192 lines
4.3 KiB
Plaintext
192 lines
4.3 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Euler Problem 35\n",
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"\n",
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"The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\n",
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"\n",
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"There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\n",
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"\n",
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"How many circular primes are there below one million?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"First we get all primes into a look-up table. Then we iterate them and check whether they are circular."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def get_primes_smaller(number):\n",
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" primes = []\n",
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" prospects = [n for n in range(2, number)]\n",
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" while prospects:\n",
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" p = prospects[0]\n",
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" prospects = [x for x in prospects if x % p != 0]\n",
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" primes.append(p)\n",
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" if p * p > number:\n",
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" return primes + prospects\n",
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" return primes\n",
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"\n",
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"ps = get_primes_smaller(1000000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def get_combinations(xs):\n",
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" if not xs:\n",
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" return []\n",
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" rs = []\n",
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" for i in range(len(xs)):\n",
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" yss = get_combinations(xs[:i] + xs[i + 1:])\n",
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" if not yss:\n",
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" rs.append(xs[i])\n",
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" for ys in yss:\n",
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" rs.append(xs[i] + ys)\n",
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" return rs\n",
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"\n",
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"assert(get_combinations(\"ab\") == [\"ab\", \"ba\"])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from itertools import permutations\n",
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"prime_set = set(ps)\n",
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"\n",
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"def is_circular(p):\n",
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" cs = permutations(str(p))\n",
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" for c in cs:\n",
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" if not int(\"\".join(c)) in prime_set:\n",
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" return False\n",
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" return True\n",
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"\n",
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"assert(is_circular(\"2\") == True)\n",
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"assert(is_circular(\"11\") == True)\n",
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"assert(is_circular(\"47\") == False)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"False solution 22\n"
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]
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}
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],
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"source": [
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"s = len([p for p in ps if is_circular(p)])\n",
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"print(\"False solution {}\".format(s))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We did not read the problem properly. Cycles are obviously not the same as permutations. If we change that we should get the solution in no time."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def cyles(xs):\n",
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" if len(xs) <= 1:\n",
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" return xs\n",
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" return [xs[i:] + xs[:i] for i in range(len(xs))]\n",
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"\n",
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"prime_set = set(ps)\n",
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"\n",
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"def is_circular(p):\n",
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" cs = cyles(str(p))\n",
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" for c in cs:\n",
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" if not int(\"\".join(c)) in prime_set:\n",
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" return False\n",
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" return True"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"55"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"s = len([p for p in ps if is_circular(p)])\n",
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"s"
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]
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}
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],
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"metadata": {
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"completion_date": "Tue, 13 Feb 2018, 09:14",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.4"
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},
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"tags": [
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"circular",
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"combinations"
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]
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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