euler61.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "code",
   5    "execution_count": 2,
   6    "metadata": {},
   7    "outputs": [
   8     {
   9      "data": {
  10       "text/plain": [
  11        "true"
  12       ]
  13      },
  14      "execution_count": 2,
  15      "metadata": {},
  16      "output_type": "execute_result"
  17     }
  18    ],
  19    "source": [
  20     "require_relative 'array-numbers'"
  21    ]
  22   },
  23   {
  24    "cell_type": "code",
  25    "execution_count": 3,
  26    "metadata": {},
  27    "outputs": [
  28     {
  29      "data": {
  30       "text/plain": [
  31        ":valid_set"
  32       ]
  33      },
  34      "execution_count": 3,
  35      "metadata": {},
  36      "output_type": "execute_result"
  37     }
  38    ],
  39    "source": [
  40     "def valid_set(&block)\n",
  41     "  (1..150).map {|i| block.call i}.select {|i| i >= 1000 && i <= 10000 && i % 10 != 0}\n",
  42     "end"
  43    ]
  44   },
  45   {
  46    "cell_type": "code",
  47    "execution_count": 4,
  48    "metadata": {},
  49    "outputs": [
  50     {
  51      "data": {
  52       "text/plain": [
  53        "[[1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1596, 1653, 1711, 1891, 1953, 2016, 2145, 2211, 2278, 2346, 2415, 2485, 2556, 2628, 2701, 2775, 2926, 3003, 3081, 3321, 3403, 3486, 3655, 3741, 3828, 3916, 4005, 4095, 4186, 4278, 4371, 4465, 4656, 4753, 4851, 5151, 5253, 5356, 5565, 5671, 5778, 5886, 5995, 6105, 6216, 6328, 6441, 6555, 6786, 6903, 7021, 7381, 7503, 7626, 7875, 8001, 8128, 8256, 8385, 8515, 8646, 8778, 8911, 9045, 9316, 9453, 9591], [1001, 1162, 1247, 1335, 1426, 1617, 1717, 1926, 2035, 2147, 2262, 2501, 2625, 2752, 2882, 3015, 3151, 3432, 3577, 3725, 3876, 4187, 4347, 4676, 4845, 5017, 5192, 5551, 5735, 5922, 6112, 6305, 6501, 6902, 7107, 7315, 7526, 7957, 8177, 8626, 8855, 9087, 9322, 9801], [1071, 1177, 1288, 1404, 1525, 1651, 1782, 1918, 2059, 2205, 2356, 2512, 2673, 2839, 3186, 3367, 3553, 3744, 4141, 4347, 4558, 4774, 4995, 5221, 5452, 5688, 5929, 6175, 6426, 6682, 6943, 7209, 7756, 8037, 8323, 8614, 9211, 9517, 9828], [1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801], [1035, 1128, 1225, 1326, 1431, 1653, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 3003, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4753, 5151, 5356, 5565, 5778, 5995, 6216, 6441, 6903, 7381, 7626, 7875, 8128, 8385, 8646, 8911, 9453], [1045, 1281, 1408, 1541, 1825, 1976, 2133, 2296, 2465, 2821, 3008, 3201, 3605, 3816, 4033, 4256, 4485, 4961, 5208, 5461, 5985, 6256, 6533, 6816, 7105, 7701, 8008, 8321, 8965, 9296, 9633, 9976]]"
  54       ]
  55      },
  56      "execution_count": 4,
  57      "metadata": {},
  58      "output_type": "execute_result"
  59     }
  60    ],
  61    "source": [
  62     "triangles = valid_set {|n| n * (n + 1) / 2}\n",
  63     "pentagonals = valid_set {|n| n * (3 * n - 1) / 2}\n",
  64     "heptagonals = valid_set {|n| n * (5 * n - 3) / 2}\n",
  65     "squares = valid_set {|n| n * n}\n",
  66     "hexagonals = valid_set {|n| n * (2 * n - 1)}\n",
  67     "octagonals = valid_set {|n| n * (3 * n - 2)}\n",
  68     "[triangles, pentagonals, heptagonals, squares, hexagonals, octagonals]"
  69    ]
  70   },
  71   {
  72    "cell_type": "code",
  73    "execution_count": 5,
  74    "metadata": {},
  75    "outputs": [
  76     {
  77      "data": {
  78       "text/plain": [
  79        ":connects"
  80       ]
  81      },
  82      "execution_count": 5,
  83      "metadata": {},
  84      "output_type": "execute_result"
  85     }
  86    ],
  87    "source": [
  88     "def connects(n1, n2)\n",
  89     "  n1.to_digits[2..3] == n2.to_digits[0..1]\n",
  90     "end"
  91    ]
  92   },
  93   {
  94    "cell_type": "code",
  95    "execution_count": 6,
  96    "metadata": {},
  97    "outputs": [
  98     {
  99      "data": {
 100       "text/plain": [
 101        "true"
 102       ]
 103      },
 104      "execution_count": 6,
 105      "metadata": {},
 106      "output_type": "execute_result"
 107     }
 108    ],
 109    "source": [
 110     "connects(1234, 3456)"
 111    ]
 112   },
 113   {
 114    "cell_type": "code",
 115    "execution_count": 7,
 116    "metadata": {},
 117    "outputs": [
 118     {
 119      "data": {
 120       "text/plain": [
 121        "false"
 122       ]
 123      },
 124      "execution_count": 7,
 125      "metadata": {},
 126      "output_type": "execute_result"
 127     }
 128    ],
 129    "source": [
 130     "connects(1234, 1234)"
 131    ]
 132   },
 133   {
 134    "cell_type": "code",
 135    "execution_count": 8,
 136    "metadata": {},
 137    "outputs": [
 138     {
 139      "data": {
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:type=>7}], {:number=>6816, :type=>8}=>[{:number=>1653, :type=>3}, {:number=>1681, :type=>4}, {:number=>1617, :type=>5}, {:number=>1653, :type=>6}, {:number=>1651, :type=>7}], {:number=>7105, :type=>8}=>[], {:number=>7701, :type=>8}=>[], {:number=>8008, :type=>8}=>[], {:number=>8321, :type=>8}=>[{:number=>2145, :type=>3}, {:number=>2116, :type=>4}, {:number=>2147, :type=>5}, {:number=>2145, :type=>6}], {:number=>8965, :type=>8}=>[{:number=>6555, :type=>3}, {:number=>6561, :type=>4}, {:number=>6501, :type=>5}], {:number=>9296, :type=>8}=>[{:number=>9604, :type=>4}], {:number=>9633, :type=>8}=>[{:number=>3321, :type=>3}, {:number=>3364, :type=>4}, {:number=>3321, :type=>6}, {:number=>3367, :type=>7}], {:number=>9976, :type=>8}=>[{:number=>7626, :type=>3}, {:number=>7626, :type=>6}]}"
 142       ]
 143      },
 144      "execution_count": 8,
 145      "metadata": {},
 146      "output_type": "execute_result"
 147     }
 148    ],
 149    "source": [
 150     "connections = {}\n",
 151     "triangles.each do |n|\n",
 152     "  connections[{number: n, type: 3}] = []\n",
 153     "end\n",
 154     "squares.each do |n|\n",
 155     "  connections[{number: n, type: 4}] = []\n",
 156     "end\n",
 157     "pentagonals.each do |n|\n",
 158     "  connections[{number: n, type: 5}] = []\n",
 159     "end\n",
 160     "hexagonals.each do |n|\n",
 161     "  connections[{number: n, type: 6}] = []\n",
 162     "end\n",
 163     "heptagonals.each do |n|\n",
 164     "  connections[{number: n, type: 7}] = []\n",
 165     "end\n",
 166     "octagonals.each do |n|\n",
 167     "  connections[{number: n, type: 8}] = []\n",
 168     "end\n",
 169     "\n",
 170     "connections.keys.each do |nt| \n",
 171     "  connections.keys.select {|other| connects(nt[:number], other[:number]) && nt[:type] != other[:type]}.each do |other|\n",
 172     "    connections[nt] << other\n",
 173     "  end\n",
 174     "end\n",
 175     "\n",
 176     "connections  "
 177    ]
 178   },
 179   {
 180    "cell_type": "code",
 181    "execution_count": 9,
 182    "metadata": {},
 183    "outputs": [
 184     {
 185      "data": {
 186       "text/plain": [
 187        ":initial_chains"
 188       ]
 189      },
 190      "execution_count": 9,
 191      "metadata": {},
 192      "output_type": "execute_result"
 193     }
 194    ],
 195    "source": [
 196     "def initial_chains(connections)\n",
 197     "  connections.keys.select {|nt| nt[:type] == 8}.map {|nt| [nt]}\n",
 198     "end"
 199    ]
 200   },
 201   {
 202    "cell_type": "code",
 203    "execution_count": 10,
 204    "metadata": {},
 205    "outputs": [
 206     {
 207      "data": {
 208       "text/plain": [
 209        "[[{:number=>1045, :type=>8}], [{:number=>1281, :type=>8}], [{:number=>1408, :type=>8}], [{:number=>1541, :type=>8}], [{:number=>1825, :type=>8}], [{:number=>1976, :type=>8}], [{:number=>2133, :type=>8}], [{:number=>2296, :type=>8}], [{:number=>2465, :type=>8}], [{:number=>2821, :type=>8}], [{:number=>3008, :type=>8}], [{:number=>3201, :type=>8}], [{:number=>3605, :type=>8}], [{:number=>3816, :type=>8}], [{:number=>4033, :type=>8}], [{:number=>4256, :type=>8}], [{:number=>4485, :type=>8}], [{:number=>4961, :type=>8}], [{:number=>5208, :type=>8}], [{:number=>5461, :type=>8}], [{:number=>5985, :type=>8}], [{:number=>6256, :type=>8}], [{:number=>6533, :type=>8}], [{:number=>6816, :type=>8}], [{:number=>7105, :type=>8}], [{:number=>7701, :type=>8}], [{:number=>8008, :type=>8}], [{:number=>8321, :type=>8}], [{:number=>8965, :type=>8}], [{:number=>9296, :type=>8}], [{:number=>9633, :type=>8}], [{:number=>9976, :type=>8}]]"
 210       ]
 211      },
 212      "execution_count": 10,
 213      "metadata": {},
 214      "output_type": "execute_result"
 215     }
 216    ],
 217    "source": [
 218     "initial_chains connections"
 219    ]
 220   },
 221   {
 222    "cell_type": "code",
 223    "execution_count": 36,
 224    "metadata": {},
 225    "outputs": [
 226     {
 227      "data": {
 228       "text/plain": [
 229        ":can_add?"
 230       ]
 231      },
 232      "execution_count": 36,
 233      "metadata": {},
 234      "output_type": "execute_result"
 235     }
 236    ],
 237    "source": [
 238     "def can_add?(chain, item, connections)\n",
 239     "  connections[chain.last].include?(item) &&\n",
 240     "  (! chain.map {|nt| nt[:type]}.include?(item[:type]))\n",
 241     "end"
 242    ]
 243   },
 244   {
 245    "cell_type": "code",
 246    "execution_count": 38,
 247    "metadata": {},
 248    "outputs": [
 249     {
 250      "data": {
 251       "text/plain": [
 252        "true"
 253       ]
 254      },
 255      "execution_count": 38,
 256      "metadata": {},
 257      "output_type": "execute_result"
 258     }
 259    ],
 260    "source": [
 261     "connections[initial_chains(connections)[0].last].include?({:number=>4558, :type=>7})"
 262    ]
 263   },
 264   {
 265    "cell_type": "code",
 266    "execution_count": 39,
 267    "metadata": {},
 268    "outputs": [
 269     {
 270      "data": {
 271       "text/plain": [
 272        "[8]"
 273       ]
 274      },
 275      "execution_count": 39,
 276      "metadata": {},
 277      "output_type": "execute_result"
 278     }
 279    ],
 280    "source": [
 281     "initial_chains(connections)[0].map {|nt| nt[:type]}"
 282    ]
 283   },
 284   {
 285    "cell_type": "code",
 286    "execution_count": 40,
 287    "metadata": {},
 288    "outputs": [
 289     {
 290      "data": {
 291       "text/plain": [
 292        ":extend_chain"
 293       ]
 294      },
 295      "execution_count": 40,
 296      "metadata": {},
 297      "output_type": "execute_result"
 298     }
 299    ],
 300    "source": [
 301     "def extend_chain(chain, connections)\n",
 302     "  connections[chain.last].select {|e| can_add? chain, e, connections}.map {|e| chain + [e]}\n",
 303     "end"
 304    ]
 305   },
 306   {
 307    "cell_type": "code",
 308    "execution_count": 43,
 309    "metadata": {},
 310    "outputs": [
 311     {
 312      "data": {
 313       "text/plain": [
 314        "[[{:number=>1281, :type=>8}, {:number=>8128, :type=>3}], [{:number=>1281, :type=>8}, {:number=>8177, :type=>5}], [{:number=>1281, :type=>8}, {:number=>8128, :type=>6}]]"
 315       ]
 316      },
 317      "execution_count": 43,
 318      "metadata": {},
 319      "output_type": "execute_result"
 320     }
 321    ],
 322    "source": [
 323     "extend_chain(initial_chains(connections)[1], connections)"
 324    ]
 325   },
 326   {
 327    "cell_type": "code",
 328    "execution_count": 53,
 329    "metadata": {},
 330    "outputs": [
 331     {
 332      "data": {
 333       "text/plain": [
 334        ":complete?"
 335       ]
 336      },
 337      "execution_count": 53,
 338      "metadata": {},
 339      "output_type": "execute_result"
 340     }
 341    ],
 342    "source": [
 343     "def complete?(chain, connections)\n",
 344     "  chain.length == 6 && Set.new(chain.map {|nt| nt[:type]}).length == 6 && connections[chain.last].include?(chain.first)\n",
 345     "end"
 346    ]
 347   },
 348   {
 349    "cell_type": "code",
 350    "execution_count": 56,
 351    "metadata": {
 352     "scrolled": true
 353    },
 354    "outputs": [
 355     {
 356      "data": {
 357       "text/plain": [
 358        "28684"
 359       ]
 360      },
 361      "execution_count": 56,
 362      "metadata": {},
 363      "output_type": "execute_result"
 364     }
 365    ],
 366    "source": [
 367     "agenda = initial_chains(connections)\n",
 368     "while ! complete?(agenda.first, connections)\n",
 369     "  # puts agenda.first, agenda.length\n",
 370     "  new_chains = extend_chain(agenda.first, connections)\n",
 371     "  agenda = agenda.drop(1) + new_chains\n",
 372     "end\n",
 373     "agenda.first.map{|nt| nt[:number]}.sum"
 374    ]
 375   },
 376   {
 377    "cell_type": "code",
 378    "execution_count": 58,
 379    "metadata": {},
 380    "outputs": [
 381     {
 382      "data": {
 383       "text/plain": [
 384        "224"
 385       ]
 386      },
 387      "execution_count": 58,
 388      "metadata": {},
 389      "output_type": "execute_result"
 390     }
 391    ],
 392    "source": [
 393     "agenda.length"
 394    ]
 395   },
 396   {
 397    "cell_type": "code",
 398    "execution_count": null,
 399    "metadata": {
 400     "collapsed": true
 401    },
 402    "outputs": [],
 403    "source": []
 404   }
 405  ],
 406  "metadata": {
 407   "kernelspec": {
 408    "display_name": "Ruby 2.4.0",
 409    "language": "ruby",
 410    "name": "ruby"
 411   },
 412   "language_info": {
 413    "file_extension": ".rb",
 414    "mimetype": "application/x-ruby",
 415    "name": "ruby",
 416    "version": "2.4.0"
 417   }
 418  },
 419  "nbformat": 4,
 420  "nbformat_minor": 2
 421 }