      "['cart', 'hart', 'hark', 'harm']\n",
+      "['cart', 'hart', 'hark', 'harp']\n",
+      "['cart', 'hart', 'harm', 'farm']\n",
+      "['cart', 'hart', 'harm', 'warm']\n",
+      "['cart', 'hart', 'harm', 'hard']\n",
+      "['cart', 'hart', 'harm', 'hare']\n",
+      "['cart', 'hart', 'harm', 'hark']\n",
+      "['cart', 'hart', 'harm', 'harp']\n",
+      "['cart', 'hart', 'harp', 'carp']\n",
+      "['cart', 'hart', 'harp', 'tarp']\n",
+      "['cart', 'hart', 'harp', 'warp']\n",
+      "['cart', 'hart', 'harp', 'hasp']\n",
+      "['cart', 'hart', 'harp', 'hard']\n",
+      "['cart', 'hart', 'harp', 'hare']\n",
+      "['cart', 'hart', 'harp', 'hark']\n",
+      "['cart', 'hart', 'harp', 'harm']\n",
+      "['cart', 'mart', 'dart', 'hart']\n",
+      "['cart', 'mart', 'dart', 'part']\n",
+      "['cart', 'mart', 'dart', 'tart']\n",
+      "['cart', 'mart', 'dart', 'wart']\n",
+      "['cart', 'mart', 'dart', 'dirt']\n",
+      "['cart', 'mart', 'dart', 'daft']\n",
+      "['cart', 'mart', 'dart', 'dare']\n",
+      "['cart', 'mart', 'dart', 'dark']\n",
+      "['cart', 'mart', 'dart', 'darn']\n",
+      "['cart', 'mart', 'hart', 'dart']\n",
+      "['cart', 'mart', 'hart', 'part']\n",
+      "['cart', 'mart', 'hart', 'tart']\n",
+      "['cart', 'mart', 'hart', 'wart']\n",
+      "['cart', 'mart', 'hart', 'hurt']\n",
+      "['cart', 'mart', 'hart', 'haft']\n",
+      "['cart', 'mart', 'hart', 'halt']\n",
+      "['cart', 'mart', 'hart', 'hard']\n",
+      "['cart', 'mart', 'hart', 'hare']\n",
+      "['cart', 'mart', 'hart', 'hark']\n",
+      "['cart', 'mart', 'hart', 'harm']\n",
+      "['cart', 'mart', 'hart', 'harp']\n",
+      "['cart', 'mart', 'part', 'dart']\n",
+      "['cart', 'mart', 'part', 'hart']\n",
+      "['cart', 'mart', 'part', 'tart']\n",
+      "['cart', 'mart', 'part', 'wart']\n",
+      "['cart', 'mart', 'part', 'pert']\n",
+      "['cart', 'mart', 'part', 'port']\n",
+      "['cart', 'mart', 'part', 'pact']\n",
+      "['cart', 'mart', 'part', 'pant']\n",
+      "['cart', 'mart', 'part', 'past']\n",
+      "['cart', 'mart', 'part', 'pare']\n",
+      "['cart', 'mart', 'part', 'park']\n",
+      "['cart', 'mart', 'part', 'pars']\n",
+      "['cart', 'mart', 'tart', 'dart']\n",
+      "['cart', 'mart', 'tart', 'hart']\n",
+      "['cart', 'mart', 'tart', 'part']\n",
+      "['cart', 'mart', 'tart', 'wart']\n",
+      "['cart', 'mart', 'tart', 'tort']\n",
+      "['cart', 'mart', 'tart', 'tact']\n",
+      "['cart', 'mart', 'tart', 'taut']\n",
+      "['cart', 'mart', 'tart', 'tare']\n",
+      "['cart', 'mart', 'tart', 'taro']\n",
+      "['cart', 'mart', 'tart', 'tarp']\n",
+      "['cart', 'mart', 'tart', 'tars']\n",
+      "['cart', 'mart', 'wart', 'dart']\n",
+      "['cart', 'mart', 'wart', 'hart']\n",
+      "['cart', 'mart', 'wart', 'part']\n",
+      "['cart', 'mart', 'wart', 'tart']\n",
+      "['cart', 'mart', 'wart', 'waft']\n",
+      "['cart', 'mart', 'wart', 'wait']\n",
+      "['cart', 'mart', 'wart', 'want']\n",
+      "['cart', 'mart', 'wart', 'watt']\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['cart', 'mart', 'wart', 'ward']\n",
+      "['cart', 'mart', 'wart', 'ware']\n",
+      "['cart', 'mart', 'wart', 'warm']\n",
+      "['cart', 'mart', 'wart', 'warn']\n",
+      "['cart', 'mart', 'wart', 'warp']\n",
+      "['cart', 'mart', 'wart', 'wars']\n",
+      "['cart', 'mart', 'wart', 'wary']\n",
+      "['cart', 'mart', 'malt', 'halt']\n",
+      "['cart', 'mart', 'malt', 'salt']\n",
+      "['cart', 'mart', 'malt', 'melt']\n",
+      "['cart', 'mart', 'malt', 'mast']\n",
+      "['cart', 'mart', 'malt', 'matt']\n",
+      "['cart', 'mart', 'malt', 'male']\n",
+      "['cart', 'mart', 'malt', 'mall']\n",
+      "['cart', 'mart', 'mast', 'bast']\n",
+      "['cart', 'mart', 'mast', 'cast']\n",
+      "['cart', 'mart', 'mast', 'east']\n",
+      "['cart', 'mart', 'mast', 'fast']\n",
+      "['cart', 'mart', 'mast', 'last']\n",
+      "['cart', 'mart', 'mast', 'past']\n",
+      "['cart', 'mart', 'mast', 'vast']\n",
+      "['cart', 'mart', 'mast', 'mist']\n",
+      "['cart', 'mart', 'mast', 'most']\n",
+      "['cart', 'mart', 'mast', 'must']\n",
+      "['cart', 'mart', 'mast', 'malt']\n",
+      "['cart', 'mart', 'mast', 'matt']\n",
+      "['cart', 'mart', 'mast', 'mash']\n",
+      "['cart', 'mart', 'mast', 'mask']\n",
+      "['cart', 'mart', 'mast', 'mass']\n",
+      "['cart', 'mart', 'matt', 'watt']\n",
+      "['cart', 'mart', 'matt', 'mitt']\n",
+      "['cart', 'mart', 'matt', 'mutt']\n",
+      "['cart', 'mart', 'matt', 'malt']\n",
+      "['cart', 'mart', 'matt', 'mast']\n",
+      "['cart', 'mart', 'matt', 'mate']\n",
+      "['cart', 'mart', 'matt', 'math']\n",
+      "['cart', 'mart', 'matt', 'mats']\n",
+      "['cart', 'mart', 'mare', 'bare']\n",
+      "['cart', 'mart', 'mare', 'care']\n",
+      "['cart', 'mart', 'mare', 'dare']\n",
+      "['cart', 'mart', 'mare', 'fare']\n",
+      "['cart', 'mart', 'mare', 'hare']\n",
+      "['cart', 'mart', 'mare', 'pare']\n",
+      "['cart', 'mart', 'mare', 'rare']\n",
+      "['cart', 'mart', 'mare', 'tare']\n",
+      "['cart', 'mart', 'mare', 'ware']\n",
+      "['cart', 'mart', 'mare', 'mere']\n",
+      "['cart', 'mart', 'mare', 'mire']\n",
+      "['cart', 'mart', 'mare', 'more']\n",
+      "['cart', 'mart', 'mare', 'mace']\n",
+      "['cart', 'mart', 'mare', 'made']\n",
+      "['cart', 'mart', 'mare', 'make']\n",
+      "['cart', 'mart', 'mare', 'male']\n",
+      "['cart', 'mart', 'mare', 'mane']\n",
+      "['cart', 'mart', 'mare', 'mate']\n",
+      "['cart', 'mart', 'mare', 'maze']\n",
+      "['cart', 'mart', 'mare', 'mark']\n",
+      "['cart', 'mart', 'mare', 'mars']\n",
+      "['cart', 'mart', 'mark', 'bark']\n",
+      "['cart', 'mart', 'mark', 'dark']\n",
+      "['cart', 'mart', 'mark', 'hark']\n",
+      "['cart', 'mart', 'mark', 'lark']\n",
+      "['cart', 'mart', 'mark', 'nark']\n",
+      "['cart', 'mart', 'mark', 'park']\n",
+      "['cart', 'mart', 'mark', 'murk']\n",
+      "['cart', 'mart', 'mark', 'mask']\n",
+      "['cart', 'mart', 'mark', 'mare']\n",
+      "['cart', 'mart', 'mark', 'mars']\n",
+      "['cart', 'mart', 'mars', 'bars']\n",
+      "['cart', 'mart', 'mars', 'cars']\n",
+      "['cart', 'mart', 'mars', 'ears']\n",
+      "['cart', 'mart', 'mars', 'jars']\n",
+      "['cart', 'mart', 'mars', 'oars']\n",
+      "['cart', 'mart', 'mars', 'pars']\n",
+      "['cart', 'mart', 'mars', 'tars']\n",
+      "['cart', 'mart', 'mars', 'wars']\n",
+      "['cart', 'mart', 'mars', 'mads']\n",
+      "['cart', 'mart', 'mars', 'mans']\n",
+      "['cart', 'mart', 'mars', 'maps']\n",
+      "['cart', 'mart', 'mars', 'mass']\n",
+      "['cart', 'mart', 'mars', 'mats']\n",
+      "['cart', 'mart', 'mars', 'maws']\n",
+      "['cart', 'mart', 'mars', 'mare']\n",
+      "['cart', 'mart', 'mars', 'mark']\n",
+      "['cart', 'part', 'dart', 'hart']\n",
+      "['cart', 'part', 'dart', 'mart']\n",
+      "['cart', 'part', 'dart', 'tart']\n",
+      "['cart', 'part', 'dart', 'wart']\n",
+      "['cart', 'part', 'dart', 'dirt']\n",
+      "['cart', 'part', 'dart', 'daft']\n",
+      "['cart', 'part', 'dart', 'dare']\n",
+      "['cart', 'part', 'dart', 'dark']\n",
+      "['cart', 'part', 'dart', 'darn']\n",
+      "['cart', 'part', 'hart', 'dart']\n",
+      "['cart', 'part', 'hart', 'mart']\n",
+      "['cart', 'part', 'hart', 'tart']\n",
+      "['cart', 'part', 'hart', 'wart']\n",
+      "['cart', 'part', 'hart', 'hurt']\n",
+      "['cart', 'part', 'hart', 'haft']\n",
+      "['cart', 'part', 'hart', 'halt']\n",
+      "['cart', 'part', 'hart', 'hard']\n",
+      "['cart', 'part', 'hart', 'hare']\n",
+      "['cart', 'part', 'hart', 'hark']\n",
+      "['cart', 'part', 'hart', 'harm']\n",
+      "['cart', 'part', 'hart', 'harp']\n",
+      "['cart', 'part', 'mart', 'dart']\n",
+      "['cart', 'part', 'mart', 'hart']\n",
+      "['cart', 'part', 'mart', 'tart']\n",
+      "['cart', 'part', 'mart', 'wart']\n",
+      "['cart', 'part', 'mart', 'malt']\n",
+      "['cart', 'part', 'mart', 'mast']\n",
+      "['cart', 'part', 'mart', 'matt']\n",
+      "['cart', 'part', 'mart', 'mare']\n",
+      "['cart', 'part', 'mart', 'mark']\n",
+      "['cart', 'part', 'mart', 'mars']\n",
+      "['cart', 'part', 'tart', 'dart']\n",
+      "['cart', 'part', 'tart', 'hart']\n",
+      "['cart', 'part', 'tart', 'mart']\n",
+      "['cart', 'part', 'tart', 'wart']\n",
+      "['cart', 'part', 'tart', 'tort']\n",
+      "['cart', 'part', 'tart', 'tact']\n",
+      "['cart', 'part', 'tart', 'taut']\n",
+      "['cart', 'part', 'tart', 'tare']\n",
+      "['cart', 'part', 'tart', 'taro']\n",
+      "['cart', 'part', 'tart', 'tarp']\n",
+      "['cart', 'part', 'tart', 'tars']\n",
+      "['cart', 'part', 'wart', 'dart']\n",
+      "['cart', 'part', 'wart', 'hart']\n",
+      "['cart', 'part', 'wart', 'mart']\n",
+      "['cart', 'part', 'wart', 'tart']\n",
+      "['cart', 'part', 'wart', 'waft']\n",
+      "['cart', 'part', 'wart', 'wait']\n",
+      "['cart', 'part', 'wart', 'want']\n",
+      "['cart', 'part', 'wart', 'watt']\n",
+      "['cart', 'part', 'wart', 'ward']\n",
+      "['cart', 'part', 'wart', 'ware']\n",
+      "['cart', 'part', 'wart', 'warm']\n",
+      "['cart', 'part', 'wart', 'warn']\n",
+      "['cart', 'part', 'wart', 'warp']\n",
+      "['cart', 'part', 'wart', 'wars']\n",
+      "['cart', 'part', 'wart', 'wary']\n",
+      "['cart', 'part', 'pert', 'port']\n",
+      "['cart', 'part', 'pert', 'peat']\n",
+      "['cart', 'part', 'pert', 'pelt']\n",
+      "['cart', 'part', 'pert', 'pent']\n",
+      "['cart', 'part', 'pert', 'pest']\n",
+      "['cart', 'part', 'pert', 'perk']\n",
+      "['cart', 'part', 'pert', 'perm']\n",
+      "['cart', 'part', 'port', 'fort']\n",
+      "['cart', 'part', 'port', 'sort']\n",
+      "['cart', 'part', 'port', 'tort']\n",
+      "['cart', 'part', 'port', 'pert']\n",
+      "['cart', 'part', 'port', 'poet']\n",
+      "['cart', 'part', 'port', 'post']\n",
+      "['cart', 'part', 'port', 'pout']\n",
+      "['cart', 'part', 'port', 'pore']\n",
+      "['cart', 'part', 'port', 'pork']\n",
+      "['cart', 'part', 'port', 'porn']\n",
+      "['cart', 'part', 'pact', 'fact']\n",
+      "['cart', 'part', 'pact', 'tact']\n",
+      "['cart', 'part', 'pact', 'pant']\n",
+      "['cart', 'part', 'pact', 'past']\n",
+      "['cart', 'part', 'pact', 'pace']\n",
+      "['cart', 'part', 'pact', 'pack']\n",
+      "['cart', 'part', 'pant', 'cant']\n",
+      "['cart', 'part', 'pant', 'rant']\n",
+      "['cart', 'part', 'pant', 'want']\n",
+      "['cart', 'part', 'pant', 'pent']\n",
+      "['cart', 'part', 'pant', 'pint']\n",
+      "['cart', 'part', 'pant', 'punt']\n",
+      "['cart', 'part', 'pant', 'pact']\n",
+      "['cart', 'part', 'pant', 'past']\n",
+      "['cart', 'part', 'pant', 'pane']\n",
+      "['cart', 'part', 'pant', 'pang']\n",
+      "['cart', 'part', 'pant', 'pans']\n",
+      "['cart', 'part', 'past', 'bast']\n",
+      "['cart', 'part', 'past', 'cast']\n",
+      "['cart', 'part', 'past', 'east']\n",
+      "['cart', 'part', 'past', 'fast']\n",
+      "['cart', 'part', 'past', 'last']\n",
+      "['cart', 'part', 'past', 'mast']\n",
+      "['cart', 'part', 'past', 'vast']\n",
+      "['cart', 'part', 'past', 'pest']\n",
+      "['cart', 'part', 'past', 'post']\n",
+      "['cart', 'part', 'past', 'psst']\n",
+      "['cart', 'part', 'past', 'pact']\n",
+      "['cart', 'part', 'past', 'pant']\n",
+      "['cart', 'part', 'past', 'pass']\n",
+      "['cart', 'part', 'pare', 'bare']\n",
+      "['cart', 'part', 'pare', 'care']\n",
+      "['cart', 'part', 'pare', 'dare']\n",
+      "['cart', 'part', 'pare', 'fare']\n",
+      "['cart', 'part', 'pare', 'hare']\n",
+      "['cart', 'part', 'pare', 'mare']\n",
+      "['cart', 'part', 'pare', 'rare']\n",
+      "['cart', 'part', 'pare', 'tare']\n",
+      "['cart', 'part', 'pare', 'ware']\n",
+      "['cart', 'part', 'pare', 'pore']\n",
+      "['cart', 'part', 'pare', 'pure']\n",
+      "['cart', 'part', 'pare', 'pyre']\n",
+      "['cart', 'part', 'pare', 'pace']\n",
+      "['cart', 'part', 'pare', 'page']\n",
+      "['cart', 'part', 'pare', 'pale']\n",
+      "['cart', 'part', 'pare', 'pane']\n",
+      "['cart', 'part', 'pare', 'pate']\n",
+      "['cart', 'part', 'pare', 'pave']\n",
+      "['cart', 'part', 'pare', 'park']\n",
+      "['cart', 'part', 'pare', 'pars']\n",
+      "['cart', 'part', 'park', 'bark']\n",
+      "['cart', 'part', 'park', 'dark']\n",
+      "['cart', 'part', 'park', 'hark']\n",
+      "['cart', 'part', 'park', 'lark']\n",
+      "['cart', 'part', 'park', 'mark']\n",
+      "['cart', 'part', 'park', 'nark']\n",
+      "['cart', 'part', 'park', 'perk']\n",
+      "['cart', 'part', 'park', 'pork']\n",
+      "['cart', 'part', 'park', 'pack']\n",
+      "['cart', 'part', 'park', 'pare']\n",
+      "['cart', 'part', 'park', 'pars']\n",
+      "['cart', 'part', 'pars', 'bars']\n",
+      "['cart', 'part', 'pars', 'cars']\n",
+      "['cart', 'part', 'pars', 'ears']\n",
+      "['cart', 'part', 'pars', 'jars']\n",
+      "['cart', 'part', 'pars', 'mars']\n",
+      "['cart', 'part', 'pars', 'oars']\n",
+      "['cart', 'part', 'pars', 'tars']\n",
+      "['cart', 'part', 'pars', 'wars']\n",
+      "['cart', 'part', 'pars', 'pads']\n",
+      "['cart', 'part', 'pars', 'pals']\n",
+      "['cart', 'part', 'pars', 'pans']\n",
+      "['cart', 'part', 'pars', 'paps']\n",
+      "['cart', 'part', 'pars', 'pass']\n",
+      "['cart', 'part', 'pars', 'pats']\n",
+      "['cart', 'part', 'pars', 'paws']\n",
+      "['cart', 'part', 'pars', 'pays']\n",
+      "['cart', 'part', 'pars', 'pare']\n",
+      "['cart', 'part', 'pars', 'park']\n",
+      "['cart', 'tart', 'dart', 'hart']\n",
+      "['cart', 'tart', 'dart', 'mart']\n",
+      "['cart', 'tart', 'dart', 'part']\n",
+      "['cart', 'tart', 'dart', 'wart']\n",
+      "['cart', 'tart', 'dart', 'dirt']\n",
+      "['cart', 'tart', 'dart', 'daft']\n",
+      "['cart', 'tart', 'dart', 'dare']\n",
+      "['cart', 'tart', 'dart', 'dark']\n",
+      "['cart', 'tart', 'dart', 'darn']\n",
+      "['cart', 'tart', 'hart', 'dart']\n",
+      "['cart', 'tart', 'hart', 'mart']\n",
+      "['cart', 'tart', 'hart', 'part']\n",
+      "['cart', 'tart', 'hart', 'wart']\n",
+      "['cart', 'tart', 'hart', 'hurt']\n",
+      "['cart', 'tart', 'hart', 'haft']\n",
+      "['cart', 'tart', 'hart', 'halt']\n",
+      "['cart', 'tart', 'hart', 'hard']\n",
+      "['cart', 'tart', 'hart', 'hare']\n",
+      "['cart', 'tart', 'hart', 'hark']\n",
+      "['cart', 'tart', 'hart', 'harm']\n",
+      "['cart', 'tart', 'hart', 'harp']\n",
+      "['cart', 'tart', 'mart', 'dart']\n",
+      "['cart', 'tart', 'mart', 'hart']\n",
+      "['cart', 'tart', 'mart', 'part']\n",
+      "['cart', 'tart', 'mart', 'wart']\n",
+      "['cart', 'tart', 'mart', 'malt']\n",
+      "['cart', 'tart', 'mart', 'mast']\n",
+      "['cart', 'tart', 'mart', 'matt']\n",
+      "['cart', 'tart', 'mart', 'mare']\n",
+      "['cart', 'tart', 'mart', 'mark']\n",
+      "['cart', 'tart', 'mart', 'mars']\n",
+      "['cart', 'tart', 'part', 'dart']\n",
+      "['cart', 'tart', 'part', 'hart']\n",
+      "['cart', 'tart', 'part', 'mart']\n",
+      "['cart', 'tart', 'part', 'wart']\n",
+      "['cart', 'tart', 'part', 'pert']\n",
+      "['cart', 'tart', 'part', 'port']\n",
+      "['cart', 'tart', 'part', 'pact']\n",
+      "['cart', 'tart', 'part', 'pant']\n",
+      "['cart', 'tart', 'part', 'past']\n",
+      "['cart', 'tart', 'part', 'pare']\n",
+      "['cart', 'tart', 'part', 'park']\n",
+      "['cart', 'tart', 'part', 'pars']\n",
+      "['cart', 'tart', 'wart', 'dart']\n",
+      "['cart', 'tart', 'wart', 'hart']\n",
+      "['cart', 'tart', 'wart', 'mart']\n",
+      "['cart', 'tart', 'wart', 'part']\n",
+      "['cart', 'tart', 'wart', 'waft']\n",
+      "['cart', 'tart', 'wart', 'wait']\n",
+      "['cart', 'tart', 'wart', 'want']\n",
+      "['cart', 'tart', 'wart', 'watt']\n",
+      "['cart', 'tart', 'wart', 'ward']\n",
+      "['cart', 'tart', 'wart', 'ware']\n",
+      "['cart', 'tart', 'wart', 'warm']\n",
+      "['cart', 'tart', 'wart', 'warn']\n",
+      "['cart', 'tart', 'wart', 'warp']\n",
+      "['cart', 'tart', 'wart', 'wars']\n",
+      "['cart', 'tart', 'wart', 'wary']\n",
+      "['cart', 'tart', 'tort', 'fort']\n",
+      "['cart', 'tart', 'tort', 'port']\n",
+      "['cart', 'tart', 'tort', 'sort']\n",
+      "['cart', 'tart', 'tort', 'toot']\n",
+      "['cart', 'tart', 'tort', 'tost']\n",
+      "['cart', 'tart', 'tort', 'tout']\n",
+      "['cart', 'tart', 'tort', 'tore']\n",
+      "['cart', 'tart', 'tort', 'torn']\n",
+      "['cart', 'tart', 'tort', 'tors']\n",
+      "['cart', 'tart', 'tact', 'fact']\n",
+      "['cart', 'tart', 'tact', 'pact']\n",
+      "['cart', 'tart', 'tact', 'taut']\n",
+      "['cart', 'tart', 'tact', 'tack']\n",
+      "['cart', 'tart', 'tact', 'taco']\n",
+      "['cart', 'tart', 'taut', 'tout']\n",
+      "['cart', 'tart', 'taut', 'tact']\n",
+      "['cart', 'tart', 'tare', 'bare']\n",
+      "['cart', 'tart', 'tare', 'care']\n",
+      "['cart', 'tart', 'tare', 'dare']\n",
+      "['cart', 'tart', 'tare', 'fare']\n",
+      "['cart', 'tart', 'tare', 'hare']\n",
+      "['cart', 'tart', 'tare', 'mare']\n",
+      "['cart', 'tart', 'tare', 'pare']\n",
+      "['cart', 'tart', 'tare', 'rare']\n",
+      "['cart', 'tart', 'tare', 'ware']\n",
+      "['cart', 'tart', 'tare', 'tire']\n",
+      "['cart', 'tart', 'tare', 'tore']\n",
+      "['cart', 'tart', 'tare', 'tyre']\n",
+      "['cart', 'tart', 'tare', 'take']\n",
+      "['cart', 'tart', 'tare', 'tale']\n",
+      "['cart', 'tart', 'tare', 'tame']\n",
+      "['cart', 'tart', 'tare', 'tape']\n",
+      "['cart', 'tart', 'tare', 'taro']\n",
+      "['cart', 'tart', 'tare', 'tarp']\n",
+      "['cart', 'tart', 'tare', 'tars']\n",
+      "['cart', 'tart', 'taro', 'tiro']\n",
+      "['cart', 'tart', 'taro', 'tyro']\n",
+      "['cart', 'tart', 'taro', 'taco']\n",
+      "['cart', 'tart', 'taro', 'tare']\n",
+      "['cart', 'tart', 'taro', 'tarp']\n",
+      "['cart', 'tart', 'taro', 'tars']\n",
+      "['cart', 'tart', 'tarp', 'carp']\n",
+      "['cart', 'tart', 'tarp', 'harp']\n",
+      "['cart', 'tart', 'tarp', 'warp']\n",
+      "['cart', 'tart', 'tarp', 'tamp']\n",
+      "['cart', 'tart', 'tarp', 'tare']\n",
+      "['cart', 'tart', 'tarp', 'taro']\n",
+      "['cart', 'tart', 'tarp', 'tars']\n",
+      "['cart', 'tart', 'tars', 'bars']\n",
+      "['cart', 'tart', 'tars', 'cars']\n",
+      "['cart', 'tart', 'tars', 'ears']\n",
+      "['cart', 'tart', 'tars', 'jars']\n",
+      "['cart', 'tart', 'tars', 'mars']\n",
+      "['cart', 'tart', 'tars', 'oars']\n",
+      "['cart', 'tart', 'tars', 'pars']\n",
+      "['cart', 'tart', 'tars', 'wars']\n",
+      "['cart', 'tart', 'tars', 'tors']\n",
+      "['cart', 'tart', 'tars', 'tabs']\n",
+      "['cart', 'tart', 'tars', 'tads']\n",
+      "['cart', 'tart', 'tars', 'tags']\n",
+      "['cart', 'tart', 'tars', 'tams']\n",
+      "['cart', 'tart', 'tars', 'tans']\n",
+      "['cart', 'tart', 'tars', 'taps']\n",
+      "['cart', 'tart', 'tars', 'tats']\n",
+      "['cart', 'tart', 'tars', 'tare']\n",
+      "['cart', 'tart', 'tars', 'taro']\n",
+      "['cart', 'tart', 'tars', 'tarp']\n",
+      "['cart', 'wart', 'dart', 'hart']\n",
+      "['cart', 'wart', 'dart', 'mart']\n",
+      "['cart', 'wart', 'dart', 'part']\n",
+      "['cart', 'wart', 'dart', 'tart']\n",
+      "['cart', 'wart', 'dart', 'dirt']\n",
+      "['cart', 'wart', 'dart', 'daft']\n",
+      "['cart', 'wart', 'dart', 'dare']\n",
+      "['cart', 'wart', 'dart', 'dark']\n",
+      "['cart', 'wart', 'dart', 'darn']\n",
+      "['cart', 'wart', 'hart', 'dart']\n",
+      "['cart', 'wart', 'hart', 'mart']\n",
+      "['cart', 'wart', 'hart', 'part']\n",
+      "['cart', 'wart', 'hart', 'tart']\n",
+      "['cart', 'wart', 'hart', 'hurt']\n",
+      "['cart', 'wart', 'hart', 'haft']\n",
+      "['cart', 'wart', 'hart', 'halt']\n",
+      "['cart', 'wart', 'hart', 'hard']\n",
+      "['cart', 'wart', 'hart', 'hare']\n",
+      "['cart', 'wart', 'hart', 'hark']\n",
+      "['cart', 'wart', 'hart', 'harm']\n",
+      "['cart', 'wart', 'hart', 'harp']\n",
+      "['cart', 'wart', 'mart', 'dart']\n",
+      "['cart', 'wart', 'mart', 'hart']\n",
+      "['cart', 'wart', 'mart', 'part']\n",
+      "['cart', 'wart', 'mart', 'tart']\n",
+      "['cart', 'wart', 'mart', 'malt']\n",
+      "['cart', 'wart', 'mart', 'mast']\n",
+      "['cart', 'wart', 'mart', 'matt']\n",
+      "['cart', 'wart', 'mart', 'mare']\n",
+      "['cart', 'wart', 'mart', 'mark']\n",
+      "['cart', 'wart', 'mart', 'mars']\n",
+      "['cart', 'wart', 'part', 'dart']\n",
+      "['cart', 'wart', 'part', 'hart']\n",
+      "['cart', 'wart', 'part', 'mart']\n",
+      "['cart', 'wart', 'part', 'tart']\n",
+      "['cart', 'wart', 'part', 'pert']\n",
+      "['cart', 'wart', 'part', 'port']\n",
+      "['cart', 'wart', 'part', 'pact']\n",
+      "['cart', 'wart', 'part', 'pant']\n",
+      "['cart', 'wart', 'part', 'past']\n",
+      "['cart', 'wart', 'part', 'pare']\n",
+      "['cart', 'wart', 'part', 'park']\n",
+      "['cart', 'wart', 'part', 'pars']\n",
+      "['cart', 'wart', 'tart', 'dart']\n",
+      "['cart', 'wart', 'tart', 'hart']\n",
+      "['cart', 'wart', 'tart', 'mart']\n",
+      "['cart', 'wart', 'tart', 'part']\n",
+      "['cart', 'wart', 'tart', 'tort']\n",
+      "['cart', 'wart', 'tart', 'tact']\n",
+      "['cart', 'wart', 'tart', 'taut']\n",
+      "['cart', 'wart', 'tart', 'tare']\n",
+      "['cart', 'wart', 'tart', 'taro']\n",
+      "['cart', 'wart', 'tart', 'tarp']\n",
+      "['cart', 'wart', 'tart', 'tars']\n",
+      "['cart', 'wart', 'waft', 'daft']\n",
+      "['cart', 'wart', 'waft', 'haft']\n",
+      "['cart', 'wart', 'waft', 'raft']\n",
+      "['cart', 'wart', 'waft', 'weft']\n",
+      "['cart', 'wart', 'waft', 'wait']\n",
+      "['cart', 'wart', 'waft', 'want']\n",
+      "['cart', 'wart', 'waft', 'watt']\n",
+      "['cart', 'wart', 'wait', 'bait']\n",
+      "['cart', 'wart', 'wait', 'gait']\n",
+      "['cart', 'wart', 'wait', 'whit']\n",
+      "['cart', 'wart', 'wait', 'writ']\n",
+      "['cart', 'wart', 'wait', 'waft']\n",
+      "['cart', 'wart', 'wait', 'want']\n",
+      "['cart', 'wart', 'wait', 'watt']\n",
+      "['cart', 'wart', 'wait', 'waif']\n",
+      "['cart', 'wart', 'wait', 'wail']\n",
+      "['cart', 'wart', 'want', 'cant']\n",
+      "['cart', 'wart', 'want', 'pant']\n",
+      "['cart', 'wart', 'want', 'rant']\n",
+      "['cart', 'wart', 'want', 'went']\n",
+      "['cart', 'wart', 'want', 'wont']\n",
+      "['cart', 'wart', 'want', 'waft']\n",
+      "['cart', 'wart', 'want', 'wait']\n",
+      "['cart', 'wart', 'want', 'watt']\n",
+      "['cart', 'wart', 'want', 'wand']\n",
+      "['cart', 'wart', 'want', 'wane']\n",
+      "['cart', 'wart', 'watt', 'matt']\n",
+      "['cart', 'wart', 'watt', 'waft']\n",
+      "['cart', 'wart', 'watt', 'wait']\n",
+      "['cart', 'wart', 'watt', 'want']\n",
+      "['cart', 'wart', 'ward', 'bard']\n",
+      "['cart', 'wart', 'ward', 'card']\n",
+      "['cart', 'wart', 'ward', 'hard']\n",
+      "['cart', 'wart', 'ward', 'lard']\n",
+      "['cart', 'wart', 'ward', 'yard']\n",
+      "['cart', 'wart', 'ward', 'word']\n",
+      "['cart', 'wart', 'ward', 'wand']\n",
+      "['cart', 'wart', 'ward', 'ware']\n",
+      "['cart', 'wart', 'ward', 'warm']\n",
+      "['cart', 'wart', 'ward', 'warn']\n",
+      "['cart', 'wart', 'ward', 'warp']\n",
+      "['cart', 'wart', 'ward', 'wars']\n",
+      "['cart', 'wart', 'ward', 'wary']\n",
+      "['cart', 'wart', 'ware', 'bare']\n",
+      "['cart', 'wart', 'ware', 'care']\n",
+      "['cart', 'wart', 'ware', 'dare']\n",
+      "['cart', 'wart', 'ware', 'fare']\n",
+      "['cart', 'wart', 'ware', 'hare']\n",
+      "['cart', 'wart', 'ware', 'mare']\n",
+      "['cart', 'wart', 'ware', 'pare']\n",
+      "['cart', 'wart', 'ware', 'rare']\n",
+      "['cart', 'wart', 'ware', 'tare']\n",
+      "['cart', 'wart', 'ware', 'were']\n",
+      "['cart', 'wart', 'ware', 'wire']\n",
+      "['cart', 'wart', 'ware', 'wore']\n",
+      "['cart', 'wart', 'ware', 'wade']\n",
+      "['cart', 'wart', 'ware', 'wage']\n",
+      "['cart', 'wart', 'ware', 'wake']\n",
+      "['cart', 'wart', 'ware', 'wale']\n",
+      "['cart', 'wart', 'ware', 'wane']\n",
+      "['cart', 'wart', 'ware', 'wave']\n",
+      "['cart', 'wart', 'ware', 'ward']\n",
+      "['cart', 'wart', 'ware', 'warm']\n",
+      "['cart', 'wart', 'ware', 'warn']\n",
+      "['cart', 'wart', 'ware', 'warp']\n",
+      "['cart', 'wart', 'ware', 'wars']\n",
+      "['cart', 'wart', 'ware', 'wary']\n",
+      "['cart', 'wart', 'warm', 'farm']\n",
+      "['cart', 'wart', 'warm', 'harm']\n",
+      "['cart', 'wart', 'warm', 'worm']\n",
+      "['cart', 'wart', 'warm', 'ward']\n",
+      "['cart', 'wart', 'warm', 'ware']\n",
+      "['cart', 'wart', 'warm', 'warn']\n",
+      "['cart', 'wart', 'warm', 'warp']\n",
+      "['cart', 'wart', 'warm', 'wars']\n",
+      "['cart', 'wart', 'warm', 'wary']\n",
+      "['cart', 'wart', 'warn', 'barn']\n",
+      "['cart', 'wart', 'warn', 'darn']\n",
+      "['cart', 'wart', 'warn', 'earn']\n",
+      "['cart', 'wart', 'warn', 'yarn']\n",
+      "['cart', 'wart', 'warn', 'worn']\n",
+      "['cart', 'wart', 'warn', 'ward']\n",
+      "['cart', 'wart', 'warn', 'ware']\n",
+      "['cart', 'wart', 'warn', 'warm']\n",
+      "['cart', 'wart', 'warn', 'warp']\n",
+      "['cart', 'wart', 'warn', 'wars']\n",
+      "['cart', 'wart', 'warn', 'wary']\n",
+      "['cart', 'wart', 'warp', 'carp']\n",
+      "['cart', 'wart', 'warp', 'harp']\n",
+      "['cart', 'wart', 'warp', 'tarp']\n",
+      "['cart', 'wart', 'warp', 'wasp']\n",
+      "['cart', 'wart', 'warp', 'ward']\n",
+      "['cart', 'wart', 'warp', 'ware']\n",
+      "['cart', 'wart', 'warp', 'warm']\n",
+      "['cart', 'wart', 'warp', 'warn']\n",
+      "['cart', 'wart', 'warp', 'wars']\n",
+      "['cart', 'wart', 'warp', 'wary']\n",
+      "['cart', 'wart', 'wars', 'bars']\n",
+      "['cart', 'wart', 'wars', 'cars']\n",
+      "['cart', 'wart', 'wars', 'ears']\n",
+      "['cart', 'wart', 'wars', 'jars']\n",
+      "['cart', 'wart', 'wars', 'mars']\n",
+      "['cart', 'wart', 'wars', 'oars']\n",
+      "['cart', 'wart', 'wars', 'pars']\n",
+      "['cart', 'wart', 'wars', 'tars']\n",
+      "['cart', 'wart', 'wars', 'wads']\n",
+      "['cart', 'wart', 'wars', 'wags']\n",
+      "['cart', 'wart', 'wars', 'ways']\n",
+      "['cart', 'wart', 'wars', 'ward']\n",
+      "['cart', 'wart', 'wars', 'ware']\n",
+      "['cart', 'wart', 'wars', 'warm']\n",
+      "['cart', 'wart', 'wars', 'warn']\n",
+      "['cart', 'wart', 'wars', 'warp']\n",
+      "['cart', 'wart', 'wars', 'wary']\n",
+      "['cart', 'wart', 'wary', 'nary']\n",
+      "['cart', 'wart', 'wary', 'vary']\n",
+      "['cart', 'wart', 'wary', 'wiry']\n",
+      "['cart', 'wart', 'wary', 'wavy']\n",
+      "['cart', 'wart', 'wary', 'waxy']\n",
+      "['cart', 'wart', 'wary', 'ward']\n",
+      "['cart', 'wart', 'wary', 'ware']\n",
+      "['cart', 'wart', 'wary', 'warm']\n",
+      "['cart', 'wart', 'wary', 'warn']\n",
+      "['cart', 'wart', 'wary', 'warp']\n",
+      "['cart', 'wart', 'wary', 'wars']\n",
+      "['cart', 'curt', 'hurt', 'hart']\n",
+      "['cart', 'curt', 'hurt', 'hunt']\n",
+      "['cart', 'curt', 'hurt', 'hurl']\n",
+      "['cart', 'curt', 'cult', 'colt']\n",
+      "['cart', 'curt', 'cult', 'cull']\n",
+      "['cart', 'curt', 'curb', 'curd']\n",
+      "['cart', 'curt', 'curb', 'cure']\n",
+      "['cart', 'curt', 'curb', 'curl']\n",
+      "['cart', 'curt', 'curb', 'curs']\n",
+      "['cart', 'curt', 'curd', 'turd']\n",
+      "['cart', 'curt', 'curd', 'card']\n",
+      "['cart', 'curt', 'curd', 'cord']\n",
+      "['cart', 'curt', 'curd', 'cued']\n",
+      "['cart', 'curt', 'curd', 'curb']\n",
+      "['cart', 'curt', 'curd', 'cure']\n",
+      "['cart', 'curt', 'curd', 'curl']\n",
+      "['cart', 'curt', 'curd', 'curs']\n",
+      "['cart', 'curt', 'cure', 'lure']\n",
+      "['cart', 'curt', 'cure', 'pure']\n",
+      "['cart', 'curt', 'cure', 'sure']\n",
+      "['cart', 'curt', 'cure', 'care']\n",
+      "['cart', 'curt', 'cure', 'core']\n",
+      "['cart', 'curt', 'cure', 'cube']\n",
+      "['cart', 'curt', 'cure', 'cute']\n",
+      "['cart', 'curt', 'cure', 'curb']\n",
+      "['cart', 'curt', 'cure', 'curd']\n",
+      "['cart', 'curt', 'cure', 'curl']\n",
+      "['cart', 'curt', 'cure', 'curs']\n",
+      "['cart', 'curt', 'curl', 'furl']\n",
+      "['cart', 'curt', 'curl', 'hurl']\n",
+      "['cart', 'curt', 'curl', 'purl']\n",
+      "['cart', 'curt', 'curl', 'cull']\n",
+      "['cart', 'curt', 'curl', 'curb']\n",
+      "['cart', 'curt', 'curl', 'curd']\n",
+      "['cart', 'curt', 'curl', 'cure']\n",
+      "['cart', 'curt', 'curl', 'curs']\n",
+      "['cart', 'curt', 'curs', 'burs']\n",
+      "['cart', 'curt', 'curs', 'furs']\n",
+      "['cart', 'curt', 'curs', 'ours']\n",
+      "['cart', 'curt', 'curs', 'cars']\n",
+      "['cart', 'curt', 'curs', 'cubs']\n",
+      "['cart', 'curt', 'curs', 'cuds']\n",
+      "['cart', 'curt', 'curs', 'cues']\n",
+      "['cart', 'curt', 'curs', 'cums']\n",
+      "['cart', 'curt', 'curs', 'cups']\n",
+      "['cart', 'curt', 'curs', 'cuss']\n",
+      "['cart', 'curt', 'curs', 'cuts']\n",
+      "['cart', 'curt', 'curs', 'curb']\n",
+      "['cart', 'curt', 'curs', 'curd']\n",
+      "['cart', 'curt', 'curs', 'cure']\n",
+      "['cart', 'curt', 'curs', 'curl']\n",
+      "['cart', 'cant', 'pant', 'rant']\n",
+      "['cart', 'cant', 'pant', 'want']\n",
+      "['cart', 'cant', 'pant', 'pent']\n",
+      "['cart', 'cant', 'pant', 'pint']\n",
+      "['cart', 'cant', 'pant', 'punt']\n",
+      "['cart', 'cant', 'pant', 'pact']\n",
+      "['cart', 'cant', 'pant', 'part']\n",
+      "['cart', 'cant', 'pant', 'past']\n",
+      "['cart', 'cant', 'pant', 'pane']\n",
+      "['cart', 'cant', 'pant', 'pang']\n",
+      "['cart', 'cant', 'pant', 'pans']\n",
+      "['cart', 'cant', 'rant', 'pant']\n",
+      "['cart', 'cant', 'rant', 'want']\n",
+      "['cart', 'cant', 'rant', 'rent']\n",
+      "['cart', 'cant', 'rant', 'runt']\n",
+      "['cart', 'cant', 'rant', 'raft']\n",
+      "['cart', 'cant', 'rant', 'rapt']\n",
+      "['cart', 'cant', 'rant', 'rang']\n",
+      "['cart', 'cant', 'rant', 'rank']\n",
+      "['cart', 'cant', 'want', 'pant']\n",
+      "['cart', 'cant', 'want', 'rant']\n",
+      "['cart', 'cant', 'want', 'went']\n",
+      "['cart', 'cant', 'want', 'wont']\n",
+      "['cart', 'cant', 'want', 'waft']\n",
+      "['cart', 'cant', 'want', 'wait']\n",
+      "['cart', 'cant', 'want', 'wart']\n",
+      "['cart', 'cant', 'want', 'watt']\n",
+      "['cart', 'cant', 'want', 'wand']\n",
+      "['cart', 'cant', 'want', 'wane']\n",
+      "['cart', 'cant', 'cent', 'bent']\n",
+      "['cart', 'cant', 'cent', 'dent']\n",
+      "['cart', 'cant', 'cent', 'gent']\n",
+      "['cart', 'cant', 'cent', 'lent']\n",
+      "['cart', 'cant', 'cent', 'pent']\n",
+      "['cart', 'cant', 'cent', 'rent']\n",
+      "['cart', 'cant', 'cent', 'sent']\n",
+      "['cart', 'cant', 'cent', 'tent']\n",
+      "['cart', 'cant', 'cent', 'vent']\n",
+      "['cart', 'cant', 'cent', 'went']\n",
+      "['cart', 'cant', 'cast', 'bast']\n",
+      "['cart', 'cant', 'cast', 'east']\n",
+      "['cart', 'cant', 'cast', 'fast']\n",
+      "['cart', 'cant', 'cast', 'last']\n",
+      "['cart', 'cant', 'cast', 'mast']\n",
+      "['cart', 'cant', 'cast', 'past']\n",
+      "['cart', 'cant', 'cast', 'vast']\n",
+      "['cart', 'cant', 'cast', 'cost']\n",
+      "['cart', 'cant', 'cast', 'cyst']\n",
+      "['cart', 'cant', 'cast', 'case']\n",
+      "['cart', 'cant', 'cast', 'cash']\n",
+      "['cart', 'cant', 'cast', 'cask']\n",
+      "['cart', 'cant', 'cane', 'bane']\n",
+      "['cart', 'cant', 'cane', 'lane']\n",
+      "['cart', 'cant', 'cane', 'mane']\n",
+      "['cart', 'cant', 'cane', 'pane']\n",
+      "['cart', 'cant', 'cane', 'sane']\n",
+      "['cart', 'cant', 'cane', 'vane']\n",
+      "['cart', 'cant', 'cane', 'wane']\n",
+      "['cart', 'cant', 'cane', 'cone']\n",
+      "['cart', 'cant', 'cane', 'cafe']\n",
+      "['cart', 'cant', 'cane', 'cage']\n",
+      "['cart', 'cant', 'cane', 'cake']\n",
+      "['cart', 'cant', 'cane', 'came']\n",
+      "['cart', 'cant', 'cane', 'cape']\n",
+      "['cart', 'cant', 'cane', 'care']\n",
+      "['cart', 'cant', 'cane', 'case']\n",
+      "['cart', 'cant', 'cane', 'cave']\n",
+      "['cart', 'cant', 'cane', 'cans']\n",
+      "['cart', 'cant', 'cans', 'bans']\n",
+      "['cart', 'cant', 'cans', 'fans']\n",
+      "['cart', 'cant', 'cans', 'mans']\n",
+      "['cart', 'cant', 'cans', 'pans']\n",
+      "['cart', 'cant', 'cans', 'sans']\n",
+      "['cart', 'cant', 'cans', 'tans']\n",
+      "['cart', 'cant', 'cans', 'vans']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['cart', 'cant', 'cans', 'vans']"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bfs_search('cart', 'vans', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['cart', 'cant', 'cane', 'vane']"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bfs_search('cart', 'vane')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['cart',\n",
+       " 'dart',\n",
+       " 'hart',\n",
+       " 'mart',\n",
+       " 'part',\n",
+       " 'tart',\n",
+       " 'wart',\n",
+       " 'waft',\n",
+       " 'daft',\n",
+       " 'haft',\n",
+       " 'raft',\n",
+       " 'rift',\n",
+       " 'gift',\n",
+       " 'lift',\n",
+       " 'sift',\n",
+       " 'soft',\n",
+       " 'loft',\n",
+       " 'left',\n",
+       " 'deft',\n",
+       " 'heft',\n",
+       " 'weft',\n",
+       " 'welt',\n",
+       " 'belt',\n",
+       " 'felt',\n",
+       " 'gelt',\n",
+       " 'melt',\n",
+       " 'pelt',\n",
+       " 'peat',\n",
+       " 'beat',\n",
+       " 'feat',\n",
+       " 'heat',\n",
+       " 'meat',\n",
+       " 'neat',\n",
+       " 'seat',\n",
+       " 'teat',\n",
+       " 'that',\n",
+       " 'chat',\n",
+       " 'shat',\n",
+       " 'what',\n",
+       " 'whet',\n",
+       " 'whit',\n",
+       " 'chit',\n",
+       " 'chic',\n",
+       " 'chid',\n",
+       " 'chin',\n",
+       " 'shin',\n",
+       " 'thin',\n",
+       " 'twin',\n",
+       " 'twig',\n",
+       " 'swig',\n",
+       " 'swag',\n",
+       " 'shag',\n",
+       " 'slag',\n",
+       " 'flag',\n",
+       " 'flog',\n",
+       " 'blog',\n",
+       " 'clog',\n",
+       " 'slog',\n",
+       " 'smog',\n",
+       " 'smug',\n",
+       " 'slug',\n",
+       " 'plug',\n",
+       " 'plum',\n",
+       " 'alum',\n",
+       " 'glum',\n",
+       " 'slum',\n",
+       " 'scum',\n",
+       " 'swum',\n",
+       " 'swam',\n",
+       " 'scam',\n",
+       " 'seam',\n",
+       " 'beam',\n",
+       " 'ream',\n",
+       " 'team',\n",
+       " 'tram',\n",
+       " 'cram',\n",
+       " 'dram',\n",
+       " 'gram',\n",
+       " 'pram',\n",
+       " 'prim',\n",
+       " 'brim',\n",
+       " 'grim',\n",
+       " 'trim',\n",
+       " 'trig',\n",
+       " 'brig',\n",
+       " 'brag',\n",
+       " 'crag',\n",
+       " 'drag',\n",
+       " 'drug',\n",
+       " 'drub',\n",
+       " 'grub',\n",
+       " 'grab',\n",
+       " 'crab',\n",
+       " 'drab',\n",
+       " 'draw',\n",
+       " 'craw',\n",
+       " 'claw',\n",
+       " 'flaw',\n",
+       " 'slaw',\n",
+       " 'slew',\n",
+       " 'blew',\n",
+       " 'clew',\n",
+       " 'flew',\n",
+       " 'flow',\n",
+       " 'blow',\n",
+       " 'glow',\n",
+       " 'slow',\n",
+       " 'scow',\n",
+       " 'show',\n",
+       " 'chow',\n",
+       " 'crow',\n",
+       " 'brow',\n",
+       " 'grow',\n",
+       " 'prow',\n",
+       " 'prod',\n",
+       " 'trod',\n",
+       " 'trot',\n",
+       " 'toot',\n",
+       " 'boot',\n",
+       " 'coot',\n",
+       " 'foot',\n",
+       " 'hoot',\n",
+       " 'loot',\n",
+       " 'moot',\n",
+       " 'root',\n",
+       " 'soot',\n",
+       " 'shot',\n",
+       " 'slot',\n",
+       " 'blot',\n",
+       " 'clot',\n",
+       " 'plot',\n",
+       " 'plod',\n",
+       " 'clod',\n",
+       " 'clad',\n",
+       " 'glad',\n",
+       " 'goad',\n",
+       " 'load',\n",
+       " 'road',\n",
+       " 'toad',\n",
+       " 'toed',\n",
+       " 'coed',\n",
+       " 'hoed',\n",
+       " 'heed',\n",
+       " 'deed',\n",
+       " 'feed',\n",
+       " 'geed',\n",
+       " 'need',\n",
+       " 'peed',\n",
+       " 'reed',\n",
+       " 'seed',\n",
+       " 'teed',\n",
+       " 'weed',\n",
+       " 'weld',\n",
+       " 'geld',\n",
+       " 'held',\n",
+       " 'meld',\n",
+       " 'veld',\n",
+       " 'vend',\n",
+       " 'bend',\n",
+       " 'fend',\n",
+       " 'lend',\n",
+       " 'mend',\n",
+       " 'rend',\n",
+       " 'send',\n",
+       " 'tend',\n",
+       " 'wend',\n",
+       " 'wand',\n",
+       " 'band',\n",
+       " 'hand',\n",
+       " 'land',\n",
+       " 'sand',\n",
+       " 'said',\n",
+       " 'laid',\n",
+       " 'maid',\n",
+       " 'paid',\n",
+       " 'raid',\n",
+       " 'rail',\n",
+       " 'bail',\n",
+       " 'fail',\n",
+       " 'hail',\n",
+       " 'jail',\n",
+       " 'mail',\n",
+       " 'nail',\n",
+       " 'pail',\n",
+       " 'sail',\n",
+       " 'tail',\n",
+       " 'wail',\n",
+       " 'wall',\n",
+       " 'ball',\n",
+       " 'call',\n",
+       " 'fall',\n",
+       " 'gall',\n",
+       " 'hall',\n",
+       " 'mall',\n",
+       " 'pall',\n",
+       " 'tall',\n",
+       " 'tell',\n",
+       " 'bell',\n",
+       " 'cell',\n",
+       " 'dell',\n",
+       " 'fell',\n",
+       " 'hell',\n",
+       " 'jell',\n",
+       " 'sell',\n",
+       " 'well',\n",
+       " 'yell',\n",
+       " 'yelp',\n",
+       " 'help',\n",
+       " 'kelp',\n",
+       " 'keep',\n",
+       " 'beep',\n",
+       " 'deep',\n",
+       " 'jeep',\n",
+       " 'peep',\n",
+       " 'seep',\n",
+       " 'veep',\n",
+       " 'weep',\n",
+       " 'week',\n",
+       " 'geek',\n",
+       " 'leek',\n",
+       " 'meek',\n",
+       " 'peek',\n",
+       " 'reek',\n",
+       " 'seek',\n",
+       " 'seem',\n",
+       " 'deem',\n",
+       " 'teem',\n",
+       " 'them',\n",
+       " 'thee',\n",
+       " 'tree',\n",
+       " 'free',\n",
+       " 'flee',\n",
+       " 'glee',\n",
+       " 'glue',\n",
+       " 'blue',\n",
+       " 'clue',\n",
+       " 'flue',\n",
+       " 'slue',\n",
+       " 'sloe',\n",
+       " 'aloe',\n",
+       " 'floe',\n",
+       " 'flop',\n",
+       " 'clop',\n",
+       " 'glop',\n",
+       " 'plop',\n",
+       " 'slop',\n",
+       " 'shop',\n",
+       " 'chop',\n",
+       " 'coop',\n",
+       " 'goop',\n",
+       " 'hoop',\n",
+       " 'loop',\n",
+       " 'poop',\n",
+       " 'prop',\n",
+       " 'crop',\n",
+       " 'drop',\n",
+       " 'drip',\n",
+       " 'grip',\n",
+       " 'trip',\n",
+       " 'trap',\n",
+       " 'tray',\n",
+       " 'bray',\n",
+       " 'dray',\n",
+       " 'fray',\n",
+       " 'gray',\n",
+       " 'pray',\n",
+       " 'play',\n",
+       " 'clay',\n",
+       " 'flay',\n",
+       " 'slay',\n",
+       " 'spay',\n",
+       " 'stay',\n",
+       " 'sway',\n",
+       " 'away',\n",
+       " 'awry',\n",
+       " 'aery',\n",
+       " 'eery',\n",
+       " 'very',\n",
+       " 'vary',\n",
+       " 'nary',\n",
+       " 'wary',\n",
+       " 'wiry',\n",
+       " 'airy',\n",
+       " 'airs',\n",
+       " 'firs',\n",
+       " 'sirs',\n",
+       " 'sics',\n",
+       " 'tics',\n",
+       " 'ties',\n",
+       " 'dies',\n",
+       " 'hies',\n",
+       " 'lies',\n",
+       " 'pies',\n",
+       " 'vies',\n",
+       " 'vied',\n",
+       " 'died',\n",
+       " 'hied',\n",
+       " 'lied',\n",
+       " 'pied',\n",
+       " 'tied',\n",
+       " 'tier',\n",
+       " 'bier',\n",
+       " 'pier',\n",
+       " 'peer',\n",
+       " 'beer',\n",
+       " 'deer',\n",
+       " 'jeer',\n",
+       " 'leer',\n",
+       " 'seer',\n",
+       " 'veer',\n",
+       " 'weer',\n",
+       " 'wear',\n",
+       " 'bear',\n",
+       " 'dear',\n",
+       " 'fear',\n",
+       " 'gear',\n",
+       " 'hear',\n",
+       " 'near',\n",
+       " 'pear',\n",
+       " 'rear',\n",
+       " 'sear',\n",
+       " 'tear',\n",
+       " 'year',\n",
+       " 'yeah',\n",
+       " 'yeas',\n",
+       " 'leas',\n",
+       " 'peas',\n",
+       " 'seas',\n",
+       " 'teas',\n",
+       " 'tees',\n",
+       " 'bees',\n",
+       " 'fees',\n",
+       " 'gees',\n",
+       " 'lees',\n",
+       " 'pees',\n",
+       " 'sees',\n",
+       " 'wees',\n",
+       " 'woes',\n",
+       " 'does',\n",
+       " 'foes',\n",
+       " 'goes',\n",
+       " 'hoes',\n",
+       " 'noes',\n",
+       " 'roes',\n",
+       " 'toes',\n",
+       " 'togs',\n",
+       " 'bogs',\n",
+       " 'cogs',\n",
+       " 'dogs',\n",
+       " 'fogs',\n",
+       " 'hogs',\n",
+       " 'jogs',\n",
+       " 'logs',\n",
+       " 'lags',\n",
+       " 'bags',\n",
+       " 'fags',\n",
+       " 'gags',\n",
+       " 'hags',\n",
+       " 'jags',\n",
+       " 'nags',\n",
+       " 'rags',\n",
+       " 'sags',\n",
+       " 'tags',\n",
+       " 'wags',\n",
+       " 'wigs',\n",
+       " 'digs',\n",
+       " 'figs',\n",
+       " 'gigs',\n",
+       " 'jigs',\n",
+       " 'pigs',\n",
+       " 'rigs',\n",
+       " 'rugs',\n",
+       " 'bugs',\n",
+       " 'hugs',\n",
+       " 'jugs',\n",
+       " 'lugs',\n",
+       " 'mugs',\n",
+       " 'pugs',\n",
+       " 'tugs',\n",
+       " 'tubs',\n",
+       " 'cubs',\n",
+       " 'dubs',\n",
+       " 'hubs',\n",
+       " 'nubs',\n",
+       " 'pubs',\n",
+       " 'rubs',\n",
+       " 'subs',\n",
+       " 'sobs',\n",
+       " 'bobs',\n",
+       " 'cobs',\n",
+       " 'fobs',\n",
+       " 'gobs',\n",
+       " 'hobs',\n",
+       " 'jobs',\n",
+       " 'lobs',\n",
+       " 'mobs',\n",
+       " 'robs',\n",
+       " 'ribs',\n",
+       " 'bibs',\n",
+       " 'fibs',\n",
+       " 'jibs',\n",
+       " 'nibs',\n",
+       " 'nabs',\n",
+       " 'cabs',\n",
+       " 'dabs',\n",
+       " 'gabs',\n",
+       " 'jabs',\n",
+       " 'labs',\n",
+       " 'tabs',\n",
+       " 'tads',\n",
+       " 'cads',\n",
+       " 'dads',\n",
+       " 'fads',\n",
+       " 'gads',\n",
+       " 'lads',\n",
+       " 'mads',\n",
+       " 'pads',\n",
+       " 'wads',\n",
+       " 'weds',\n",
+       " 'beds',\n",
+       " 'feds',\n",
+       " 'reds',\n",
+       " 'rids',\n",
+       " 'aids',\n",
+       " 'bids',\n",
+       " 'kids',\n",
+       " 'lids',\n",
+       " 'lips',\n",
+       " 'dips',\n",
+       " 'hips',\n",
+       " 'nips',\n",
+       " 'pips',\n",
+       " 'rips',\n",
+       " 'sips',\n",
+       " 'tips',\n",
+       " 'yips',\n",
+       " 'zips',\n",
+       " 'zaps',\n",
+       " 'caps',\n",
+       " 'gaps',\n",
+       " 'laps',\n",
+       " 'maps',\n",
+       " 'naps',\n",
+       " 'paps',\n",
+       " 'raps',\n",
+       " 'saps',\n",
+       " 'taps',\n",
+       " 'yaps',\n",
+       " 'yeps',\n",
+       " 'peps',\n",
+       " 'reps',\n",
+       " 'refs',\n",
+       " 'reis',\n",
+       " 'leis',\n",
+       " 'legs',\n",
+       " 'begs',\n",
+       " 'kegs',\n",
+       " 'megs',\n",
+       " 'pegs',\n",
+       " 'pens',\n",
+       " 'dens',\n",
+       " 'fens',\n",
+       " 'hens',\n",
+       " 'kens',\n",
+       " 'lens',\n",
+       " 'tens',\n",
+       " 'wens',\n",
+       " 'yens',\n",
+       " 'yews',\n",
+       " 'hews',\n",
+       " 'mews',\n",
+       " 'news',\n",
+       " 'pews',\n",
+       " 'sews',\n",
+       " 'saws',\n",
+       " 'caws',\n",
+       " 'haws',\n",
+       " 'jaws',\n",
+       " 'laws',\n",
+       " 'maws',\n",
+       " 'paws',\n",
+       " 'yaws',\n",
+       " 'yaks',\n",
+       " 'oaks',\n",
+       " 'oafs',\n",
+       " 'oars',\n",
+       " 'bars',\n",
+       " 'cars',\n",
+       " 'ears',\n",
+       " 'jars',\n",
+       " 'mars',\n",
+       " 'pars',\n",
+       " 'tars',\n",
+       " 'wars',\n",
+       " 'ways',\n",
+       " 'bays',\n",
+       " 'days',\n",
+       " 'gays',\n",
+       " 'hays',\n",
+       " 'jays',\n",
+       " 'lays',\n",
+       " 'nays',\n",
+       " 'pays',\n",
+       " 'rays',\n",
+       " 'says',\n",
+       " 'sacs',\n",
+       " 'secs',\n",
+       " 'sets',\n",
+       " 'bets',\n",
+       " 'gets',\n",
+       " 'jets',\n",
+       " 'lets',\n",
+       " 'nets',\n",
+       " 'pets',\n",
+       " 'vets',\n",
+       " 'wets',\n",
+       " 'wits',\n",
+       " 'bits',\n",
+       " 'fits',\n",
+       " 'hits',\n",
+       " 'kits',\n",
+       " 'nits',\n",
+       " 'pits',\n",
+       " 'sits',\n",
+       " 'tits',\n",
+       " 'tats',\n",
+       " 'bats',\n",
+       " 'cats',\n",
+       " 'eats',\n",
+       " 'fats',\n",
+       " 'hats',\n",
+       " 'lats',\n",
+       " 'mats',\n",
+       " 'oats',\n",
+       " 'pats',\n",
+       " 'rats',\n",
+       " 'vats',\n",
+       " 'vans',\n",
+       " 'bans',\n",
+       " 'cans',\n",
+       " 'fans',\n",
+       " 'mans',\n",
+       " 'pans',\n",
+       " 'sans',\n",
+       " 'tans',\n",
+       " 'tins',\n",
+       " 'bins',\n",
+       " 'dins',\n",
+       " 'fins',\n",
+       " 'gins',\n",
+       " 'pins',\n",
+       " 'sins',\n",
+       " 'wins',\n",
+       " 'wind',\n",
+       " 'bind',\n",
+       " 'find',\n",
+       " 'hind',\n",
+       " 'kind',\n",
+       " 'mind',\n",
+       " 'rind',\n",
+       " 'ring',\n",
+       " 'ding',\n",
+       " 'king',\n",
+       " 'ping',\n",
+       " 'sing',\n",
+       " 'ting',\n",
+       " 'wing',\n",
+       " 'wine',\n",
+       " 'dine',\n",
+       " 'fine',\n",
+       " 'line',\n",
+       " 'mine',\n",
+       " 'nine',\n",
+       " 'pine',\n",
+       " 'sine',\n",
+       " 'tine',\n",
+       " 'vine',\n",
+       " 'vane']"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dfs_search('cart', 'vane')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar_search(start, target, debug=False):\n",
+    "    return astar([(distance(start, target), [start])], target, debug=debug)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar(agenda, goal, debug=False):\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        _, current = heapq.heappop(agenda)\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            for s in successors:\n",
+    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['cart']\n",
+      "['cart', 'cant']\n",
+      "['cart', 'cant', 'cane']\n",
+      "['cart', 'cant', 'cane', 'vane']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['cart', 'cant', 'cane', 'vane']"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('cart', 'vane', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Mutually-reachable sets\n",
+    "\n",
+    "Find the transitive closure of the `neighbours` relation, so we can see which words can be transformed into which other words."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "94"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "candidates = [set([k] + neighbours[k]) for k in neighbours]\n",
+    "reachables = []\n",
+    "while candidates:\n",
+    "    current = set(candidates.pop())\n",
+    "    altered = False\n",
+    "    for other in candidates:\n",
+    "        if current.intersection(other):\n",
+    "            altered = True\n",
+    "            current.update(other)\n",
+    "            candidates.remove(other)\n",
+    "    if altered:\n",
+    "        candidates.append(current)\n",
+    "    else:\n",
+    "        reachables.append(current)\n",
+    "\n",
+    "len(reachables)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2204"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(max(reachables, key=len))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(min(reachables, key=len))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Counter({1: 75, 2: 6, 3: 7, 4: 2, 5: 2, 6: 1, 2204: 1})"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "collections.Counter(len(r) for r in reachables)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[5]"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'abbe' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[{'abbe', 'able', 'ably', 'ally', 'axle'}]"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[r for r in reachables if 'abbe' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['buns', 'bunk', 'punk']"
+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('buns', 'punk')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for a in reachables:\n",
+    "    for b in reachables:\n",
+    "        if a != b:\n",
+    "            if not a.isdisjoint(b):\n",
+    "                print(a, b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# longest_chain = []\n",
+    "# with open('all-chains-4.txt', 'w', 1) as f:\n",
+    "#     for ws in reachables:\n",
+    "#         for s in ws:\n",
+    "#             for t in ws:\n",
+    "#                 if s < t:\n",
+    "#                     chain = astar_search(s, t)\n",
+    "#                     if chain:\n",
+    "#                         f.write('{}\\n'.format(chain))\n",
+    "#                         if len(chain) > len(longest_chain):\n",
+    "#                             longest_chain = chain\n",
+    "\n",
+    "# longest_chain"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "bigset = max(reachables, key=len)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['over', 'ever', 'eves', 'eyes', 'dyes', 'does', 'toes', 'tors', 'tars', 'taro', 'tyro']\n",
+      "['aide', 'aids', 'bids', 'bits', 'bats', 'mats']\n",
+      "['miff', 'riff', 'rife', 'rise', 'risk', 'rusk']\n",
+      "['hims', 'hems', 'hens', 'lens', 'lent']\n",
+      "['tipi', 'tips', 'tits', 'tots', 'cots', 'cote']\n",
+      "['apex', 'aped', 'sped', 'sued', 'sues', 'subs', 'tubs', 'tabs', 'tabu']\n",
+      "['wino', 'wind', 'wild', 'gild', 'gilt']\n",
+      "['rasp', 'ramp', 'lamp', 'limp', 'limn']\n",
+      "['paps', 'caps', 'cars', 'card', 'cord', 'lord', 'loud']\n",
+      "['lava', 'lama', 'lamp', 'ramp']\n",
+      "['ways', 'bays', 'boys', 'boos', 'coos', 'coop', 'coup']\n",
+      "['boob', 'boor', 'boar', 'bear', 'beer', 'jeer', 'jeez']\n",
+      "['troy', 'trod', 'prod', 'plod', 'pled', 'pied', 'died', 'diet']\n",
+      "['vest', 'lest', 'less', 'loss', 'lows', 'rows']\n",
+      "['shop', 'shot', 'soot', 'sort', 'sore', 'sire', 'dire', 'dike']\n",
+      "['sing', 'zing']\n",
+      "['beak', 'beat', 'belt', 'welt', 'wilt', 'wily', 'oily', 'only']\n",
+      "['spry', 'spay', 'spas', 'seas', 'secs', 'sics', 'sirs', 'sire', 'tire', 'tiro']\n",
+      "['gosh', 'bosh', 'boss', 'bogs', 'begs', 'bees', 'byes']\n",
+      "['racy', 'race', 'rape', 'raps', 'saps', 'sops']\n"
+     ]
+    }
+   ],
+   "source": [
+    "for _ in range(20):\n",
+    "    start, goal = random.sample(bigset, 2)\n",
+    "    print(astar_search(start, goal))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['cops', 'coos', 'coon', 'coin', 'chin', 'thin', 'this', 'thus', 'thug']"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('cops', 'thug')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2204]"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'love' in r if 'hate' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['hate', 'have', 'hove', 'love']"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('hate', 'love')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['wars', 'ware', 'wave', 'wove', 'love']"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('wars', 'love')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['fear', 'feat', 'fest', 'lest', 'lost', 'lose', 'love']"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('fear', 'love')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['fail', 'fall', 'pall', 'pals', 'pass']"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('fail', 'pass')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['star', 'soar', 'boar', 'boor', 'boon', 'born']"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('star', 'born')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['open',\n",
+       " 'oven',\n",
+       " 'even',\n",
+       " 'eves',\n",
+       " 'eyes',\n",
+       " 'byes',\n",
+       " 'bees',\n",
+       " 'begs',\n",
+       " 'bags',\n",
+       " 'bass',\n",
+       " 'pass']"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('open', 'pass')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['bass',\n",
+       " 'lass',\n",
+       " 'mass',\n",
+       " 'sass',\n",
+       " 'puss',\n",
+       " 'pads',\n",
+       " 'pals',\n",
+       " 'pans',\n",
+       " 'paps',\n",
+       " 'pars',\n",
+       " 'pats',\n",
+       " 'paws',\n",
+       " 'pays',\n",
+       " 'past']"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "neighbours['pass']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1]"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'exam' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2204]"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'star' in r if 'born' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/word-chains/word-chain-solution.ipynb b/word-chains/word-chain-solution.ipynb
new file mode 100644 (file)
index 0000000..0052abc
--- /dev/null
+++ b/word-chains/word-chain-solution.ipynb
@@ -0,0 +1,583 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Word chains\n",
+    "\n",
+    "\"Word chain\" puzzles are where you transform one word into another, by changing one letter at a time, with all the intermediate steps being valid words. \n",
+    "\n",
+    "For instance, you can transform 'rash' to 'jags' like this:\n",
+    "\n",
+    "```\n",
+    "rash\n",
+    "Bash\n",
+    "basS\n",
+    "baGs\n",
+    "Jags\n",
+    "```\n",
+    "\n",
+    "(the capital letter is the one changed in each step).\n",
+    "\n",
+    "## Part 1\n",
+    "\n",
+    "Given this [list of words](words4.txt), what is the minimum number of steps to go from `vice` to `wars`?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import string\n",
+    "import heapq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2336"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "words = [w.strip() for w in open('words4.txt').readlines()]\n",
+    "len(words)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def adjacents(word):\n",
+    "    return [word[0:i] + l + word[i+1:]\n",
+    "           for i in range(len(word))\n",
+    "           for l in string.ascii_lowercase\n",
+    "           if l != word[i]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
+    "             for w in words}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def distance(w1, w2):\n",
+    "    return sum(1 for i in range(len(w1))\n",
+    "               if w1[i] != w2[i])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extend(chain):\n",
+    "    return [chain + [s] for s in neighbours[chain[-1]]\n",
+    "           if s not in chain]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search(start, target, debug=False):\n",
+    "    return bfs([[start]], target, debug=debug)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs(agenda, goal, debug=False):\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dfs_search(start, target, debug=False):\n",
+    "    return dfs([[start]], target, debug=debug)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dfs(agenda, goal, debug=False):\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = successors + agenda[1:]\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar_search(start, target, debug=False):\n",
+    "    agenda = [(distance(start, target), [start])]\n",
+    "    heapq.heapify(agenda)\n",
+    "    return astar(agenda, target, debug=debug)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar(agenda, goal, debug=False):\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        _, current = heapq.heappop(agenda)\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            for s in successors:\n",
+    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 60,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(astar_search('vice', 'wars'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(bfs_search('vice', 'wars'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "793"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(dfs_search('vice', 'wars'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10000 loops, best of 3: 154 µs per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 1min 40s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "bfs_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 86.3 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "dfs_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Part 2\n",
+    "\n",
+    "The example shows that `jags` is reachable in four steps from `rash`. There are 11 words one step away from `rash`: \n",
+    "`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, and `wash`. \n",
+    "\n",
+    "There are 47 words reachable in one or two steps from `rash`. They are `base`, `bash`, `bask`, `bass`, `bast`, `bath`, `bosh`, `bush`, `case`, `cash`, `cask`, `cast`, `dash`, `dish`, `gash`, `gasp`, `gosh`, `gush`, `hash`, `hasp`, `hath`, `hush`, `lash`, `lass`, `last`, `lath`, `lush`, `mash`, `mask`, `mass`, `mast`, `math`, `mesh`, `mush`, `push`, `ramp`, `rasp`, `ruse`, `rush`, `rusk`, `rust`, `sash`, `sass`, `tush`, `wash`, `wasp`, and `wish`.\n",
+    "\n",
+    "There are 180 words reachable in up to three steps from `rash`.\n",
+    "\n",
+    "How many words are reachable in up to ten steps from `vice`?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def reachable_in(word, n, trim_extras=False):\n",
+    "    reachable = set()\n",
+    "    boundary = set([word])\n",
+    "    for i in range(n):\n",
+    "        extras = set()\n",
+    "        for w in boundary:\n",
+    "            extras.update(neighbours[w])\n",
+    "        if trim_extras:\n",
+    "            extras.difference_update(reachable)\n",
+    "        reachable.update(boundary)\n",
+    "        boundary = extras.copy()\n",
+    "    return reachable.union(extras).difference(set([word]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(11,\n",
+       " '`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, `wash`')"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 1)), ', '.join(sorted('`{}`'.format(r) for r in reachable_in('rash', 1)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(47,\n",
+       " '`base`, `bash`, `bask`, `bass`, `bast`, `bath`, `bosh`, `bush`, `case`, `cash`, `cask`, `cast`, `dash`, `dish`, `gash`, `gasp`, `gosh`, `gush`, `hash`, `hasp`, `hath`, `hush`, `lash`, `lass`, `last`, `lath`, `lush`, `mash`, `mask`, `mass`, `mast`, `math`, `mesh`, `mush`, `push`, `ramp`, `rasp`, `ruse`, `rush`, `rusk`, `rust`, `sash`, `sass`, `tush`, `wash`, `wasp`, `wish`')"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 2)), ', '.join(sorted('`{}`'.format(r) for r in reachable_in('rash', 2)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "180"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 3))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2195"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 10))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2192"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('vice', 10))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "100 loops, best of 3: 5.97 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "len(reachable_in('rash', 10))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "100 loops, best of 3: 3.1 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "len(reachable_in('rash', 10, trim_extras=True))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/word-chains/words4.txt b/word-chains/words4.txt
new file mode 100644 (file)
index 0000000..028c8cf
--- /dev/null
+++ b/word-chains/words4.txt
@@ -0,0 +1,2336 @@
+abbe
+abed
+abet
+able
+ably
+abut
+aced
+aces
+ache
+achy
+acid
+acme
+acne
+acre
+acts
+adds
+adze
+aeon
+aery
+afar
+agar
+aged
+ages
+agog
+ague
+ahem
+ahoy
+aide
+aids
+ails
+aims
+airs
+airy
+ajar
+akin
+alas
+albs
+ales
+alga
+alit
+ally
+alms
+aloe
+also
+alto
+alum
+amen
+amid
+amir
+ammo
+amok
+amps
+anal
+anew
+ankh
+anon
+ante
+anti
+ants
+anus
+aped
+apes
+apex
+apse
+aqua
+arch
+arcs
+area
+ares
+aria
+arid
+arks
+arms
+army
+arts
+arty
+ashy
+asks
+asps
+atom
+atop
+auks
+aunt
+aura
+auto
+aver
+avid
+avow
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\ No newline at end of file