honeycomb_puzzle_bits.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "id": "951180ec",
   6    "metadata": {},
   7    "source": [
   8     "# Honeycomb letter puzzle\n",
   9     "Solving the puzzle as posted on [FiveThirtyEight](https://fivethirtyeight.com/features/can-you-solve-the-vexing-vexillology/), also solved by [David Robinson](http://varianceexplained.org/r/honeycomb-puzzle/).\n"
  10    ]
  11   },
  12   {
  13    "cell_type": "code",
  14    "execution_count": 1,
  15    "id": "6f6fa3e7",
  16    "metadata": {},
  17    "outputs": [],
  18    "source": [
  19     "import string\n",
  20     "import collections\n",
  21     "from dataclasses import dataclass\n",
  22     "import itertools\n",
  23     "import ctypes\n",
  24     "import cProfile"
  25    ]
  26   },
  27   {
  28    "cell_type": "code",
  29    "execution_count": 5,
  30    "id": "88f00e4c",
  31    "metadata": {},
  32    "outputs": [
  33     {
  34      "data": {
  35       "text/plain": [
  36        "172820"
  37       ]
  38      },
  39      "execution_count": 5,
  40      "metadata": {},
  41      "output_type": "execute_result"
  42     }
  43    ],
  44    "source": [
  45     "with open('enable1.txt') as f:\n",
  46     "    words = [line.strip() for line in f]"
  47    ]
  48   },
  49   {
  50    "cell_type": "code",
  51    "execution_count": 6,
  52    "id": "1e75fba2",
  53    "metadata": {},
  54    "outputs": [],
  55    "source": [
  56     "words = set(w for w in words \n",
  57     "            if len(w) >= 4\n",
  58     "            if len(frozenset(w)) <= 7\n",
  59     "            if 's' not in w)"
  60    ]
  61   },
  62   {
  63    "cell_type": "code",
  64    "execution_count": 8,
  65    "id": "e1f9b35e",
  66    "metadata": {},
  67    "outputs": [
  68     {
  69      "data": {
  70       "text/plain": [
  71        "21661"
  72       ]
  73      },
  74      "execution_count": 8,
  75      "metadata": {},
  76      "output_type": "execute_result"
  77     }
  78    ],
  79    "source": [
  80     "word_sets = collections.defaultdict(set)\n",
  81     "for w in words:\n",
  82     "    letters = frozenset(w)\n",
  83     "    word_sets[letters].add(w)"
  84    ]
  85   },
  86   {
  87    "cell_type": "code",
  88    "execution_count": 11,
  89    "id": "95dc0eed-c759-481e-8598-9b861e3def8f",
  90    "metadata": {},
  91    "outputs": [],
  92    "source": [
  93     "def encode(letters):\n",
  94     "    encoded = 0\n",
  95     "    for l in string.ascii_lowercase:\n",
  96     "        encoded <<= 1\n",
  97     "        if l in letters:\n",
  98     "            encoded |= 1\n",
  99     "    return encoded"
 100    ]
 101   },
 102   {
 103    "cell_type": "code",
 104    "execution_count": 12,
 105    "id": "53d9ae67-a5b5-4d01-9e69-930acca023bc",
 106    "metadata": {},
 107    "outputs": [],
 108    "source": [
 109     "def decode(letter_bits):\n",
 110     "    letters = set()\n",
 111     "    for l in string.ascii_lowercase:\n",
 112     "        e = encode(l)\n",
 113     "        if (e & letter_bits):\n",
 114     "            letters.add(l)\n",
 115     "    return letters"
 116    ]
 117   },
 118   {
 119    "cell_type": "code",
 120    "execution_count": 13,
 121    "id": "ab295a0a-6cb0-4f24-b57b-cb9f99517067",
 122    "metadata": {},
 123    "outputs": [],
 124    "source": [
 125     "def subset(this, that):\n",
 126     "    return this & that == this"
 127    ]
 128   },
 129   {
 130    "cell_type": "code",
 131    "execution_count": 19,
 132    "id": "267130ba",
 133    "metadata": {},
 134    "outputs": [],
 135    "source": [
 136     "@dataclass(frozen=True, init=False)\n",
 137     "class Honeycomb():\n",
 138     "    mandatory: int\n",
 139     "    letters: int\n",
 140     "    \n",
 141     "    def __init__(self, mandatory, letters):\n",
 142     "        object.__setattr__(self, 'mandatory', encode(mandatory))\n",
 143     "        object.__setattr__(self, 'letters', encode(letters))\n",
 144     "            \n",
 145     "    def __repr__(self):\n",
 146     "        return f'{\"\".join(decode(self.mandatory))}|{\"\".join(sorted(decode(self.letters) - set(decode(self.mandatory))))}'"
 147    ]
 148   },
 149   {
 150    "cell_type": "code",
 151    "execution_count": 21,
 152    "id": "bb848e88",
 153    "metadata": {},
 154    "outputs": [],
 155    "source": [
 156     "def present(target, honeycomb):\n",
 157     "    return (subset(honeycomb.mandatory, target)\n",
 158     "           and subset(target, honeycomb.letters))"
 159    ]
 160   },
 161   {
 162    "cell_type": "code",
 163    "execution_count": 25,
 164    "id": "3c6f212e",
 165    "metadata": {},
 166    "outputs": [],
 167    "source": [
 168     "def score(present_set):\n",
 169     "    score = 0\n",
 170     "    for w in word_sets[present_set]:\n",
 171     "        if len(w) == 4:\n",
 172     "            score += 1\n",
 173     "        else:\n",
 174     "            score += len(w)\n",
 175     "    if len(present_set) == 7:\n",
 176     "        score += len(word_sets[present_set]) * 7\n",
 177     "    return score"
 178    ]
 179   },
 180   {
 181    "cell_type": "code",
 182    "execution_count": 28,
 183    "id": "979d9ed5",
 184    "metadata": {},
 185    "outputs": [],
 186    "source": [
 187     "scored_sets = {s: score(s) for s in word_sets}\n",
 188     "encoded_scored_sets = {encode(s): scored_sets[s] for s in scored_sets}"
 189    ]
 190   },
 191   {
 192    "cell_type": "code",
 193    "execution_count": 30,
 194    "id": "78d423a5",
 195    "metadata": {},
 196    "outputs": [],
 197    "source": [
 198     "def raw_score_honeycomb(honeycomb):\n",
 199     "    return sum(sc for letters, sc in scored_sets.items() \n",
 200     "               # if honeycomb.mandatory in letters\n",
 201     "               # if letters.issubset(honeycomb.letters)\n",
 202     "               if present(letters, honeycomb)\n",
 203     "              )"
 204    ]
 205   },
 206   {
 207    "cell_type": "code",
 208    "execution_count": 31,
 209    "id": "eb0d2af1-437b-4be5-8736-0a18022e9de2",
 210    "metadata": {},
 211    "outputs": [],
 212    "source": [
 213     "def score_honeycomb(honeycomb):\n",
 214     "    return sum(sc for letters, sc in encoded_scored_sets.items() \n",
 215     "               # if honeycomb.mandatory in letters\n",
 216     "               # if letters.issubset(honeycomb.letters)\n",
 217     "               if present(letters, honeycomb)\n",
 218     "              )"
 219    ]
 220   },
 221   {
 222    "cell_type": "code",
 223    "execution_count": 40,
 224    "id": "febee1c1",
 225    "metadata": {},
 226    "outputs": [
 227     {
 228      "name": "stdout",
 229      "output_type": "stream",
 230      "text": [
 231       "pangram sets: 7986\n"
 232      ]
 233     }
 234    ],
 235    "source": [
 236     "pangram_sets = [s for s in word_sets.keys() if len(s) == 7 if 's' not in s]"
 237    ]
 238   },
 239   {
 240    "cell_type": "code",
 241    "execution_count": 41,
 242    "id": "54a06bdf",
 243    "metadata": {},
 244    "outputs": [],
 245    "source": [
 246     "with open('pangaram_words.txt', 'w') as f:\n",
 247     "    for s in pangram_sets:\n",
 248     "        for w in word_sets[s]:\n",
 249     "            f.write(f'{w}\\n')"
 250    ]
 251   },
 252   {
 253    "cell_type": "code",
 254    "execution_count": 42,
 255    "id": "c0b0807c",
 256    "metadata": {},
 257    "outputs": [
 258     {
 259      "name": "stdout",
 260      "output_type": "stream",
 261      "text": [
 262       "55902 honeycombs\n"
 263      ]
 264     }
 265    ],
 266    "source": [
 267     "# ps_honeycombs = []\n",
 268     "\n",
 269     "# for ps in pangram_sets:\n",
 270     "#     for mand in ps:\n",
 271     "#         ps_honeycombs.append(Honeycomb(mandatory=mand, letters=ps))\n",
 272     "\n",
 273     "ps_honeycombs = [Honeycomb(mandatory=mand, letters=ps) \n",
 274     "                 for ps in pangram_sets\n",
 275     "                 for mand in ps]"
 276    ]
 277   },
 278   {
 279    "cell_type": "code",
 280    "execution_count": 48,
 281    "id": "914fece8",
 282    "metadata": {},
 283    "outputs": [
 284     {
 285      "data": {
 286       "text/plain": [
 287        "26"
 288       ]
 289      },
 290      "execution_count": 48,
 291      "metadata": {},
 292      "output_type": "execute_result"
 293     }
 294    ],
 295    "source": [
 296     "partitioned_scored_sets = {encode(l): {s: encoded_scored_sets[s] \n",
 297     "                               for s in encoded_scored_sets \n",
 298     "                               if subset(encode(l), s)}\n",
 299     "                           for l in string.ascii_lowercase}"
 300    ]
 301   },
 302   {
 303    "cell_type": "code",
 304    "execution_count": 50,
 305    "id": "f1454ccd",
 306    "metadata": {},
 307    "outputs": [],
 308    "source": [
 309     "def partitioned_score_honeycomb(honeycomb):\n",
 310     "    return sum(sc for letters, sc in partitioned_scored_sets[honeycomb.mandatory].items() \n",
 311     "               if subset(letters, honeycomb.letters)\n",
 312     "              )"
 313    ]
 314   },
 315   {
 316    "cell_type": "code",
 317    "execution_count": 51,
 318    "id": "7380dbd6",
 319    "metadata": {},
 320    "outputs": [
 321     {
 322      "name": "stdout",
 323      "output_type": "stream",
 324      "text": [
 325       "r|aegint 3898\n",
 326       "r|aegint 3898\n"
 327      ]
 328     },
 329     {
 330      "ename": "KeyboardInterrupt",
 331      "evalue": "",
 332      "output_type": "error",
 333      "traceback": [
 334       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
 335       "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
 336       "\u001b[0;32m/tmp/ipykernel_1590851/2427168464.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_cell_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'timeit'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'best_honyecomb = max(ps_honeycombs, key=partitioned_score_honeycomb)\\nprint(best_honyecomb, partitioned_score_honeycomb(best_honyecomb))\\n'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
 337       "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_cell_magic\u001b[0;34m(self, magic_name, line, cell)\u001b[0m\n\u001b[1;32m   2401\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2402\u001b[0m                 \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mmagic_arg_s\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcell\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2403\u001b[0;31m                 \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2404\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2405\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
 338       "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/decorator.py\u001b[0m in \u001b[0;36mfun\u001b[0;34m(*args, **kw)\u001b[0m\n\u001b[1;32m    230\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mkwsyntax\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    231\u001b[0m                 \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkw\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkw\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 232\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mcaller\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mextras\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    233\u001b[0m     \u001b[0mfun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    234\u001b[0m     \u001b[0mfun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
 339       "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(f, *a, **k)\u001b[0m\n\u001b[1;32m    185\u001b[0m     \u001b[0;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    186\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 187\u001b[0;31m         \u001b[0mcall\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    188\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    189\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
 340       "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n\u001b[1;32m   1171\u001b[0m                     \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1172\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1173\u001b[0;31m         \u001b[0mall_runs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtimer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrepeat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrepeat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1174\u001b[0m         \u001b[0mbest\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_runs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mnumber\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1175\u001b[0m         \u001b[0mworst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_runs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mnumber\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
 341       "\u001b[0;32m~/anaconda3/lib/python3.8/timeit.py\u001b[0m in \u001b[0;36mrepeat\u001b[0;34m(self, repeat, number)\u001b[0m\n\u001b[1;32m    203\u001b[0m         \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    204\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrepeat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 205\u001b[0;31m             \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimeit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    206\u001b[0m             \u001b[0mr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    207\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
 342       "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, number)\u001b[0m\n\u001b[1;32m    167\u001b[0m         \u001b[0mgc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdisable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    168\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 169\u001b[0;31m             \u001b[0mtiming\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minner\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    170\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mgcold\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
 343       "\u001b[0;32m<magic-timeit>\u001b[0m in \u001b[0;36minner\u001b[0;34m(_it, _timer)\u001b[0m\n",
 344       "\u001b[0;32m/tmp/ipykernel_1590851/3736129931.py\u001b[0m in \u001b[0;36mpartitioned_score_honeycomb\u001b[0;34m(honeycomb)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mpartitioned_score_honeycomb\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhoneycomb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     return sum(sc for letters, sc in partitioned_scored_sets[honeycomb.mandatory].items() \n\u001b[0m\u001b[1;32m      3\u001b[0m                \u001b[0;32mif\u001b[0m \u001b[0msubset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mletters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhoneycomb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mletters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m               )\n",
 345       "\u001b[0;32m/tmp/ipykernel_1590851/3736129931.py\u001b[0m in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mpartitioned_score_honeycomb\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhoneycomb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     return sum(sc for letters, sc in partitioned_scored_sets[honeycomb.mandatory].items() \n\u001b[0;32m----> 3\u001b[0;31m                \u001b[0;32mif\u001b[0m \u001b[0msubset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mletters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhoneycomb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mletters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m               )\n",
 346       "\u001b[0;32m/tmp/ipykernel_1590851/3073138769.py\u001b[0m in \u001b[0;36msubset\u001b[0;34m(this, that)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0msubset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mthat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mthis\u001b[0m \u001b[0;34m&\u001b[0m \u001b[0mthat\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mthis\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
 347       "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
 348      ]
 349     }
 350    ],
 351    "source": [
 352     "# %%timeit\n",
 353     "# best_honyecomb = max(ps_honeycombs, key=partitioned_score_honeycomb)\n",
 354     "# print(best_honyecomb, partitioned_score_honeycomb(best_honyecomb))"
 355    ]
 356   },
 357   {
 358    "cell_type": "code",
 359    "execution_count": null,
 360    "id": "0ecd0647-11df-4b5b-a487-cb30cfa080c0",
 361    "metadata": {},
 362    "outputs": [],
 363    "source": [
 364     "# %%timeit\n",
 365     "best_honyecomb = max(ps_honeycombs, key=score_honeycomb)\n",
 366     "print(best_honyecomb, score_honeycomb(best_honyecomb))"
 367    ]
 368   },
 369   {
 370    "cell_type": "code",
 371    "execution_count": null,
 372    "id": "7e4173b4-26a9-4198-b572-d57db321fe94",
 373    "metadata": {
 374     "lines_to_next_cell": 2
 375    },
 376    "outputs": [],
 377    "source": [
 378     "# cProfile.run('max(ps_honeycombs, key=score_honeycomb)')"
 379    ]
 380   },
 381   {
 382    "cell_type": "code",
 383    "execution_count": null,
 384    "id": "9a9070b7-a866-499e-a910-82337ecbd052",
 385    "metadata": {},
 386    "outputs": [],
 387    "source": [
 388     "# cProfile.run('max(ps_honeycombs, key=partitioned_score_honeycomb)')"
 389    ]
 390   },
 391   {
 392    "cell_type": "code",
 393    "execution_count": null,
 394    "id": "a77ce9b1-d5d8-4c8f-8666-5840af23c265",
 395    "metadata": {},
 396    "outputs": [],
 397    "source": []
 398   }
 399  ],
 400  "metadata": {
 401   "jupytext": {
 402    "formats": "ipynb,py:light"
 403   },
 404   "kernelspec": {
 405    "display_name": "Python 3 (ipykernel)",
 406    "language": "python",
 407    "name": "python3"
 408   },
 409   "language_info": {
 410    "codemirror_mode": {
 411     "name": "ipython",
 412     "version": 3
 413    },
 414    "file_extension": ".py",
 415    "mimetype": "text/x-python",
 416    "name": "python",
 417    "nbconvert_exporter": "python",
 418    "pygments_lexer": "ipython3",
 419    "version": "3.8.8"
 420   }
 421  },
 422  "nbformat": 4,
 423  "nbformat_minor": 5
 424 }