From: Neil Smith Date: Thu, 18 May 2017 16:17:06 +0000 (+0100) Subject: Done word chains puzzle X-Git-Url: https://git.njae.me.uk/?a=commitdiff_plain;h=a0fc23654a764a8fdec3fa9858b0453c58bc5f34;p=ou-summer-of-code-2017.git Done word chains puzzle --- diff --git a/word-chains/build-word-lists.ipynb b/word-chains/build-word-lists.ipynb new file mode 100644 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 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', 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'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", + 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'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 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 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 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