"source": [
"# Laser display boards\n",
"\n",
- "You need to navigate your way through Heathwick Airport to find the correct gate. The bad news is that all the display boards have gone down. The good news is that the terminal staff are handing out the machine-code instructions to generate the messages on the board. \n",
+ "You're off on your first sightseening trip of your holiday and you need to catch the right llama-rickshaw to get there. You arrive all keen at the llama-rickshaw station, only to find a scene of chaos. The bad news is that there are lots of llama-rickshaws heading to different places. The good news is that above each bay is a display board that shows where that llama-rickshaw is heading. The bad news is that all the display boards have gone down. The good news is that the station staff are handing out the machine-code instructions to generate the messages on the board. \n",
"\n",
"Given your l33t haxor skilz, it will be no problem to recreate the messages on the display boards.\n",
"\n",
"The board is grid, 80 pixels wide and 8 pixels tall, with row 1 being the top row and column 1 being the left column. The pixels are changed with these commands:\n",
"\n",
"* `top A B` switches the state of the pixels in the topmost row from columns A to B inclusive. If a pixel was lit, it becomes dark; if it was dark, it becomes lit.\n",
- "* `left A B` is similar, but works on the left edge, toggling the state of pixles in the leftmost column in rows A to B inclusive. \n",
+ "* `left A B` is similar, but works on the left edge, toggling the state of pixels in the leftmost column in rows A to B inclusive. \n",
"* `rotate column A B` rotates column A by B spaces down. Pixels that are moved beyond the bottom edge \"wrap around\" to the top edge.\n",
"* `rotate row A B` rotates row A by B spaces to the right. Pixels that are moved beyond the right edge \"wrap around\" to the left edge.\n",
"\n",
".*........\n",
"```\n",
"\n",
- "* `rotate column 8 1` moves the one lit pixel in column 8 down one row.\n",
+ "* `rotate column 8 5` moves the one lit pixel in column 8 down five rows, wrapping it all the way around the display and leaving the board with one lit pixel in that column one row lower.\n",
"```\n",
"*.....*.**\n",
".......*..\n",
"metadata": {},
"source": [
"## Part 1\n",
- "You're standing in front of gate 9¾. You have [the instructions](05-pixels.txt). How many pixels would be lit on the board, if it was working?"
+ "You're standing in front of gate 9¾. You have [the instructions](05-pixels.txt). How many pixels would be lit on the board, if it were working?"
]
},
{
--- /dev/null
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Given a sequence of {F|L|R}, each of which is \"move forward one step\", \"turn left, then move forward one step\", \"turn right, then move forward one step\":\n",
+ "1. which tours are closed?\n",
+ "2. what is the area enclosed by the tour?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 69,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import collections\n",
+ "import enum\n",
+ "import random"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "class Direction(enum.Enum):\n",
+ " UP = 1\n",
+ " RIGHT = 2\n",
+ " DOWN = 3\n",
+ " LEFT = 4\n",
+ " \n",
+ "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
+ " Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
+ "\n",
+ "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
+ " Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
+ "\n",
+ "def turn_left(d):\n",
+ " return turn_lefts[d]\n",
+ "\n",
+ "def turn_right(d):\n",
+ " return turn_rights[d]\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def advance(step, d):\n",
+ " if d == Direction.UP:\n",
+ " return Step(step.x, step.y+1, d)\n",
+ " elif d == Direction.DOWN:\n",
+ " return Step(step.x, step.y-1, d)\n",
+ " elif d == Direction.LEFT:\n",
+ " return Step(step.x-1, step.y, d)\n",
+ " elif d == Direction.RIGHT:\n",
+ " return Step(step.x+1, step.y, d)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def trace_tour(tour):\n",
+ " current = Step(0, 0, Direction.RIGHT)\n",
+ " trace = [current]\n",
+ " for s in tour:\n",
+ " if s == 'F':\n",
+ " current = advance(current, current.dir)\n",
+ " elif s == 'L':\n",
+ " current = advance(current, turn_left(current.dir))\n",
+ " elif s == 'R':\n",
+ " current = advance(current, turn_right(current.dir))\n",
+ " trace += [current]\n",
+ " return trace "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "k = Step(1, 2, 3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Step(x=1, y=2, dir=3)"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "k"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "__main__.Step"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Step"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<Direction.UP: 1>"
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "d = Direction.UP\n",
+ "d"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<Direction.RIGHT: 2>"
+ ]
+ },
+ "execution_count": 23,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "turn_right(d)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{<Direction.LEFT: 4>: <Direction.UP: 1>,\n",
+ " <Direction.UP: 1>: <Direction.RIGHT: 2>,\n",
+ " <Direction.DOWN: 3>: <Direction.LEFT: 4>,\n",
+ " <Direction.RIGHT: 2>: <Direction.DOWN: 3>}"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "turn_rights"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
+ " Step(x=2, y=1, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=2, y=2, dir=<Direction.UP: 1>)]"
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "trace_tour('FLRL')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=2, y=1, dir=<Direction.UP: 1>),\n",
+ " Step(x=3, y=1, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
+ " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=1, y=1, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
+ ]
+ },
+ "execution_count": 33,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "trace_tour('FFLRLLFLRL')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
+ " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-1, y=1, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-2, y=-1, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-1, y=-3, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=0, y=-3, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=-3, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=-2, dir=<Direction.UP: 1>),\n",
+ " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
+ " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-1, y=-1, dir=<Direction.UP: 1>),\n",
+ " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
+ " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
+ ]
+ },
+ "execution_count": 34,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "trace_tour('FLLFFLFFFLFFLFLLRRFR')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
+ " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
+ " Step(x=4, y=1, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
+ " Step(x=3, y=2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=0, y=2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=0, y=3, dir=<Direction.UP: 1>),\n",
+ " Step(x=0, y=4, dir=<Direction.UP: 1>),\n",
+ " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-1, y=3, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-2, y=3, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-2, y=2, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-1, y=2, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=-1, y=1, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=-1, y=-1, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
+ ]
+ },
+ "execution_count": 35,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 112,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def positions(trace):\n",
+ " return [(s.x, s.y) for s in trace]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 113,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[(0, 0),\n",
+ " (1, 0),\n",
+ " (2, 0),\n",
+ " (2, -1),\n",
+ " (3, -1),\n",
+ " (3, 0),\n",
+ " (3, 1),\n",
+ " (4, 1),\n",
+ " (4, 2),\n",
+ " (3, 2),\n",
+ " (2, 2),\n",
+ " (1, 2),\n",
+ " (0, 2),\n",
+ " (0, 3),\n",
+ " (0, 4),\n",
+ " (-1, 4),\n",
+ " (-1, 3),\n",
+ " (-2, 3),\n",
+ " (-2, 2),\n",
+ " (-1, 2),\n",
+ " (-1, 1),\n",
+ " (-2, 1),\n",
+ " (-2, 0),\n",
+ " (-1, 0),\n",
+ " (-1, -1),\n",
+ " (0, -1),\n",
+ " (0, 0)]"
+ ]
+ },
+ "execution_count": 113,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "positions(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 114,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def valid(trace):\n",
+ " return (trace[-1].x == 0 \n",
+ " and trace[-1].y == 0 \n",
+ " and len(set(positions(trace))) + 1 == len(trace))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 115,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "True"
+ ]
+ },
+ "execution_count": 115,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 116,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 116,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLLFF'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 117,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 117,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid(trace_tour('FFLLLFRR'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 118,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 118,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid(trace_tour('F'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 119,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "True"
+ ]
+ },
+ "execution_count": 119,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid(trace_tour('LLLL'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 120,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def chunks(items, n=2):\n",
+ " return [items[i:i+n] for i in range(len(items) - n + 1)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 121,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['abcdefg',\n",
+ " 'bcdefgh',\n",
+ " 'cdefghi',\n",
+ " 'defghij',\n",
+ " 'efghijk',\n",
+ " 'fghijkl',\n",
+ " 'ghijklm',\n",
+ " 'hijklmn',\n",
+ " 'ijklmno',\n",
+ " 'jklmnop',\n",
+ " 'klmnopq',\n",
+ " 'lmnopqr',\n",
+ " 'mnopqrs',\n",
+ " 'nopqrst',\n",
+ " 'opqrstu',\n",
+ " 'pqrstuv',\n",
+ " 'qrstuvw',\n",
+ " 'rstuvwx',\n",
+ " 'stuvwxy',\n",
+ " 'tuvwxyz']"
+ ]
+ },
+ "execution_count": 121,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "import string\n",
+ "chunks(string.ascii_lowercase, 7)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 122,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def shoelace(trace):\n",
+ " return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 123,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "4"
+ ]
+ },
+ "execution_count": 123,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "shoelace(trace_tour('FFLRLLFLRL'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 124,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "9"
+ ]
+ },
+ "execution_count": 124,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "shoelace(trace_tour('FLLFFLFFFLFFLFLLRRFR'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 125,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "15"
+ ]
+ },
+ "execution_count": 125,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "shoelace(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 329,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def step(s, current):\n",
+ " if s == 'F':\n",
+ " return advance(current, current.dir)\n",
+ " elif s == 'L':\n",
+ " return advance(current, turn_left(current.dir))\n",
+ " elif s == 'R':\n",
+ " return advance(current, turn_right(current.dir))\n",
+ " else:\n",
+ " raise ValueError"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 507,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def valid_prefix(tour):\n",
+ " current = Step(0, 0, Direction.RIGHT)\n",
+ " prefix = []\n",
+ " posns = []\n",
+ " for s in tour:\n",
+ " current = step(s, current)\n",
+ " prefix += [s]\n",
+ " if (current.x, current.y) in posns:\n",
+ " return ''\n",
+ " elif current.x == 0 and current.y == 0: \n",
+ " return ''.join(prefix)\n",
+ " posns += [(current.x, current.y)]\n",
+ " if current.x == 0 and current.y == 0:\n",
+ " return ''.join(prefix)\n",
+ " else:\n",
+ " return ''"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 552,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def mistake_positions(tour, debug=False):\n",
+ " mistakes = []\n",
+ " current = Step(0, 0, Direction.RIGHT)\n",
+ " posns = [(0, 0)]\n",
+ " for i, s in enumerate(tour):\n",
+ " current = step(s, current)\n",
+ " if (current.x, current.y) in posns:\n",
+ " if debug: print(i, current)\n",
+ " mistakes += [(i+1, current)]\n",
+ " posns += [(current.x, current.y)]\n",
+ " if (current.x, current.y) == (0, 0):\n",
+ " return mistakes[:-1]\n",
+ " else:\n",
+ " return mistakes + [(len(tour)+1, current)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 550,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def returns_to_origin(mistake_positions):\n",
+ " return [i for i, m in mistake_positions\n",
+ " if (m.x, m.y) == (0, 0)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 492,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 493,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'FFLRLLFLRL'"
+ ]
+ },
+ "execution_count": 493,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid_prefix(sample_tours[0])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 494,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "True"
+ ]
+ },
+ "execution_count": 494,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "all(valid_prefix(t) == t for t in sample_tours)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 495,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 495,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid_prefix(sample_tours[0] + 'FLLLL') == sample_tours[0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 526,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "9 Step(x=0, y=0, dir=<Direction.DOWN: 3>)\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "[(10, Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
+ " (12, Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
+ ]
+ },
+ "execution_count": 526,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "mistake_positions(sample_tours[0] + 'F')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 527,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "9 Step(x=0, y=0, dir=<Direction.DOWN: 3>)\n",
+ "12 Step(x=1, y=0, dir=<Direction.UP: 1>)\n",
+ "13 Step(x=0, y=0, dir=<Direction.LEFT: 4>)\n",
+ "14 Step(x=0, y=-1, dir=<Direction.DOWN: 3>)\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "[(10, Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
+ " (13, Step(x=1, y=0, dir=<Direction.UP: 1>)),\n",
+ " (14, Step(x=0, y=0, dir=<Direction.LEFT: 4>)),\n",
+ " (15, Step(x=0, y=-1, dir=<Direction.DOWN: 3>)),\n",
+ " (16, Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
+ ]
+ },
+ "execution_count": 527,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "mistake_positions(sample_tours[0] + 'FLLLL')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 528,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'FFLRLLFLRL'"
+ ]
+ },
+ "execution_count": 528,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "(sample_tours[0] + 'FLLLL')[:10]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def random_walk(steps=1000):\n",
+ " return ''.join(random.choice('FLR') for _ in range(steps))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 548,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "''"
+ ]
+ },
+ "execution_count": 548,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid_prefix(random_walk(1000))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 342,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'FLFFLRFRLFRRRR'"
+ ]
+ },
+ "execution_count": 342,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "valid_prefix(random_walk(1000), allowed_mistakes=1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 440,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "walks = []\n",
+ "while len(walks) < 10:\n",
+ " w = valid_prefix(random_walk())\n",
+ " if len(w) > 30: walks += [w]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 441,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['LFRRFLLRFLRLLRFLRLFLRFLFFFRLLRLL',\n",
+ " 'LRFFLFFFRLLRFRFFLRRFRLFLRFRLFRLRFFFF',\n",
+ " 'FFFLRFRLRLFLRLFLFFFFFRFFRLLFFFLRLFFLRF',\n",
+ " 'LFRLFFFFRLLRFFLLFFFRFFLLRFRLFLRFLF',\n",
+ " 'LFLRRFLLRRFRFLFFRFFFFRRLLRFLRFRRLF',\n",
+ " 'FLRLRLRFRLRFRLLFRFFRRLFRFLFLRRLR',\n",
+ " 'RFRRFFFFRLRFLFRRLRFFFFRRFFLLFFRF',\n",
+ " 'FFLFLRLFRLFFRFFLLFFRLLFRRLLRLFFF',\n",
+ " 'RFFLFRRLRRLRLLFRFRLLRRLRFRLLRRFFRLFFLR',\n",
+ " 'RFLFFLFRLFLRLFLRRLFFLRFLFLFRLLRF']"
+ ]
+ },
+ "execution_count": 441,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "walks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 350,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
+ " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
+ ]
+ },
+ "execution_count": 350,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "trace_tour('FLLL')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 147,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(-1, 3)"
+ ]
+ },
+ "execution_count": 147,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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aZghIUsMMAUlqmCEgSQ3rFAJJPpzkn5McTXLeceo2J9mb5IdJru3SpiSpP11nAnuA/wz8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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ef4c240>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline\n",
+ "plt.axis('on')\n",
+ "plt.arrow(0, 0, 0.8, 0, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
+ "plt.arrow(0.2, 0, 0, 1, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
+ "plt.xlim([-1, 2])\n",
+ "plt.ylim([-1, 3])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 135,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def bounds(trace):\n",
+ " return (max(s.x for s in trace),\n",
+ " max(s.y for s in trace),\n",
+ " min(s.x for s in trace),\n",
+ " min(s.y for s in trace))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 136,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(0, 2, -13, -13)"
+ ]
+ },
+ "execution_count": 136,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bounds(trace_tour('RFRFFLRFLFFRRFFRRRRLLLRRRRRRFRLFRFFRFFRRFRLRRFLLFRLLFRFLFLFRFRLLFRLFRFLRRLLFRRRFRRRRLLFLFRFRRFFRRLLLRLRRFRLRRFFRRFLFRRLLRRFFRFRRRRRFLLLLLRRFFFLLFFFRRLFLFFLRRRFRFLLFFRRLLRFLLRRF'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 148,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
+ " Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 214,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def plot_trace(trace):\n",
+ " plt.axis('on')\n",
+ " plt.axes().set_aspect('equal')\n",
+ " for s, t in chunks(trace, 2):\n",
+ " w, h = plot_wh[t.dir]\n",
+ " plt.arrow(s.x, s.y, w, h, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
+ " xh, yh, xl, yl = bounds(trace)\n",
+ " plt.xlim([xl-1, xh+1])\n",
+ " plt.ylim([yl-1, yh+1])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 514,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ef71c50>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 215,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ef505f8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour('FFFLLFFL'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 216,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=1, y=-1, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=1, y=-2, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=0, y=-2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-1, y=-3, dir=<Direction.DOWN: 3>),\n",
+ " Step(x=-2, y=-3, dir=<Direction.LEFT: 4>),\n",
+ " Step(x=-2, y=-2, dir=<Direction.UP: 1>),\n",
+ " Step(x=-2, y=-1, dir=<Direction.UP: 1>),\n",
+ " Step(x=-1, y=-1, dir=<Direction.RIGHT: 2>),\n",
+ " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
+ " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
+ ]
+ },
+ "execution_count": 216,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "trace_tour(walks[3])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 405,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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uvSSeEHJ5KC0tZcuWLZgZ1dXVrFy5MumROqRnh4hIAFTGIiIBUBmLiARAZSwiEgCVsYhI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\nsYhIAFTGIiIB+C+pi+rYc+DkNgAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85eaef0f0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(walks[3]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 442,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "10"
+ ]
+ },
+ "execution_count": 442,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "long_walks = [w for w in walks if len(w) >= 30]\n",
+ "len(long_walks)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 443,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ebd9f28>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[0]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 444,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc8640290b8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[1]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 445,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85eddf7b8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[2]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 446,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ef41048>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[3]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 447,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ef240f0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[4]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 448,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc87c3185c0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[5]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 449,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ec78198>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[6]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 450,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85f006a90>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[7]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 451,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85efd7208>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(long_walks[8]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 416,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['RFLRFFRFFFFRLRFRFFRLLFFFFFRRLRRL',\n",
+ " 'FFFFRFRLRLFRLRLRFRRLLFFRFRLFLRRFLRRL',\n",
+ " 'RLLRLFFFRFFLLRRLLFRLLRRFLLRRLLFFFFLRFLRF',\n",
+ " 'FFLRRLFRLFLFFFFLLRFRLFFFFLLRLRRL',\n",
+ " 'FLFRFLFRFFFLFRLFRLLFFLRRFLRLLFRLRLRRLLFFFRFLFLRLRL',\n",
+ " 'LRFRLRFLFFFFFRRFLRLRFRLRLFRLFFRRLR',\n",
+ " 'LRFLFLRLRRFLFFRRFFFLFRFFLRFRFLLRFFRRLLRFFRLRRFFLLRLR',\n",
+ " 'LFRLFFFRLLRLLFFRRLLRLFFFLRRLLFFL',\n",
+ " 'FLRFFLFFRLFRLLFRLLFFFRLFRRLFLFFL',\n",
+ " 'LLRFRLRRLRLFRFFFFRLRFFLRFFRLRRLFRFFL']"
+ ]
+ },
+ "execution_count": 416,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "walks"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 452,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85eaed1d0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour('FLFFLRFRLFRRRR'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 582,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(408, [8, 16, 20])"
+ ]
+ },
+ "execution_count": 582,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "w = random_walk()\n",
+ "ms = mistake_positions(w)\n",
+ "len(ms), returns_to_origin(ms)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 583,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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n5ua67FetPiVSQs+vmyAIgvAKGtgjFHeMn2qPv2rGH7V0wThhiHOu2TAcKBwN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\nCYIgIoz/D/EoAGQ0K3jsAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85ce54208>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(w))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 488,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "walks_m = {i: list() for i in range(4)}\n",
+ "while all(len(w_m) < 10 for w_m in walks_m.values()):\n",
+ " w = random_walk()\n",
+ " ps = mistake_positions(w)\n",
+ " if not ps or ps[0][0] > 30:\n",
+ " walks_m[0] += [w[:ps[0][0]]]\n",
+ " if len(ps) >= 2\n",
+ " \n",
+ " if len(w) > 30: \n",
+ " walks_m[i] += [w]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 489,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{0: ['LRLRLRLFRFLFFLRFRRLRLFLLRFLRRLLFFFLRLRLLRLF',\n",
+ " 'FFRLLFFFFRFLRFRLLRFFRFFFFFFLLRRLRRFFR',\n",
+ " 'LFRRFLLRFFLFRLRFLRRLLFRRFLFLRRFFLFFLRFFLFFLFLFRRR',\n",
+ " 'FLFLFFLRRFFFFLFRFFLFRFFLFFRLFRRR',\n",
+ " 'LLFLLRFFRLLFRFLFRLRFFRFFLFFLRLFRLLFLFF',\n",
+ " 'RFRRLRLLRRFLFFRRLRFFFLFRRLFLFLRRR',\n",
+ " 'FFLFFRFLFLRLFFLLFRRFFFRLLFFFRFFRRR',\n",
+ " 'LRRLFRFLRFFFFRLLRLRFLRFLLRRFRLLRFRLFLFLRRR',\n",
+ " 'LRLFLRRFLFRRLRFRFLFLRLLFRRFFRLRFLLFL',\n",
+ " 'RLRRLFLFRRLLFFRFRFLFFLRLFLRLRFLLFRFFFLRRFRFLFFRFLFRLFFRRR'],\n",
+ " 1: ['RRFLRRLLFLRLRRLFRLFFFRLLFRFLFRRLLLL',\n",
+ " 'LRLFFLRRFLLRLRRLLRLRFLRLFFLLLFLRRR',\n",
+ " 'RFRRLFRLRLRRFLLRFLFFLRRFLRRFRRL',\n",
+ " 'FFFRFLFRLFFLFLLLFLFFLRFFRFFFRRLRRLF',\n",
+ " 'FLFRFFRLLRFRLLRFFRFLFLFLRFFFLRRLLLF',\n",
+ " 'FRRLRLLFRFLRFRLRRFRFFFLRFFRLRFFLLFRFLRFFRLFRRLLL',\n",
+ " 'FFLRLRFLFLRRFFLFFRRRFRLFLFRRLLFRFRLLFFLLF',\n",
+ " 'FLRRFLRLFFFFRFLFLLLFFRFLFRLLFRRLLL',\n",
+ " 'RFFFRFLLRFFRFFFRRRFLRLFRFFLRLLFLF',\n",
+ " 'FFRFLFLLRRLRLFFRLFFLFRLFLRFFLLFFLF'],\n",
+ " 2: ['FFLRFRFRLFRFFFFLRFRLRFRLFLLLRLFLRLFLLRLR',\n",
+ " 'FFLFRLLRLRRFFRLFLRFFFFRLFLRFFLLLFRFLFRRLR',\n",
+ " 'RRLFRRFFFLLRFFLFFLFFLFLRFRLLRFFLFFLFRLLFRF',\n",
+ " 'FFRFLRLLRRFFRRLFFFFFFLLLFRFLFRFL',\n",
+ " 'FFRFFFLFLFRLRFRRLRLLFFLLLFLRFLRFLLLL',\n",
+ " 'FFFFFFFFFFFFFFLLFLFLFRLRFFLRFFRFLFRFLFRRLLRLRLRLFRFLFLLLL',\n",
+ " 'LFFRFFRFFFFRFRLFFRLFRLFFLLRFRLLFLRFLRRLLFR',\n",
+ " 'FRFRLRLLFFRFFLRFLRFRFLLFLRLFFLLL',\n",
+ " 'LRLLLLRFLRRFFLFRFRFFLFLLRRLFRLFRLFLFFFFFFRFRFLFRLFFLRFFLRFRRLLRFFRRLRRL',\n",
+ " 'FLRFLRLLRLRFRLRLLRFLFFLRLRLFRRRLLFLFFRFLLRLLRFLRLFRFLFRRR']}"
+ ]
+ },
+ "execution_count": 489,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "walks_m"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 490,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAALMAAAEACAYAAAD4PUecAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTwAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x7fc85eae9c88>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plot_trace(trace_tour(walks_m[0][0]))"
+ ]
+ },
+ {
+ "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
+}
+++ /dev/null
-{
- "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
-}
+++ /dev/null
-{
- "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, closed=None):\n",
- " if closed:\n",
- " nbrs = set(neighbours[chain[-1]]) - closed\n",
- " else:\n",
- " nbrs = neighbours[chain[-1]]\n",
- " return [chain + [s] for s in nbrs\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, goal, debug=False):\n",
- " agenda = [[start]]\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": 16,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def bfs_search_closed(start, goal, debug=False):\n",
- " agenda = [[start]]\n",
- " closed = set()\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",
- " closed.add(current[-1])\n",
- " successors = extend(current, closed)\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, goal, debug=False):\n",
- " agenda = [[start]]\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": 19,
- "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": 19,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "dfs_search('abbe', 'ally', debug=True)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "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"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "['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",
- "['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",
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- "['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",
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- "['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",
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- "['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"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "['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": 20,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bfs_search('cart', 'vans', debug=True)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['cart', 'cant', 'cane', 'vane']"
- ]
- },
- "execution_count": 21,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "bfs_search('cart', 'vane')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "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": 22,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "dfs_search('cart', 'vane')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def astar_search(start, goal, debug=False):\n",
- " agenda = [(distance(start, goal), [start])]\n",
- " heapq.heapify(agenda)\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": 24,
- "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": 24,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "astar_search('cart', 'vane', debug=True)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def astar_search_closed(start, goal, debug=False):\n",
- " agenda = [(distance(start, goal), [start])]\n",
- " heapq.heapify(agenda)\n",
- " closed = set()\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",
- " closed.add(current[-1])\n",
- " successors = extend(current, closed)\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_closed('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": 77,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "94"
- ]
- },
- "execution_count": 77,
- "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": 78,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "2204"
- ]
- },
- "execution_count": 78,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(max(reachables, key=len))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 79,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "1"
- ]
- },
- "execution_count": 79,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(min(reachables, key=len))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 80,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "Counter({1: 75, 2: 6, 3: 7, 4: 2, 5: 2, 6: 1, 2204: 1})"
- ]
- },
- "execution_count": 80,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "collections.Counter(len(r) for r in reachables)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 81,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "[5]"
- ]
- },
- "execution_count": 81,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "[len(r) for r in reachables if 'abbe' in r]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 82,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "[{'abbe', 'able', 'ably', 'ally', 'axle'}]"
- ]
- },
- "execution_count": 82,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "[r for r in reachables if 'abbe' in r]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 83,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['buns', 'bunk', 'punk']"
- ]
- },
- "execution_count": 83,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "astar_search('buns', 'punk')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 84,
- "metadata": {
- "collapsed": true
- },
- "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": 85,
- "metadata": {
- "collapsed": true
- },
- "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": 86,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "bigset = max(reachables, key=len)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 87,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "['late', 'lats', 'lets', 'leas', 'seas', 'seam', 'swam', 'sway']\n",
- "['leap', 'heap', 'hear', 'dear', 'deer']\n",
- "['peel', 'peek', 'perk', 'park', 'nark']\n",
- "['sing', 'sang', 'sand', 'said', 'sail', 'hail', 'haul']\n",
- "['vats', 'bats', 'bets', 'bees', 'been', 'teen', 'then', 'thin', 'this', 'thus', 'thud']\n",
- "['sues', 'sees', 'seen', 'sewn', 'hewn']\n",
- "['rash', 'bash', 'bast', 'bait', 'bail', 'hail', 'hair', 'heir']\n",
- "['apex', 'aped', 'sped', 'seed', 'deed', 'dead', 'deal', 'veal']\n",
- "['gulf', 'golf', 'gold', 'bold', 'bond', 'bony', 'tony']\n",
- "['snag', 'shag', 'shat', 'seat', 'peat', 'pent', 'pint', 'mint']\n",
- "['rife', 'rime', 'rims', 'rums', 'cums', 'cuss']\n",
- "['diss', 'kiss', 'kits']\n",
- "['gyps', 'gaps', 'gads', 'wads', 'wade', 'wide', 'tide']\n",
- "['bilk', 'bill', 'bell', 'tell', 'teal', 'tear', 'tzar']\n",
- "['logo', 'loge', 'lode', 'lade', 'jade', 'jape']\n",
- "['hunt', 'bunt', 'buns', 'nuns', 'nubs']\n",
- "['glow', 'glop', 'plop', 'prop', 'prep', 'peep', 'keep']\n",
- "['iamb', 'lamb', 'lams', 'laps', 'lips', 'pips']\n",
- "['pain', 'lain', 'laid', 'land', 'lend', 'vend', 'veld']\n",
- "['fake', 'bake', 'bare', 'bars', 'ears', 'errs', 'ergs', 'eggs', 'egos']\n"
- ]
- }
- ],
- "source": [
- "for _ in range(20):\n",
- " start, goal = random.sample(bigset, 2)\n",
- " print(astar_search_closed(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": 61,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
- "Wall time: 210 µs\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "5"
- ]
- },
- "execution_count": 61,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search('wars', 'love'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 62,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
- "Wall time: 252 µs\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "5"
- ]
- },
- "execution_count": 62,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search_closed('wars', 'love'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 63,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n",
- "Wall time: 24.2 ms\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "404"
- ]
- },
- "execution_count": 63,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(dfs_search('wars', 'love'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 64,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 5min 20s, sys: 76 ms, total: 5min 20s\n",
- "Wall time: 5min 20s\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "5"
- ]
- },
- "execution_count": 64,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(bfs_search('wars', 'love'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 65,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 1.44 s, sys: 0 ns, total: 1.44 s\n",
- "Wall time: 1.43 s\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "5"
- ]
- },
- "execution_count": 65,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(bfs_search_closed('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": 49,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1 loop, best of 3: 7.9 s per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "astar_search('bats', 'exit')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 50,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "10 loops, best of 3: 141 ms per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "astar_search_closed('bats', 'exit')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 51,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['bats',\n",
- " 'bans',\n",
- " 'band',\n",
- " 'sand',\n",
- " 'said',\n",
- " 'skid',\n",
- " 'skit',\n",
- " 'smit',\n",
- " 'emit',\n",
- " 'exit']"
- ]
- },
- "execution_count": 51,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "astar_search_closed('bats', 'exit')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 88,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "{2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
- " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
- " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
- " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
- " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
- " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
- " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
- " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
- " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
- " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
- " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
- " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
- " 14: [['chug', 'gaff'], ['atom', 'fizz']],\n",
- " 15: [['chug', 'oxen']]}"
- ]
- },
- "execution_count": 88,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "solutions = {}\n",
- "for _ in range(10000):\n",
- " start, goal = random.sample(bigset, 2)\n",
- " solution = astar_search_closed(start, goal)\n",
- " sl = len(solution)\n",
- " if sl not in solutions:\n",
- " solutions[sl] = []\n",
- " if len(solutions[sl]) < 4:\n",
- " solutions[sl].append([start, goal])\n",
- " \n",
- "# if len(solution) >= 10:\n",
- "# solutions += [solution]\n",
- " \n",
- "solutions"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 91,
- "metadata": {},
- "outputs": [],
- "source": [
- "solutions = {2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
- " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
- " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
- " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
- " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
- " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
- " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
- " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
- " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
- " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
- " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
- " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
- " 14: [['chug', 'gaff'], ['atom', 'fizz'], ['chug', 'jinn'], ['amen', 'flog'],\n",
- " ['buzz', 'grog'], ['imps', 'pros']],\n",
- " 15: [['chug', 'oxen'], ['amen', 'doff']]}"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 54,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "[('amen', 'doff', 15), ('chug', 'jinn', 14), ('amen', 'flog', 14)]"
- ]
- },
- "execution_count": 54,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "[(s[0], s[-1], len(s)) for s in solutions if len(s) >= 14]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 55,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1 loop, best of 3: 360 ms per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "astar_search_closed('blab', 'amen')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 56,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 384 ms, sys: 0 ns, total: 384 ms\n",
- "Wall time: 385 ms\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "14"
- ]
- },
- "execution_count": 56,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search_closed('blab', 'amen'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 57,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 124 ms, sys: 0 ns, total: 124 ms\n",
- "Wall time: 121 ms\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "15"
- ]
- },
- "execution_count": 57,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search_closed('amen', 'doff'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 58,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
- "Wall time: 32.4 ms\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "14"
- ]
- },
- "execution_count": 58,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search_closed('chug', 'jinn'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 59,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 16 ms, sys: 0 ns, total: 16 ms\n",
- "Wall time: 17.1 ms\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "14"
- ]
- },
- "execution_count": 59,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search_closed('amen', 'flog'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 73,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 268 ms, sys: 4 ms, total: 272 ms\n",
- "Wall time: 272 ms\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "14"
- ]
- },
- "execution_count": 73,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search_closed('buzz', 'grog'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 74,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "CPU times: user 64 ms, sys: 0 ns, total: 64 ms\n",
- "Wall time: 64.1 ms\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "14"
- ]
- },
- "execution_count": 74,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "%time len(astar_search_closed('imps', 'pros'))"
- ]
- },
- {
- "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
-}
+++ /dev/null
-{
- "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 extend(chain, closed=None):\n",
- " if closed:\n",
- " nbrs = set(neighbours[chain[-1]]) - closed\n",
- " else:\n",
- " nbrs = neighbours[chain[-1]]\n",
- " return [chain + [s] for s in nbrs\n",
- " if s not in chain]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def extend_raw(chain):\n",
- " nbrs = [w for w in adjacents(chain[-1]) if w in words]\n",
- " return [chain + [s] for s in nbrs\n",
- " if s not in chain]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def bfs_search(start, goal, debug=False):\n",
- " agenda = [[start]]\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": 19,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def bfs_search_closed(start, goal, debug=False):\n",
- " agenda = [[start]]\n",
- " closed = set()\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",
- " closed.add(current[-1])\n",
- " successors = extend(current, closed)\n",
- " agenda = agenda[1:] + successors\n",
- " if agenda:\n",
- " return current\n",
- " else:\n",
- " return None "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def dfs_search(start, goal, debug=False):\n",
- " agenda = [[start]]\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": 11,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def astar_search(start, goal, debug=False):\n",
- " agenda = [(distance(start, goal), [start])]\n",
- " heapq.heapify(agenda)\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": 12,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "# Uses direct lookup of successors, rather than using cached neighbours in the dict\n",
- "def astar_search_raw(start, goal, debug=False):\n",
- " agenda = [(distance(start, goal), [start])]\n",
- " heapq.heapify(agenda)\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_raw(current) # Difference here\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": 13,
- "metadata": {
- "collapsed": true
- },
- "outputs": [],
- "source": [
- "def astar_search_closed(start, goal, debug=False):\n",
- " agenda = [(distance(start, goal), [start])]\n",
- " heapq.heapify(agenda)\n",
- " closed = set()\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",
- " closed.add(current[-1])\n",
- " successors = extend(current, closed)\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": 14,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
- ]
- },
- "execution_count": 14,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "astar_search('vice', 'wars')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "astar_search_raw('vice', 'wars')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "6"
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(astar_search('vice', 'wars'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "6"
- ]
- },
- "execution_count": 17,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(bfs_search('vice', 'wars'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "6"
- ]
- },
- "execution_count": 20,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(bfs_search_closed('vice', 'wars'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "793"
- ]
- },
- "execution_count": 21,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(dfs_search('vice', 'wars'))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "10000 loops, best of 3: 158 µs per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "astar_search('vice', 'wars')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 23,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "100 loops, best of 3: 15.6 ms per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "astar_search_raw('vice', 'wars')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "10000 loops, best of 3: 168 µs per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "astar_search_closed('vice', 'wars')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "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": 26,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1 loop, best of 3: 597 ms per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "bfs_search_closed('vice', 'wars')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 27,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "10 loops, best of 3: 85.5 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": 28,
- "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": 29,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(11,\n",
- " '`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, `wash`')"
- ]
- },
- "execution_count": 29,
- "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": 30,
- "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": 30,
- "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": 31,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "180"
- ]
- },
- "execution_count": 31,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(reachable_in('rash', 3))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 32,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "2195"
- ]
- },
- "execution_count": 32,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(reachable_in('rash', 10))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 33,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- "2192"
- ]
- },
- "execution_count": 33,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "len(reachable_in('vice', 10))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "100 loops, best of 3: 5.82 ms per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "len(reachable_in('rash', 10))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 35,
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "100 loops, best of 3: 2.75 ms per loop\n"
- ]
- }
- ],
- "source": [
- "%%timeit\n",
- "len(reachable_in('rash', 10, trim_extras=True))"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "collapsed": true
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- "outputs": [],
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- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
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- "pygments_lexer": "ipython3",
- "version": "3.5.2+"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
+++ /dev/null
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\ No newline at end of file
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+your
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+zinc
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+zips
+zits
+zone
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+zoos
\ No newline at end of file
--- /dev/null
+{
+ "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
+}
--- /dev/null
+{
+ "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, closed=None):\n",
+ " if closed:\n",
+ " nbrs = set(neighbours[chain[-1]]) - closed\n",
+ " else:\n",
+ " nbrs = neighbours[chain[-1]]\n",
+ " return [chain + [s] for s in nbrs\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, goal, debug=False):\n",
+ " agenda = [[start]]\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": 16,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def bfs_search_closed(start, goal, debug=False):\n",
+ " agenda = [[start]]\n",
+ " closed = set()\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",
+ " closed.add(current[-1])\n",
+ " successors = extend(current, closed)\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, goal, debug=False):\n",
+ " agenda = [[start]]\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": 19,
+ "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": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dfs_search('abbe', 'ally', debug=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "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"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "['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",
+ "['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"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "['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": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bfs_search('cart', 'vans', debug=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['cart', 'cant', 'cane', 'vane']"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bfs_search('cart', 'vane')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "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": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "dfs_search('cart', 'vane')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def astar_search(start, goal, debug=False):\n",
+ " agenda = [(distance(start, goal), [start])]\n",
+ " heapq.heapify(agenda)\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": 24,
+ "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": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "astar_search('cart', 'vane', debug=True)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def astar_search_closed(start, goal, debug=False):\n",
+ " agenda = [(distance(start, goal), [start])]\n",
+ " heapq.heapify(agenda)\n",
+ " closed = set()\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",
+ " closed.add(current[-1])\n",
+ " successors = extend(current, closed)\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_closed('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": 77,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "94"
+ ]
+ },
+ "execution_count": 77,
+ "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": 78,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2204"
+ ]
+ },
+ "execution_count": 78,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(max(reachables, key=len))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 79,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "1"
+ ]
+ },
+ "execution_count": 79,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(min(reachables, key=len))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 80,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Counter({1: 75, 2: 6, 3: 7, 4: 2, 5: 2, 6: 1, 2204: 1})"
+ ]
+ },
+ "execution_count": 80,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "collections.Counter(len(r) for r in reachables)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 81,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[5]"
+ ]
+ },
+ "execution_count": 81,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "[len(r) for r in reachables if 'abbe' in r]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 82,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[{'abbe', 'able', 'ably', 'ally', 'axle'}]"
+ ]
+ },
+ "execution_count": 82,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "[r for r in reachables if 'abbe' in r]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 83,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['buns', 'bunk', 'punk']"
+ ]
+ },
+ "execution_count": 83,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "astar_search('buns', 'punk')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 84,
+ "metadata": {
+ "collapsed": true
+ },
+ "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": 85,
+ "metadata": {
+ "collapsed": true
+ },
+ "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": 86,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "bigset = max(reachables, key=len)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 87,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "['late', 'lats', 'lets', 'leas', 'seas', 'seam', 'swam', 'sway']\n",
+ "['leap', 'heap', 'hear', 'dear', 'deer']\n",
+ "['peel', 'peek', 'perk', 'park', 'nark']\n",
+ "['sing', 'sang', 'sand', 'said', 'sail', 'hail', 'haul']\n",
+ "['vats', 'bats', 'bets', 'bees', 'been', 'teen', 'then', 'thin', 'this', 'thus', 'thud']\n",
+ "['sues', 'sees', 'seen', 'sewn', 'hewn']\n",
+ "['rash', 'bash', 'bast', 'bait', 'bail', 'hail', 'hair', 'heir']\n",
+ "['apex', 'aped', 'sped', 'seed', 'deed', 'dead', 'deal', 'veal']\n",
+ "['gulf', 'golf', 'gold', 'bold', 'bond', 'bony', 'tony']\n",
+ "['snag', 'shag', 'shat', 'seat', 'peat', 'pent', 'pint', 'mint']\n",
+ "['rife', 'rime', 'rims', 'rums', 'cums', 'cuss']\n",
+ "['diss', 'kiss', 'kits']\n",
+ "['gyps', 'gaps', 'gads', 'wads', 'wade', 'wide', 'tide']\n",
+ "['bilk', 'bill', 'bell', 'tell', 'teal', 'tear', 'tzar']\n",
+ "['logo', 'loge', 'lode', 'lade', 'jade', 'jape']\n",
+ "['hunt', 'bunt', 'buns', 'nuns', 'nubs']\n",
+ "['glow', 'glop', 'plop', 'prop', 'prep', 'peep', 'keep']\n",
+ "['iamb', 'lamb', 'lams', 'laps', 'lips', 'pips']\n",
+ "['pain', 'lain', 'laid', 'land', 'lend', 'vend', 'veld']\n",
+ "['fake', 'bake', 'bare', 'bars', 'ears', 'errs', 'ergs', 'eggs', 'egos']\n"
+ ]
+ }
+ ],
+ "source": [
+ "for _ in range(20):\n",
+ " start, goal = random.sample(bigset, 2)\n",
+ " print(astar_search_closed(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": 61,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
+ "Wall time: 210 µs\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "5"
+ ]
+ },
+ "execution_count": 61,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search('wars', 'love'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
+ "Wall time: 252 µs\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "5"
+ ]
+ },
+ "execution_count": 62,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search_closed('wars', 'love'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n",
+ "Wall time: 24.2 ms\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "404"
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(dfs_search('wars', 'love'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 5min 20s, sys: 76 ms, total: 5min 20s\n",
+ "Wall time: 5min 20s\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "5"
+ ]
+ },
+ "execution_count": 64,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(bfs_search('wars', 'love'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 1.44 s, sys: 0 ns, total: 1.44 s\n",
+ "Wall time: 1.43 s\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "5"
+ ]
+ },
+ "execution_count": 65,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(bfs_search_closed('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": 49,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1 loop, best of 3: 7.9 s per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "astar_search('bats', 'exit')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "10 loops, best of 3: 141 ms per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "astar_search_closed('bats', 'exit')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['bats',\n",
+ " 'bans',\n",
+ " 'band',\n",
+ " 'sand',\n",
+ " 'said',\n",
+ " 'skid',\n",
+ " 'skit',\n",
+ " 'smit',\n",
+ " 'emit',\n",
+ " 'exit']"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "astar_search_closed('bats', 'exit')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 88,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
+ " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
+ " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
+ " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
+ " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
+ " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
+ " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
+ " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
+ " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
+ " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
+ " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
+ " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
+ " 14: [['chug', 'gaff'], ['atom', 'fizz']],\n",
+ " 15: [['chug', 'oxen']]}"
+ ]
+ },
+ "execution_count": 88,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "solutions = {}\n",
+ "for _ in range(10000):\n",
+ " start, goal = random.sample(bigset, 2)\n",
+ " solution = astar_search_closed(start, goal)\n",
+ " sl = len(solution)\n",
+ " if sl not in solutions:\n",
+ " solutions[sl] = []\n",
+ " if len(solutions[sl]) < 4:\n",
+ " solutions[sl].append([start, goal])\n",
+ " \n",
+ "# if len(solution) >= 10:\n",
+ "# solutions += [solution]\n",
+ " \n",
+ "solutions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 91,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "solutions = {2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
+ " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
+ " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
+ " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
+ " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
+ " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
+ " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
+ " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
+ " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
+ " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
+ " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
+ " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
+ " 14: [['chug', 'gaff'], ['atom', 'fizz'], ['chug', 'jinn'], ['amen', 'flog'],\n",
+ " ['buzz', 'grog'], ['imps', 'pros']],\n",
+ " 15: [['chug', 'oxen'], ['amen', 'doff']]}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[('amen', 'doff', 15), ('chug', 'jinn', 14), ('amen', 'flog', 14)]"
+ ]
+ },
+ "execution_count": 54,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "[(s[0], s[-1], len(s)) for s in solutions if len(s) >= 14]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1 loop, best of 3: 360 ms per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "astar_search_closed('blab', 'amen')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 384 ms, sys: 0 ns, total: 384 ms\n",
+ "Wall time: 385 ms\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "14"
+ ]
+ },
+ "execution_count": 56,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search_closed('blab', 'amen'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 57,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 124 ms, sys: 0 ns, total: 124 ms\n",
+ "Wall time: 121 ms\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "15"
+ ]
+ },
+ "execution_count": 57,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search_closed('amen', 'doff'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 58,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
+ "Wall time: 32.4 ms\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "14"
+ ]
+ },
+ "execution_count": 58,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search_closed('chug', 'jinn'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 16 ms, sys: 0 ns, total: 16 ms\n",
+ "Wall time: 17.1 ms\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "14"
+ ]
+ },
+ "execution_count": 59,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search_closed('amen', 'flog'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 268 ms, sys: 4 ms, total: 272 ms\n",
+ "Wall time: 272 ms\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "14"
+ ]
+ },
+ "execution_count": 73,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search_closed('buzz', 'grog'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 64 ms, sys: 0 ns, total: 64 ms\n",
+ "Wall time: 64.1 ms\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "14"
+ ]
+ },
+ "execution_count": 74,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%time len(astar_search_closed('imps', 'pros'))"
+ ]
+ },
+ {
+ "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
+}
--- /dev/null
+{
+ "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": 3,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import string\n",
+ "import heapq"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2336"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "words = [w.strip() for w in open('09-words.txt').readlines()]\n",
+ "len(words)"
+ ]
+ },
+ {
+ "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": {
+ "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": 8,
+ "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": 9,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def extend(chain, closed=None):\n",
+ " if closed:\n",
+ " nbrs = set(neighbours[chain[-1]]) - closed\n",
+ " else:\n",
+ " nbrs = neighbours[chain[-1]]\n",
+ " return [chain + [s] for s in nbrs\n",
+ " if s not in chain]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def extend_raw(chain):\n",
+ " nbrs = [w for w in adjacents(chain[-1]) if w in words]\n",
+ " return [chain + [s] for s in nbrs\n",
+ " if s not in chain]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def bfs_search(start, goal, debug=False):\n",
+ " agenda = [[start]]\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": 12,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def bfs_search_closed(start, goal, debug=False):\n",
+ " agenda = [[start]]\n",
+ " closed = set()\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",
+ " closed.add(current[-1])\n",
+ " successors = extend(current, closed)\n",
+ " agenda = agenda[1:] + successors\n",
+ " if agenda:\n",
+ " return current\n",
+ " else:\n",
+ " return None "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def dfs_search(start, goal, debug=False):\n",
+ " agenda = [[start]]\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": 14,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def astar_search(start, goal, debug=False):\n",
+ " agenda = [(distance(start, goal), [start])]\n",
+ " heapq.heapify(agenda)\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": 15,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Uses direct lookup of successors, rather than using cached neighbours in the dict\n",
+ "def astar_search_raw(start, goal, debug=False):\n",
+ " agenda = [(distance(start, goal), [start])]\n",
+ " heapq.heapify(agenda)\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_raw(current) # Difference here\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": 16,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def astar_search_closed(start, goal, debug=False):\n",
+ " agenda = [(distance(start, goal), [start])]\n",
+ " heapq.heapify(agenda)\n",
+ " closed = set()\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",
+ " closed.add(current[-1])\n",
+ " successors = extend(current, closed)\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": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "astar_search('vice', 'wars')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
+ ]
+ },
+ "execution_count": 18,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "astar_search_raw('vice', 'wars')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "6"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(astar_search('vice', 'wars'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "6"
+ ]
+ },
+ "execution_count": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(bfs_search('vice', 'wars'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "6"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(bfs_search_closed('vice', 'wars'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "793"
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(dfs_search('vice', 'wars'))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "10000 loops, best of 3: 157 µs per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "astar_search('vice', 'wars')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "100 loops, best of 3: 15.8 ms per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "astar_search_raw('vice', 'wars')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "10000 loops, best of 3: 170 µs per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "astar_search_closed('vice', 'wars')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1 loop, best of 3: 1min 42s per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "bfs_search('vice', 'wars')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1 loop, best of 3: 557 ms per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "bfs_search_closed('vice', 'wars')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "10 loops, best of 3: 87.9 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": 29,
+ "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": 30,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(11,\n",
+ " '`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, `wash`')"
+ ]
+ },
+ "execution_count": 30,
+ "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": 31,
+ "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": 31,
+ "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": 32,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "180"
+ ]
+ },
+ "execution_count": 32,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(reachable_in('rash', 3))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2195"
+ ]
+ },
+ "execution_count": 33,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(reachable_in('rash', 10))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "2192"
+ ]
+ },
+ "execution_count": 34,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "len(reachable_in('vice', 10))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "100 loops, best of 3: 6.01 ms per loop\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%timeit\n",
+ "len(reachable_in('rash', 10))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "100 loops, best of 3: 2.92 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",
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+}
"3. [Door codes](03-door-codes)\n",
"4. [Word search](04-word-search)\n",
"5. [Display board](05-display-board)\n",
- "6. [Activity network](06-activity-network)\n",
- "7. [Word chains](07-word-chains)\n",
- "8. [Suitcase packing](08-suitacase-packing)\n",
- "9. ?\n",
- "10. ?\n"
+ "6. [Tour shapes](06-tour-shapes) [Problem B](https://www.cs.uoregon.edu/Activities/Luks_Programming_Contest/problems/Problems2017.pdf): A is check if string is a closed loop, B is find the area\n",
+ "7. [Activity network](07-activity-network)\n",
+ "8. [Filling the days](08-filling-days) [Problem C](https://www.cs.uoregon.edu/Activities/Luks_Programming_Contest/problems/Problems2017.pdf): A per the problem, B when there are multiple rooms available\n",
+ "9. [Word chains](09-word-chains)\n",
+ "10. [Suitcase packing](10-suitacase-packing)\n"
]
},
{
projects / ou-summer-of-code-2017.git / commitdiff