Started to try 35.

ipython/EulerProblem035.ipynb

@@ -0,0 +1,169 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Euler Problem 35\n",
+    "\n",
+    "The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\n",
+    "\n",
+    "There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\n",
+    "\n",
+    "How many circular primes are there below one million?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First we get all primes into a look-up table. Then we iterate them and check whether they are circular."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "78498\n"
+     ]
+    }
+   ],
+   "source": [
+    "def get_primes_smaller(number):\n",
+    "    primes = []\n",
+    "    prospects = [n for n in range(2, number)]\n",
+    "    while prospects:\n",
+    "        p = prospects[0]\n",
+    "        prospects = [x for x in prospects if x % p != 0]\n",
+    "        primes.append(p)\n",
+    "        if p * p > number:\n",
+    "            return primes + prospects\n",
+    "    return primes\n",
+    "\n",
+    "ps = get_primes_smaller(1000000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def get_combinations(xs):\n",
+    "    if not xs:\n",
+    "        return []\n",
+    "    rs = []\n",
+    "    for i in range(len(xs)):\n",
+    "        yss = get_combinations(xs[:i] + xs[i + 1:])\n",
+    "        if not yss:\n",
+    "            rs.append(xs[i])\n",
+    "        for ys in yss:\n",
+    "            rs.append(xs[i] + ys)\n",
+    "    return rs\n",
+    "\n",
+    "assert(get_combinations(\"ab\") == [\"ab\", \"ba\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "from itertools import permutations\n",
+    "prime_set = set(ps)\n",
+    "\n",
+    "def is_circular(p):\n",
+    "    cs = permutations(str(p))\n",
+    "    for c in cs:\n",
+    "        if not int(\"\".join(c)) in prime_set:\n",
+    "            return False\n",
+    "    return True\n",
+    "\n",
+    "assert(is_circular(\"2\") == True)\n",
+    "assert(is_circular(\"11\") == True)\n",
+    "assert(is_circular(\"47\") == False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "s = [p for p in ps if is_circular(p)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "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": "3.5.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}