From f0a9468751259255c113b11729e30169f9b2911e Mon Sep 17 00:00:00 2001
From: Neil Smith <neil.git@njae.me.uk>
Date: Thu, 16 Feb 2017 11:17:21 +0000
Subject: [PATCH] Done puzzle 35

---
 euler35.ipynb | 659 ++++++++++++++++++++++++++++++++++++++++++++++++++
 euler35.rb    |  56 +++++
 2 files changed, 715 insertions(+)
 create mode 100644 euler35.ipynb
 create mode 100644 euler35.rb

diff --git a/euler35.ipynb b/euler35.ipynb
new file mode 100644
index 0000000..dcd6039
--- /dev/null
+++ b/euler35.ipynb
@@ -0,0 +1,659 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "#<Primes:0x0055fc1b2516c0 @primes=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 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5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 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9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973], @cache_up_to=30, @mod_candidates=[1, 7, 11, 13, 17, 19, 23, 29]>"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "load 'primes.rb'\n",
+    "$primes = Primes.instance"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":to_r"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class Array\n",
+    "  def to_i\n",
+    "    self.map {|d| d.to_s}.join.to_i\n",
+    "  end\n",
+    "  \n",
+    "  def to_r\n",
+    "    Rational(self[0].to_i, self[1].to_i)\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":to_digits"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class Integer\n",
+    "  def to_digits\n",
+    "    self.to_s.split('').map {|d| d.to_i}\n",
+    "  end\n",
+    "end "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":all_rotations"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class Array\n",
+    "  def all_rotations\n",
+    "    (0...self.length).map {|r| self.rotate(r)}\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[[1, 2, 3], [2, 3, 1], [3, 1, 2]]"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].all_rotations"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[123, 231, 312]"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].all_rotations.map {|n| n.to_i}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[false, false, false]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].all_rotations.map {|n| n.to_i}.map {|n| $primes.include? n}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[true, true]"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "17.to_digits.all_rotations.map {|n| n.to_i}.map {|n| $primes.include? n}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "false"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[1,2,3].all_rotations.map {|n| n.to_i}.all? {|n| $primes.include? n}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "true"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "17.to_digits.all_rotations.map {|n| n.to_i}.all? {|n| $primes.include? n}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":circular_prime?"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class Integer\n",
+    "  @@primes = Primes.instance\n",
+    "  \n",
+    "  def prime?\n",
+    "    @@primes.include? self\n",
+    "  end\n",
+    "  \n",
+    "  def pl\n",
+    "    @@primes.primes.length\n",
+    "  end\n",
+    "  \n",
+    "  def circular_prime?\n",
+    "    self.to_digits.all_rotations.map {|n| n.to_i}.all? {|n| @@primes.include? n} if self.prime?\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":circular_prime?"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "class Integer\n",
+    "  @@primes = Primes.instance\n",
+    "  \n",
+    "  def prime?\n",
+    "    @@primes.include? self\n",
+    "  end\n",
+    "  \n",
+    "  def pl\n",
+    "    @@primes.primes.length\n",
+    "  end\n",
+    "  \n",
+    "  def circular_prime?\n",
+    "    self.to_digits.all_rotations.map {|n| n.to_i}.all? {|n| n.prime?} if self.prime?\n",
+    "  end\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1229"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "0.pl"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(2..100).select {|n| n.circular_prime?}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97]"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(2..100).select {|n| n.circular_prime?}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "13"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(2..100).select {|n| n.circular_prime?}.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# ps = $primes.take_while {|i| i <= 10**6}\n",
+    "# ps.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# (2..10**4).select {|n| n.circular_prime?}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time elapsed 0.125950399 seconds, going from 1229 to 1230 primes cached\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "33"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pl0 = 0.pl\n",
+    "beginning_time = Time.now\n",
+    "cps = (2..10**4).select {|n| n.circular_prime?}\n",
+    "end_time = Time.now\n",
+    "pl1 = 0.pl\n",
+    "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
+    "cps.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time elapsed 0.123380027 seconds, going from 1230 to 1230 primes cached\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "33"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pl0 = 0.pl\n",
+    "beginning_time = Time.now\n",
+    "cps = (2..10**4).select {|n| n.circular_prime?}\n",
+    "end_time = Time.now\n",
+    "pl1 = 0.pl\n",
+    "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
+    "cps.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time elapsed 9.59874264 seconds, going from 1230 to 9593 primes cached\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "43"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pl0 = 0.pl\n",
+    "beginning_time = Time.now\n",
+    "cps = (2..10**5).select {|n| n.circular_prime?}\n",
+    "end_time = Time.now\n",
+    "pl1 = 0.pl\n",
+    "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
+    "cps.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time elapsed 7.768858416 seconds, going from 9593 to 9593 primes cached\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "43"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pl0 = 0.pl\n",
+    "beginning_time = Time.now\n",
+    "cps = (2..10**5).select {|n| n.circular_prime?}\n",
+    "end_time = Time.now\n",
+    "pl1 = 0.pl\n",
+    "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
+    "cps.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time elapsed 710.264030183 seconds, going from 9593 to 78499 primes cached\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "55"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pl0 = 0.pl\n",
+    "beginning_time = Time.now\n",
+    "cps = (2..10**6).select {|n| n.circular_prime?}\n",
+    "end_time = Time.now\n",
+    "pl1 = 0.pl\n",
+    "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
+    "cps.length"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Time elapsed 597.009405584 seconds, going from 78499 to 78499 primes cached\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "55"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pl0 = 0.pl\n",
+    "beginning_time = Time.now\n",
+    "cps = (2..10**6).select {|n| n.circular_prime?}\n",
+    "end_time = Time.now\n",
+    "pl1 = 0.pl\n",
+    "puts \"Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached\"\n",
+    "cps.length"
+   ]
+  },
+  {
+   "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
+}
diff --git a/euler35.rb b/euler35.rb
new file mode 100644
index 0000000..ebe8450
--- /dev/null
+++ b/euler35.rb
@@ -0,0 +1,56 @@
+require 'ruby-prof'
+load 'primes.rb'
+
+class Array
+  def to_i
+    self.map {|d| d.to_s}.join.to_i
+  end
+  
+  def to_r
+    Rational(self[0].to_i, self[1].to_i)
+  end
+
+  def all_rotations
+    (0...self.length).map {|r| self.rotate(r)}
+  end
+end
+
+class Integer
+  @@primes = Primes.instance
+
+  def prime?
+    @@primes.include? self
+  end
+  
+  def pl
+    @@primes.primes.length
+  end
+  
+  def circular_prime?
+    self.to_digits.all_rotations.map {|n| n.to_i}.all? {|n| n.prime?} if self.prime?
+  end
+
+  def to_digits
+    self.to_s.split('').map {|d| d.to_i}
+  end
+end 
+
+
+(10**6).prime?
+
+RubyProf.start
+
+pl0 = 0.pl
+beginning_time = Time.now
+cps = (2..10**6).select {|n| n.circular_prime?}
+end_time = Time.now
+pl1 = 0.pl
+puts "Time elapsed #{(end_time - beginning_time)} seconds, going from #{pl0} to #{pl1} primes cached"
+puts cps.length
+
+result = RubyProf.stop
+
+printer = RubyProf::MultiPrinter.new(result)
+printer.print(:path => ".", :profile => "profile")
+
+
-- 
2.34.1