Done puzzle 32

diff --git a/euler32.ipynb b/euler32.ipynb
new file mode 100644 (file)
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+++ b/euler32.ipynb
@@ -0,0 +1,516 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "true"
+      ]
+     },
+     "execution_count": 66,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "require 'set'\n",
+    "require 'awesome_print'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1, 2, 3, 4, 5, 6, 7, 8, 9]"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "digits = (1..9).to_a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":full_subbags"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class Array\n",
+    "  def subbags(n)\n",
+    "    return enum_for(:subbags, n) unless block_given?\n",
+    "    if n == 1\n",
+    "      yield [self]\n",
+    "    else\n",
+    "      (0..self.length).each do |i|\n",
+    "        self.combination(i).each do |f|\n",
+    "          (self - f).subbags(n-1).each do |r|\n",
+    "            yield [f] + r\n",
+    "          end\n",
+    "        end\n",
+    "      end\n",
+    "    end\n",
+    "  end\n",
+    "  \n",
+    "  def full_subbags(n)\n",
+    "    return enum_for(:full_subbags, n) unless block_given?\n",
+    "    self.subbags(n).select {|bags| bags.all? {|b| !b.empty?}}.each do |bs|\n",
+    "      yield bs\n",
+    "    end\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1, 2, 3]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "[1,2,3].subbags(1) {|i| puts i}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[[[1, 2, 3]]]"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].subbags(1).to_a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[], [1, 2, 3]]\n",
+      "[[1], [2, 3]]\n",
+      "[[2], [1, 3]]\n",
+      "[[3], [1, 2]]\n",
+      "[[1, 2], [3]]\n",
+      "[[1, 3], [2]]\n",
+      "[[2, 3], [1]]\n",
+      "[[1, 2, 3], []]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0..3"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].subbags(2) {|i| puts i}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[[[], [1, 2, 3]], [[1], [2, 3]], [[2], [1, 3]], [[3], [1, 2]], [[1, 2], [3]], [[1, 3], [2]], [[2, 3], [1]], [[1, 2, 3], []]]"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].subbags(2).to_a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "8"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].subbags(2).to_a.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[[[], [], [1, 2, 3]], [[], [1], [2, 3]], [[], [2], [1, 3]], [[], [3], [1, 2]], [[], [1, 2], [3]], [[], [1, 3], [2]], [[], [2, 3], [1]], [[], [1, 2, 3], []], [[1], [], [2, 3]], [[1], [2], [3]], [[1], [3], [2]], [[1], [2, 3], []], [[2], [], [1, 3]], [[2], [1], [3]], [[2], [3], [1]], [[2], [1, 3], []], [[3], [], [1, 2]], [[3], [1], [2]], [[3], [2], [1]], [[3], [1, 2], []], [[1, 2], [], [3]], [[1, 2], [3], []], [[1, 3], [], [2]], [[1, 3], [2], []], [[2, 3], [], [1]], [[2, 3], [1], []], [[1, 2, 3], [], []]]"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].subbags(3).to_a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "27"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].subbags(3).to_a.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "i: 0, f: []\n",
+      "i: 1, f: [1]\n",
+      "i: 1, f: [2]\n",
+      "i: 1, f: [3]\n",
+      "i: 2, f: [1, 2]\n",
+      "i: 2, f: [1, 3]\n",
+      "i: 2, f: [2, 3]\n",
+      "i: 3, f: [1, 2, 3]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "0..3"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(0..[1,2,3].length).each do |i|\n",
+    "  [1,2,3].combination(i).each do |f|\n",
+    "    puts \"i: #{i}, f: #{f}\"\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[[[1], [2], [3, 4]], [[1], [3], [2, 4]], [[1], [4], [2, 3]], [[1], [2, 3], [4]], [[1], [2, 4], [3]], [[1], [3, 4], [2]], [[2], [1], [3, 4]], [[2], [3], [1, 4]], [[2], [4], [1, 3]], [[2], [1, 3], [4]], [[2], [1, 4], [3]], [[2], [3, 4], [1]], [[3], [1], [2, 4]], [[3], [2], [1, 4]], [[3], [4], [1, 2]], [[3], [1, 2], [4]], [[3], [1, 4], [2]], [[3], [2, 4], [1]], [[4], [1], [2, 3]], [[4], [2], [1, 3]], [[4], [3], [1, 2]], [[4], [1, 2], [3]], [[4], [1, 3], [2]], [[4], [2, 3], [1]], [[1, 2], [3], [4]], [[1, 2], [4], [3]], [[1, 3], [2], [4]], [[1, 3], [4], [2]], [[1, 4], [2], [3]], [[1, 4], [3], [2]], [[2, 3], [1], [4]], [[2, 3], [4], [1]], [[2, 4], [1], [3]], [[2, 4], [3], [1]], [[3, 4], [1], [2]], [[3, 4], [2], [1]]]"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3,4].full_subbags(3).to_a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "18150"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "digits.full_subbags(3).to_a.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":euler_product"
+      ]
+     },
+     "execution_count": 78,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def euler_product(subbags)\n",
+    "  products = []\n",
+    "  a, b, c = subbags\n",
+    "  csort = c.sort\n",
+    "  a.permutation.each do |ap|\n",
+    "    an = ap.map {|d| d.to_s}.join.to_i\n",
+    "    b.permutation.each do |bp|\n",
+    "      bn = bp.map {|d| d.to_s}.join.to_i\n",
+    "      cn = (an * bn)\n",
+    "      cp = cn.to_s.split('').map {|d| d.to_i}\n",
+    "      if cp.sort == csort\n",
+    "        products << cn\n",
+    "      end\n",
+    "    end\n",
+    "  end\n",
+    "  products\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "123"
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].map {|d| d.to_s}.join.to_i"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1, 2, 3]"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "123.to_s.split('').map {|d| d.to_i}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "12"
+      ]
+     },
+     "execution_count": 85,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3,4].full_subbags(3).flat_map {|bs| euler_product bs}.to_set"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[7254]"
+      ]
+     },
+     "execution_count": 83,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "euler_product([[3, 9], [1, 8, 6], [7, 2, 5, 4]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "45228"
+      ]
+     },
+     "execution_count": 87,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "digits.full_subbags(3).flat_map {|bs| euler_product bs}.to_set.sum"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Ruby 2.4.0",
+   "language": "ruby",
+   "name": "ruby"
+  },
+  "language_info": {
+   "file_extension": ".rb",
+   "mimetype": "application/x-ruby",
+   "name": "ruby",
+   "version": "2.4.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}