{ "cells": [ { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from __future__ import print_function, division\n", "\n", "from itertools import starmap, product\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "import pickle" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def obtainable(coins):\n", " combos = set(coins)\n", " combos.update(map(sum, product(coins, coins)))\n", " return combos" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "coins = [1, 2, 4]" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{1, 2, 3, 4, 5, 6, 8}" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "obtainable(coins)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "values = set(range(1, 11))\n", " \n", "def unobtainable(coins):\n", " return values - obtainable(coins)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{7, 9, 10}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "unobtainable(coins)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def possible_new_coin(coins, value):\n", " if value % 2 == 0:\n", " yield value // 2\n", " \n", " for coin in coins:\n", " if value > coin:\n", " yield value - coin" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{3, 5, 6}" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set(possible_new_coin(coins, 7))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{5, 7, 8}" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set(possible_new_coin(coins, 9))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{5, 6, 8, 9}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set(possible_new_coin(coins, 10))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "class Combinator:\n", " def __init__(self, n):\n", " self.values = set(range(1, n+1))\n", " self.combos = set()\n", " self.considered = set()\n", " self.smallest = 9999\n", "\n", " def unobtainable(self, coins):\n", " return self.values - obtainable(coins)\n", "\n", " def add_combo(self, coins):\n", " n = len(coins)\n", " if n < self.smallest:\n", " self.combos = set()\n", " self.smallest = n\n", " print('new smallest = ', n)\n", " self.combos.add(coins)\n", "\n", " def consider(self, coins):\n", " if len(coins) > self.smallest:\n", " return\n", " \n", " if coins in self.considered:\n", " return\n", "\n", " if len(coins) < 10:\n", " self.considered.add(coins)\n", " \n", " bad_values = self.unobtainable(coins)\n", " if len(bad_values) == 0:\n", " self.add_combo(coins)\n", " return\n", " \n", " for value in sorted(bad_values):\n", " for new_coin in sorted(possible_new_coin(coins, value)):\n", " self.consider(coins | {new_coin})\n", " \n", " def winners(self):\n", " for combo in self.combos:\n", " if len(combo) == self.smallest:\n", " yield combo" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cmap = {}" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cmap[10] = Combinator(10)\n", "cmap[10].values" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "new smallest = 5\n", "new smallest = 4\n" ] } ], "source": [ "cmap[10].consider(frozenset())" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cmap[10].smallest" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 3, 5, 6]\n", "[1, 2, 3, 7]\n", "[1, 2, 5, 8]\n", "[1, 3, 4, 9]\n", "[1, 3, 4, 5]\n", "[1, 2, 5, 7]\n", "[1, 2, 4, 5]\n", "[1, 3, 4, 6]\n" ] } ], "source": [ "for winner in cmap[10].winners():\n", " print(sorted(winner))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cmap[15] = Combinator(15)\n", "cmap[15].values" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "new smallest = 6\n", "new smallest = 5\n" ] } ], "source": [ "for winner in cmap[10].winners():\n", " cmap[15].consider(winner)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cmap[15].consider(frozenset())" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 3, 5, 7, 8]\n", "[1, 3, 4, 9, 11]\n" ] } ], "source": [ "for winner in cmap[15].winners():\n", " print(sorted(winner))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def upgrade(cmap, source, dest):\n", " cmap[dest] = Combinator(dest)\n", "\n", " for winner in cmap[source].winners():\n", " cmap[dest].consider(winner)\n", "\n", " if cmap[dest].smallest > cmap[source].smallest:\n", " print('considering 1')\n", " cmap[dest].consider(frozenset((1, 2, 5)))\n", " print('considering 2')\n", " cmap[dest].consider(frozenset((1, 2, 4)))\n", " print('considering 3')\n", " cmap[dest].consider(frozenset((1, 3, 4)))\n", " print('considering 4')\n", " cmap[dest].consider(frozenset((1, 3, 5)))\n", "\n", " cmap[dest].considered = set()\n", " for winner in cmap[dest].winners():\n", " print(sorted(winner))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "cmap = {}" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "new smallest = 5\n", "new smallest = 4\n" ] } ], "source": [ "cmap[10] = Combinator(10)\n", "cmap[10].consider(frozenset())" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "11\n", "new smallest = 4\n", "[1, 3, 5, 6]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 301 µs\n", "12\n", "new smallest = 4\n", "[1, 3, 5, 6]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 96.3 µs\n", "13\n", "new smallest = 5\n", "considering 1\n", "considering 2\n", "considering 3\n", "considering 4\n", "[1, 3, 5, 7, 8]\n", "[1, 3, 5, 6, 8]\n", "[1, 2, 5, 6, 8]\n", "[1, 2, 5, 8, 11]\n", "[1, 3, 5, 6, 10]\n", "[1, 2, 4, 6, 7]\n", "[1, 2, 4, 6, 9]\n", "[1, 2, 3, 4, 9]\n", "[1, 3, 4, 5, 8]\n", "[1, 3, 5, 6, 7]\n", "[1, 2, 5, 8, 10]\n", "[1, 3, 4, 9, 10]\n", "[1, 3, 4, 8, 9]\n", "[1, 3, 4, 9, 11]\n", "[1, 2, 4, 5, 11]\n", "[1, 3, 4, 6, 7]\n", "[1, 3, 4, 8, 10]\n", "[1, 3, 4, 6, 10]\n", "[1, 2, 5, 6, 7]\n", "[1, 3, 4, 7, 9]\n", "[1, 3, 5, 6, 12]\n", "[1, 2, 5, 7, 11]\n", "CPU times: user 8 ms, sys: 0 ns, total: 8 ms\n", "Wall time: 5.88 ms\n", "14\n", "new smallest = 5\n", "[1, 2, 5, 7, 11]\n", "[1, 3, 5, 7, 8]\n", "[1, 3, 4, 9, 11]\n", "[1, 3, 5, 6, 8]\n", "[1, 3, 4, 6, 7]\n", "[1, 2, 5, 6, 8]\n", "[1, 3, 4, 8, 10]\n", "[1, 3, 4, 6, 10]\n", "[1, 3, 4, 7, 9]\n", "[1, 3, 5, 6, 7]\n", "[1, 2, 4, 6, 7]\n", "[1, 3, 4, 9, 10]\n", "[1, 2, 5, 6, 7]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 783 µs\n", "15\n", "new smallest = 6\n", "new smallest = 5\n", "[1, 3, 5, 7, 8]\n", "[1, 3, 4, 9, 11]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 642 µs\n", "16\n", "new smallest = 5\n", "[1, 3, 5, 7, 8]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 125 µs\n", "17\n", "new smallest = 6\n", "considering 1\n", "considering 2\n", "considering 3\n", "considering 4\n", "[1, 3, 5, 7, 8, 10]\n", "[1, 3, 4, 5, 7, 12]\n", "[1, 2, 5, 6, 8, 9]\n", "[1, 2, 5, 6, 9, 11]\n", "[1, 3, 4, 7, 9, 14]\n", "[1, 3, 5, 7, 9, 10]\n", "[1, 2, 4, 5, 11, 12]\n", "[1, 3, 5, 6, 8, 9]\n", "[1, 2, 5, 7, 8, 10]\n", "[1, 3, 4, 6, 11, 12]\n", "[1, 3, 5, 7, 8, 14]\n", "[1, 2, 4, 6, 8, 11]\n", "[1, 3, 4, 7, 8, 10]\n", "[1, 3, 4, 8, 9, 14]\n", "[1, 3, 4, 7, 8, 9]\n", "[1, 3, 4, 6, 11, 13]\n", "[1, 3, 5, 7, 8, 12]\n", "[1, 2, 3, 5, 8, 12]\n", "[1, 3, 5, 6, 10, 11]\n", "[1, 2, 4, 7, 8, 13]\n", "[1, 3, 5, 6, 13, 14]\n", "[1, 2, 5, 7, 10, 11]\n", "[1, 2, 5, 6, 7, 10]\n", "[1, 3, 4, 5, 8, 14]\n", "[1, 2, 5, 6, 8, 15]\n", "[1, 3, 4, 5, 10, 12]\n", "[1, 2, 5, 8, 9, 10]\n", "[1, 3, 4, 6, 10, 14]\n", "[1, 3, 4, 8, 10, 14]\n", "[1, 2, 4, 5, 10, 12]\n", "[1, 3, 5, 6, 7, 10]\n", "[1, 2, 3, 4, 9, 14]\n", "[1, 2, 4, 5, 11, 13]\n", "[1, 2, 4, 6, 7, 15]\n", "[1, 3, 5, 6, 8, 12]\n", "[1, 3, 5, 6, 10, 14]\n", "[1, 3, 5, 6, 11, 12]\n", "[1, 3, 5, 6, 12, 13]\n", "[1, 3, 5, 7, 8, 16]\n", "[1, 3, 4, 5, 11, 12]\n", "[1, 3, 4, 5, 11, 13]\n", "[1, 2, 5, 6, 7, 15]\n", "[1, 2, 5, 7, 11, 15]\n", "[1, 2, 5, 7, 8, 9]\n", "[1, 2, 5, 8, 10, 12]\n", "[1, 3, 4, 9, 11, 13]\n", "[1, 3, 4, 7, 8, 13]\n", "[1, 2, 3, 4, 8, 13]\n", "[1, 3, 4, 6, 8, 9]\n", "[1, 3, 4, 8, 9, 11]\n", "[1, 2, 4, 6, 8, 9]\n", "[1, 3, 4, 6, 10, 11]\n", "[1, 3, 5, 6, 8, 14]\n", "[1, 3, 4, 9, 11, 16]\n", "[1, 2, 4, 7, 8, 9]\n", "[1, 3, 5, 7, 8, 9]\n", "[1, 2, 3, 4, 9, 13]\n", "CPU times: user 52 ms, sys: 0 ns, total: 52 ms\n", "Wall time: 53 ms\n", "18\n", "new smallest = 6\n", "[1, 3, 5, 7, 8, 10]\n", "[1, 2, 5, 6, 8, 9]\n", "[1, 2, 5, 6, 9, 11]\n", "[1, 3, 4, 7, 9, 14]\n", "[1, 3, 5, 7, 9, 10]\n", "[1, 3, 5, 6, 8, 9]\n", "[1, 2, 5, 7, 8, 10]\n", "[1, 3, 4, 6, 11, 12]\n", "[1, 3, 4, 7, 8, 10]\n", "[1, 3, 4, 8, 9, 14]\n", "[1, 3, 4, 7, 8, 9]\n", "[1, 3, 5, 6, 13, 14]\n", "[1, 2, 5, 7, 10, 11]\n", "[1, 3, 4, 5, 8, 14]\n", "[1, 3, 4, 6, 10, 14]\n", "[1, 3, 4, 8, 10, 14]\n", "[1, 2, 5, 8, 9, 10]\n", "[1, 2, 3, 4, 9, 14]\n", "[1, 2, 4, 5, 11, 13]\n", "[1, 3, 5, 6, 8, 12]\n", "[1, 3, 5, 6, 11, 12]\n", "[1, 3, 5, 6, 12, 13]\n", "[1, 3, 4, 5, 11, 13]\n", "[1, 2, 5, 7, 11, 15]\n", "[1, 2, 5, 7, 8, 9]\n", "[1, 2, 5, 8, 10, 12]\n", "[1, 3, 4, 9, 11, 13]\n", "[1, 3, 4, 8, 9, 11]\n", "[1, 3, 4, 6, 8, 9]\n", "[1, 2, 4, 6, 8, 9]\n", "[1, 3, 4, 9, 11, 16]\n", "[1, 2, 4, 7, 8, 9]\n", "[1, 3, 5, 7, 8, 9]\n", "[1, 2, 3, 4, 9, 13]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 1.64 ms\n", "19\n", "new smallest = 7\n", "new smallest = 6\n", "[1, 3, 5, 6, 13, 14]\n", "[1, 3, 5, 7, 9, 10]\n", "[1, 3, 4, 5, 8, 14]\n", "[1, 3, 4, 8, 9, 11]\n", "[1, 3, 5, 6, 12, 13]\n", "[1, 2, 5, 8, 9, 10]\n", "[1, 3, 4, 9, 11, 16]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 1.42 ms\n", "20\n", "new smallest = 6\n", "[1, 3, 4, 9, 11, 16]\n", "[1, 3, 5, 6, 13, 14]\n", "[1, 3, 5, 7, 9, 10]\n", "[1, 3, 4, 8, 9, 11]\n", "[1, 2, 5, 8, 9, 10]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 400 µs\n" ] } ], "source": [ "for n in range(10, 20):\n", " print(n+1)\n", " %time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "21\n", "new smallest = 7\n", "considering 1\n", "considering 2\n", "considering 3\n", "considering 4\n", "[1, 3, 4, 7, 9, 12, 13]\n", "[1, 2, 3, 4, 7, 12, 17]\n", "[1, 2, 4, 5, 11, 13, 19]\n", "[1, 2, 5, 8, 10, 13, 17]\n", "[1, 2, 3, 4, 8, 13, 16]\n", "[1, 2, 4, 5, 6, 13, 15]\n", "[1, 3, 5, 6, 7, 9, 14]\n", "[1, 2, 4, 7, 9, 10, 11]\n", "[1, 2, 4, 7, 9, 12, 13]\n", "[1, 3, 4, 7, 9, 12, 16]\n", "[1, 3, 5, 6, 11, 13, 15]\n", "[1, 2, 5, 7, 10, 11, 19]\n", "[1, 3, 5, 6, 10, 11, 18]\n", "[1, 3, 4, 7, 8, 9, 12]\n", "[1, 3, 5, 7, 9, 10, 20]\n", "[1, 3, 4, 7, 8, 12, 17]\n", "[1, 2, 4, 7, 8, 11, 13]\n", "[1, 3, 4, 9, 11, 12, 16]\n", "[1, 3, 4, 6, 7, 15, 16]\n", "[1, 3, 5, 7, 8, 12, 18]\n", "[1, 2, 5, 6, 9, 10, 12]\n", "[1, 3, 4, 9, 11, 16, 20]\n", "[1, 3, 5, 6, 13, 14, 20]\n", "[1, 2, 3, 4, 9, 12, 17]\n", "[1, 2, 4, 5, 8, 10, 17]\n", "[1, 2, 5, 7, 8, 10, 14]\n", "[1, 2, 4, 7, 8, 13, 17]\n", "[1, 3, 4, 9, 10, 12, 14]\n", "[1, 3, 5, 6, 10, 14, 18]\n", "[1, 3, 4, 5, 8, 13, 15]\n", "[1, 3, 5, 7, 8, 16, 17]\n", "[1, 3, 4, 9, 10, 12, 13]\n", "[1, 2, 5, 7, 10, 11, 12]\n", "[1, 2, 4, 7, 9, 10, 14]\n", "[1, 3, 4, 5, 8, 14, 16]\n", "[1, 2, 5, 7, 8, 9, 19]\n", "[1, 3, 4, 5, 9, 10, 16]\n", "[1, 2, 5, 8, 10, 12, 19]\n", "[1, 2, 3, 5, 8, 12, 16]\n", "[1, 3, 4, 6, 7, 12, 17]\n", "[1, 3, 4, 8, 10, 11, 13]\n", "[1, 2, 5, 8, 9, 10, 20]\n", "[1, 2, 4, 6, 8, 9, 19]\n", "[1, 3, 4, 6, 10, 13, 15]\n", "[1, 3, 5, 7, 8, 14, 15]\n", "[1, 3, 5, 6, 13, 15, 17]\n", "[1, 3, 4, 9, 11, 13, 18]\n", "[1, 3, 4, 8, 9, 11, 20]\n", "[1, 2, 5, 7, 9, 12, 13]\n", "[1, 2, 5, 7, 10, 12, 16]\n", "[1, 3, 4, 6, 10, 11, 18]\n", "[1, 2, 5, 6, 8, 12, 13]\n", "[1, 2, 5, 7, 10, 11, 17]\n", "[1, 3, 4, 5, 7, 13, 14]\n", "[1, 3, 4, 8, 9, 11, 12]\n", "[1, 2, 5, 6, 8, 10, 11]\n", "[1, 3, 4, 5, 9, 10, 12]\n", "[1, 3, 4, 6, 7, 15, 17]\n", "[1, 3, 4, 5, 10, 11, 14]\n", "[1, 3, 5, 6, 8, 12, 16]\n", "[1, 3, 5, 7, 8, 12, 13]\n", "[1, 2, 4, 5, 9, 10, 12]\n", "[1, 2, 4, 5, 7, 13, 14]\n", "[1, 3, 5, 6, 8, 12, 13]\n", "[1, 3, 4, 6, 7, 14, 15]\n", "[1, 2, 4, 5, 11, 14, 16]\n", "[1, 2, 3, 4, 9, 13, 18]\n", "[1, 3, 4, 5, 11, 13, 16]\n", "[1, 2, 4, 5, 9, 12, 15]\n", "[1, 2, 4, 6, 7, 14, 15]\n", "[1, 2, 3, 4, 9, 13, 17]\n", "[1, 2, 4, 7, 8, 13, 18]\n", "[1, 3, 4, 7, 9, 10, 14]\n", "[1, 2, 4, 6, 9, 10, 15]\n", "[1, 3, 5, 6, 9, 10, 16]\n", "[1, 2, 5, 8, 11, 13, 15]\n", "[1, 3, 4, 6, 10, 14, 18]\n", "[1, 2, 5, 6, 8, 15, 18]\n", "[1, 3, 4, 7, 9, 14, 19]\n", "[1, 3, 4, 8, 9, 11, 17]\n", "[1, 3, 5, 7, 8, 10, 14]\n", "[1, 2, 3, 5, 8, 12, 18]\n", "[1, 3, 5, 6, 13, 14, 18]\n", "[1, 3, 4, 5, 8, 14, 17]\n", "[1, 3, 4, 5, 8, 10, 16]\n", "[1, 3, 5, 6, 10, 14, 15]\n", "[1, 2, 5, 6, 8, 9, 19]\n", "[1, 3, 4, 7, 9, 14, 16]\n", "[1, 3, 4, 8, 9, 11, 13]\n", "[1, 2, 4, 5, 9, 10, 16]\n", "[1, 2, 3, 4, 8, 11, 17]\n", "[1, 2, 3, 4, 9, 12, 16]\n", "[1, 2, 4, 6, 9, 14, 15]\n", "[1, 3, 4, 6, 10, 14, 15]\n", "[1, 3, 4, 9, 10, 12, 17]\n", "[1, 2, 5, 6, 7, 15, 18]\n", "[1, 2, 4, 7, 9, 11, 17]\n", "[1, 2, 4, 7, 10, 12, 14]\n", "[1, 2, 5, 7, 9, 10, 11]\n", "[1, 3, 4, 7, 9, 10, 11]\n", "[1, 2, 5, 8, 10, 11, 12]\n", "[1, 3, 4, 5, 6, 13, 15]\n", "[1, 2, 4, 5, 10, 12, 17]\n", "[1, 2, 4, 6, 9, 10, 11]\n", "[1, 2, 5, 6, 7, 14, 17]\n", "[1, 3, 4, 5, 9, 11, 16]\n", "[1, 2, 4, 7, 8, 10, 11]\n", "[1, 3, 5, 6, 12, 13, 15]\n", "[1, 3, 4, 7, 9, 12, 17]\n", "[1, 2, 3, 4, 9, 13, 19]\n", "[1, 3, 5, 6, 12, 14, 16]\n", "[1, 2, 5, 6, 7, 13, 15]\n", "[1, 2, 3, 5, 9, 10, 16]\n", "[1, 3, 5, 6, 7, 15, 16]\n", "[1, 2, 3, 4, 8, 13, 17]\n", "[1, 2, 4, 7, 8, 12, 17]\n", "[1, 2, 5, 7, 11, 15, 19]\n", "[1, 3, 4, 5, 8, 14, 20]\n", "[1, 3, 5, 6, 10, 11, 13]\n", "[1, 2, 3, 4, 8, 13, 18]\n", "[1, 3, 4, 5, 6, 9, 16]\n", "[1, 2, 5, 8, 9, 12, 14]\n", "[1, 2, 5, 8, 9, 10, 11]\n", "[1, 3, 4, 7, 9, 15, 17]\n", "[1, 3, 5, 6, 13, 15, 16]\n", "[1, 2, 5, 6, 7, 12, 14]\n", "[1, 3, 4, 8, 9, 10, 11]\n", "[1, 3, 5, 7, 8, 10, 16]\n", "[1, 3, 5, 6, 12, 13, 20]\n", "[1, 3, 5, 6, 7, 12, 15]\n", "[1, 2, 4, 6, 8, 10, 13]\n", "[1, 3, 5, 6, 13, 14, 15]\n", "[1, 3, 4, 5, 7, 12, 17]\n", "[1, 3, 4, 9, 10, 11, 13]\n", "[1, 3, 5, 7, 8, 17, 18]\n", "[1, 2, 5, 6, 8, 13, 15]\n", "[1, 3, 4, 6, 9, 10, 17]\n", "[1, 3, 5, 6, 8, 15, 16]\n", "[1, 3, 4, 9, 11, 16, 17]\n", "[1, 2, 5, 7, 10, 13, 14]\n", "[1, 3, 5, 6, 8, 13, 14]\n", "[1, 2, 5, 6, 8, 14, 16]\n", "[1, 2, 5, 8, 9, 11, 13]\n", "[1, 3, 5, 7, 8, 13, 16]\n", "[1, 2, 4, 5, 6, 12, 15]\n", "[1, 2, 3, 4, 6, 10, 15]\n", "[1, 2, 5, 6, 7, 11, 14]\n", "[1, 2, 4, 7, 8, 9, 19]\n", "[1, 3, 4, 7, 8, 10, 11]\n", "[1, 2, 5, 7, 11, 14, 15]\n", "[1, 3, 4, 6, 9, 10, 11]\n", "[1, 2, 4, 6, 7, 14, 17]\n", "[1, 3, 4, 8, 10, 14, 18]\n", "[1, 2, 4, 5, 6, 13, 16]\n", "[1, 2, 5, 6, 7, 15, 17]\n", "[1, 3, 4, 6, 8, 10, 11]\n", "[1, 3, 5, 7, 9, 10, 11]\n", "[1, 2, 5, 8, 9, 10, 16]\n", "[1, 3, 5, 7, 8, 10, 11]\n", "[1, 3, 4, 9, 10, 15, 17]\n", "[1, 3, 5, 6, 9, 10, 11]\n", "[1, 2, 4, 5, 10, 11, 17]\n", "[1, 3, 4, 5, 8, 11, 17]\n", "[1, 2, 5, 7, 10, 11, 14]\n", "[1, 3, 5, 7, 9, 10, 12]\n", "[1, 2, 3, 4, 9, 14, 17]\n", "[1, 3, 4, 8, 10, 13, 15]\n", "[1, 3, 5, 6, 9, 10, 12]\n", "[1, 3, 5, 7, 8, 9, 12]\n", "[1, 2, 3, 4, 5, 11, 16]\n", "[1, 2, 5, 8, 10, 14, 16]\n", "[1, 3, 4, 6, 7, 13, 14]\n", "[1, 3, 5, 6, 7, 14, 15]\n", "[1, 2, 4, 6, 9, 14, 17]\n", "[1, 3, 4, 6, 7, 12, 14]\n", "[1, 2, 5, 6, 8, 15, 17]\n", "[1, 3, 5, 6, 8, 14, 18]\n", "[1, 3, 4, 8, 10, 11, 17]\n", "[1, 3, 5, 6, 8, 10, 16]\n", "[1, 3, 5, 7, 9, 10, 16]\n", "[1, 3, 4, 6, 10, 15, 17]\n", "[1, 3, 4, 8, 9, 11, 18]\n", "[1, 3, 4, 7, 8, 13, 18]\n", "[1, 3, 4, 8, 10, 11, 14]\n", "[1, 3, 4, 9, 11, 16, 18]\n", "[1, 3, 4, 7, 8, 13, 15]\n", "[1, 3, 4, 6, 10, 15, 16]\n", "[1, 3, 4, 7, 8, 10, 18]\n", "[1, 2, 3, 4, 5, 11, 17]\n", "[1, 3, 4, 8, 10, 11, 16]\n", "[1, 3, 5, 6, 8, 14, 15]\n", "[1, 2, 5, 8, 9, 10, 12]\n", "[1, 2, 5, 7, 8, 10, 19]\n", "[1, 3, 4, 8, 9, 10, 12]\n", "[1, 3, 4, 7, 8, 12, 14]\n", "[1, 2, 5, 6, 9, 10, 11]\n", "[1, 2, 5, 8, 9, 10, 13]\n", "[1, 2, 5, 7, 8, 10, 11]\n", "[1, 2, 5, 7, 10, 11, 18]\n", "[1, 3, 4, 5, 10, 12, 18]\n", "[1, 2, 5, 6, 9, 11, 19]\n", "[1, 3, 5, 6, 8, 10, 11]\n", "[1, 3, 4, 8, 10, 15, 17]\n", "[1, 2, 4, 6, 8, 10, 11]\n", "[1, 3, 4, 6, 7, 10, 15]\n", "[1, 2, 5, 7, 9, 12, 15]\n", "[1, 2, 4, 6, 7, 15, 18]\n", "[1, 2, 4, 6, 7, 13, 14]\n", "[1, 2, 4, 5, 6, 9, 15]\n", "[1, 3, 4, 6, 7, 14, 16]\n", "[1, 2, 5, 7, 8, 9, 12]\n", "[1, 3, 5, 6, 7, 13, 14]\n", "[1, 2, 5, 6, 7, 14, 16]\n", "[1, 2, 5, 8, 11, 12, 13]\n", "[1, 2, 4, 7, 10, 11, 15]\n", "[1, 2, 4, 6, 7, 15, 16]\n", "[1, 2, 5, 6, 7, 13, 16]\n", "[1, 3, 4, 6, 7, 13, 15]\n", "[1, 2, 3, 4, 9, 14, 19]\n", "[1, 3, 4, 6, 9, 11, 15]\n", "[1, 2, 5, 7, 9, 10, 12]\n", "[1, 3, 4, 6, 10, 11, 15]\n", "[1, 3, 4, 7, 8, 11, 13]\n", "[1, 3, 5, 6, 8, 12, 18]\n", "[1, 3, 4, 7, 9, 10, 12]\n", "[1, 3, 4, 6, 11, 13, 17]\n", "[1, 3, 5, 6, 7, 10, 18]\n", "[1, 2, 4, 5, 9, 11, 17]\n", "[1, 2, 5, 8, 9, 10, 19]\n", "[1, 2, 3, 4, 9, 14, 18]\n", "[1, 2, 4, 7, 8, 9, 12]\n", "[1, 3, 5, 6, 8, 11, 15]\n", "[1, 3, 5, 7, 8, 14, 17]\n", "[1, 2, 4, 7, 10, 11, 12]\n", "[1, 3, 4, 9, 10, 12, 16]\n", "[1, 2, 3, 4, 5, 10, 16]\n", "[1, 2, 3, 4, 8, 12, 17]\n", "[1, 2, 5, 6, 7, 12, 15]\n", "[1, 2, 3, 5, 6, 13, 15]\n", "[1, 3, 5, 6, 13, 14, 16]\n", "[1, 3, 5, 7, 9, 10, 14]\n", "[1, 3, 5, 7, 9, 11, 12]\n", "[1, 3, 5, 6, 7, 11, 14]\n", "[1, 3, 5, 6, 12, 14, 15]\n", "[1, 3, 5, 7, 8, 13, 14]\n", "[1, 3, 4, 9, 11, 15, 17]\n", "[1, 2, 5, 6, 9, 13, 15]\n", "[1, 2, 3, 5, 7, 10, 16]\n", "[1, 3, 5, 6, 10, 13, 16]\n", "[1, 3, 5, 7, 8, 15, 16]\n", "[1, 3, 4, 6, 8, 13, 14]\n", "[1, 3, 5, 7, 8, 10, 18]\n", "[1, 2, 4, 6, 9, 10, 17]\n", "[1, 3, 5, 7, 9, 10, 18]\n", "[1, 3, 4, 9, 10, 11, 16]\n", "[1, 3, 4, 6, 8, 12, 13]\n", "[1, 2, 5, 6, 9, 12, 14]\n", "CPU times: user 344 ms, sys: 0 ns, total: 344 ms\n", "Wall time: 346 ms\n", "22\n", "new smallest = 7\n", "[1, 3, 4, 7, 9, 12, 13]\n", "[1, 2, 4, 5, 11, 13, 19]\n", "[1, 2, 5, 8, 10, 13, 17]\n", "[1, 2, 4, 7, 9, 10, 11]\n", "[1, 2, 4, 7, 9, 12, 13]\n", "[1, 3, 5, 6, 11, 13, 15]\n", "[1, 2, 5, 7, 10, 11, 19]\n", "[1, 3, 5, 6, 10, 11, 18]\n", "[1, 2, 4, 7, 8, 11, 13]\n", "[1, 3, 4, 9, 11, 12, 16]\n", "[1, 3, 4, 6, 7, 15, 16]\n", "[1, 2, 5, 6, 9, 10, 12]\n", "[1, 3, 4, 9, 11, 16, 20]\n", "[1, 2, 4, 5, 8, 10, 17]\n", "[1, 2, 5, 7, 8, 10, 14]\n", "[1, 3, 4, 9, 10, 12, 14]\n", "[1, 3, 5, 7, 8, 16, 17]\n", "[1, 3, 4, 9, 10, 12, 13]\n", "[1, 2, 5, 7, 10, 11, 12]\n", "[1, 3, 4, 5, 8, 14, 16]\n", "[1, 2, 5, 8, 10, 12, 19]\n", "[1, 3, 4, 8, 10, 11, 13]\n", "[1, 2, 5, 8, 9, 10, 20]\n", "[1, 3, 5, 7, 8, 14, 15]\n", "[1, 3, 5, 6, 13, 15, 17]\n", "[1, 3, 4, 9, 11, 13, 18]\n", "[1, 3, 4, 8, 9, 11, 20]\n", "[1, 2, 5, 7, 9, 12, 13]\n", "[1, 2, 5, 7, 10, 12, 16]\n", "[1, 3, 4, 6, 10, 11, 18]\n", "[1, 2, 5, 7, 10, 11, 17]\n", "[1, 3, 5, 6, 8, 12, 16]\n", "[1, 3, 4, 8, 9, 11, 12]\n", "[1, 2, 5, 6, 8, 10, 11]\n", "[1, 3, 4, 5, 9, 10, 12]\n", "[1, 3, 4, 6, 7, 15, 17]\n", "[1, 3, 4, 5, 10, 11, 14]\n", "[1, 2, 4, 5, 9, 10, 12]\n", "[1, 3, 4, 6, 7, 14, 15]\n", "[1, 2, 4, 5, 11, 14, 16]\n", "[1, 2, 3, 4, 9, 13, 18]\n", "[1, 3, 4, 5, 11, 13, 16]\n", "[1, 2, 4, 6, 7, 14, 15]\n", "[1, 2, 3, 4, 9, 13, 17]\n", "[1, 2, 4, 7, 8, 13, 18]\n", "[1, 3, 5, 6, 9, 10, 16]\n", "[1, 2, 5, 8, 11, 13, 15]\n", "[1, 3, 4, 6, 10, 14, 18]\n", "[1, 3, 4, 7, 9, 14, 19]\n", "[1, 3, 4, 8, 9, 11, 17]\n", "[1, 3, 5, 7, 8, 10, 14]\n", "[1, 3, 4, 5, 8, 14, 17]\n", "[1, 3, 4, 8, 9, 11, 13]\n", "[1, 2, 3, 4, 8, 11, 17]\n", "[1, 3, 4, 9, 10, 12, 17]\n", "[1, 2, 5, 6, 7, 15, 18]\n", "[1, 2, 4, 7, 9, 11, 17]\n", "[1, 2, 4, 7, 10, 12, 14]\n", "[1, 2, 5, 7, 9, 10, 11]\n", "[1, 3, 4, 7, 9, 10, 11]\n", "[1, 2, 5, 8, 10, 11, 12]\n", "[1, 2, 4, 5, 10, 12, 17]\n", "[1, 2, 4, 6, 9, 10, 11]\n", "[1, 2, 5, 6, 7, 14, 17]\n", "[1, 3, 4, 5, 9, 11, 16]\n", "[1, 2, 4, 7, 8, 10, 11]\n", "[1, 2, 3, 4, 9, 13, 19]\n", "[1, 3, 5, 6, 12, 14, 16]\n", "[1, 2, 5, 6, 7, 13, 15]\n", "[1, 3, 5, 6, 7, 15, 16]\n", "[1, 2, 5, 7, 11, 15, 19]\n", "[1, 3, 4, 5, 8, 14, 20]\n", "[1, 3, 5, 6, 10, 11, 13]\n", "[1, 2, 3, 4, 8, 13, 18]\n", "[1, 3, 4, 5, 6, 9, 16]\n", "[1, 2, 5, 8, 9, 12, 14]\n", "[1, 3, 4, 7, 9, 15, 17]\n", "[1, 3, 5, 6, 13, 15, 16]\n", "[1, 2, 5, 8, 9, 10, 11]\n", "[1, 3, 4, 8, 9, 10, 11]\n", "[1, 3, 5, 6, 7, 12, 15]\n", "[1, 3, 4, 5, 7, 12, 17]\n", "[1, 3, 4, 9, 10, 11, 13]\n", "[1, 3, 5, 7, 8, 17, 18]\n", "[1, 3, 5, 6, 8, 15, 16]\n", "[1, 3, 4, 9, 11, 16, 17]\n", "[1, 3, 5, 6, 8, 13, 14]\n", "[1, 2, 5, 6, 8, 14, 16]\n", "[1, 2, 5, 8, 9, 11, 13]\n", "[1, 2, 5, 6, 7, 11, 14]\n", "[1, 3, 4, 7, 8, 10, 11]\n", "[1, 2, 5, 7, 11, 14, 15]\n", "[1, 3, 4, 6, 9, 10, 11]\n", "[1, 3, 4, 8, 10, 14, 18]\n", "[1, 2, 4, 5, 6, 13, 16]\n", "[1, 2, 5, 6, 7, 15, 17]\n", "[1, 3, 4, 6, 8, 10, 11]\n", "[1, 3, 5, 7, 9, 10, 11]\n", "[1, 3, 5, 7, 8, 10, 11]\n", "[1, 3, 5, 6, 9, 10, 11]\n", "[1, 2, 4, 5, 10, 11, 17]\n", "[1, 3, 4, 5, 8, 11, 17]\n", "[1, 2, 5, 7, 10, 11, 14]\n", "[1, 3, 5, 7, 9, 10, 12]\n", "[1, 2, 3, 4, 5, 11, 16]\n", "[1, 2, 5, 8, 10, 14, 16]\n", "[1, 3, 5, 6, 7, 14, 15]\n", "[1, 2, 5, 6, 8, 15, 17]\n", "[1, 3, 5, 6, 8, 14, 18]\n", "[1, 3, 4, 8, 10, 11, 17]\n", "[1, 3, 5, 6, 8, 10, 16]\n", "[1, 3, 4, 8, 9, 11, 18]\n", "[1, 3, 4, 7, 8, 13, 18]\n", "[1, 3, 4, 8, 10, 11, 14]\n", "[1, 3, 4, 9, 11, 16, 18]\n", "[1, 3, 4, 7, 8, 13, 15]\n", "[1, 3, 4, 6, 10, 15, 16]\n", "[1, 3, 4, 7, 8, 10, 18]\n", "[1, 3, 4, 8, 10, 11, 16]\n", "[1, 3, 5, 6, 8, 14, 15]\n", "[1, 2, 5, 8, 9, 10, 12]\n", "[1, 3, 4, 8, 9, 10, 12]\n", "[1, 3, 4, 7, 8, 12, 14]\n", "[1, 2, 5, 6, 9, 10, 11]\n", "[1, 2, 5, 8, 9, 10, 13]\n", "[1, 2, 5, 7, 8, 10, 11]\n", "[1, 2, 5, 7, 10, 11, 18]\n", "[1, 3, 4, 5, 10, 12, 18]\n", "[1, 2, 5, 6, 9, 11, 19]\n", "[1, 3, 5, 6, 8, 10, 11]\n", "[1, 2, 4, 6, 8, 10, 11]\n", "[1, 3, 4, 6, 7, 10, 15]\n", "[1, 2, 5, 7, 9, 12, 15]\n", "[1, 2, 4, 6, 7, 15, 18]\n", "[1, 3, 4, 6, 7, 14, 16]\n", "[1, 2, 5, 8, 11, 12, 13]\n", "[1, 2, 5, 6, 7, 14, 16]\n", "[1, 3, 5, 6, 9, 10, 12]\n", "[1, 2, 4, 7, 10, 11, 15]\n", "[1, 2, 4, 6, 7, 15, 16]\n", "[1, 2, 5, 6, 7, 13, 16]\n", "[1, 3, 4, 6, 7, 13, 15]\n", "[1, 2, 3, 4, 9, 14, 19]\n", "[1, 3, 4, 6, 9, 11, 15]\n", "[1, 2, 5, 7, 9, 10, 12]\n", "[1, 3, 4, 6, 10, 11, 15]\n", "[1, 3, 4, 7, 8, 11, 13]\n", "[1, 3, 4, 7, 9, 10, 12]\n", "[1, 3, 4, 6, 11, 13, 17]\n", "[1, 2, 4, 5, 9, 11, 17]\n", "[1, 2, 3, 4, 9, 14, 18]\n", "[1, 3, 5, 6, 8, 11, 15]\n", "[1, 3, 5, 7, 8, 14, 17]\n", "[1, 2, 4, 7, 10, 11, 12]\n", "[1, 3, 4, 9, 10, 12, 16]\n", "[1, 2, 5, 6, 7, 12, 15]\n", "[1, 3, 5, 6, 13, 14, 16]\n", "[1, 3, 5, 7, 9, 11, 12]\n", "[1, 3, 5, 6, 7, 11, 14]\n", "[1, 3, 5, 7, 8, 13, 14]\n", "[1, 3, 4, 9, 11, 15, 17]\n", "[1, 2, 5, 6, 9, 13, 15]\n", "[1, 3, 5, 6, 10, 13, 16]\n", "[1, 3, 5, 7, 8, 15, 16]\n", "[1, 3, 4, 6, 8, 13, 14]\n", "[1, 3, 4, 9, 10, 11, 16]\n", "[1, 2, 3, 4, 5, 11, 17]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 4.66 ms\n", "23\n", "new smallest = 8\n", "new smallest = 7\n", "[1, 2, 4, 5, 11, 13, 19]\n", "[1, 2, 5, 8, 10, 13, 17]\n", "[1, 3, 4, 7, 8, 13, 15]\n", "[1, 3, 5, 6, 8, 14, 15]\n", "[1, 3, 5, 6, 10, 11, 18]\n", "[1, 3, 4, 9, 10, 11, 13]\n", "[1, 3, 5, 7, 8, 17, 18]\n", "[1, 3, 5, 6, 8, 15, 16]\n", "[1, 2, 5, 8, 11, 13, 15]\n", "[1, 2, 5, 8, 9, 10, 13]\n", "[1, 2, 5, 7, 10, 11, 18]\n", "[1, 3, 4, 5, 10, 12, 18]\n", "[1, 3, 4, 7, 9, 14, 19]\n", "[1, 3, 4, 9, 11, 12, 16]\n", "[1, 3, 4, 6, 7, 15, 16]\n", "[1, 3, 4, 9, 11, 16, 20]\n", "[1, 3, 4, 6, 7, 14, 16]\n", "[1, 2, 5, 8, 11, 12, 13]\n", "[1, 2, 5, 6, 7, 14, 16]\n", "[1, 2, 5, 6, 7, 15, 17]\n", "[1, 2, 4, 6, 7, 15, 16]\n", "[1, 2, 5, 6, 7, 13, 16]\n", "[1, 2, 3, 4, 9, 14, 19]\n", "[1, 3, 4, 9, 10, 12, 14]\n", "[1, 3, 5, 7, 8, 16, 17]\n", "[1, 3, 4, 6, 11, 13, 17]\n", "[1, 3, 4, 9, 10, 12, 13]\n", "[1, 2, 3, 4, 9, 14, 18]\n", "[1, 2, 5, 7, 10, 11, 12]\n", "[1, 3, 5, 6, 8, 11, 15]\n", "[1, 2, 4, 7, 10, 11, 12]\n", "[1, 2, 5, 6, 7, 15, 18]\n", "[1, 3, 4, 8, 10, 11, 13]\n", "[1, 2, 5, 8, 10, 11, 12]\n", "[1, 3, 5, 7, 8, 14, 15]\n", "[1, 3, 5, 6, 13, 15, 17]\n", "[1, 3, 5, 7, 9, 11, 12]\n", "[1, 2, 5, 6, 7, 14, 17]\n", "[1, 3, 4, 8, 9, 11, 20]\n", "[1, 2, 5, 6, 8, 15, 17]\n", "[1, 2, 5, 7, 10, 12, 16]\n", "[1, 2, 3, 4, 9, 13, 19]\n", "[1, 3, 5, 6, 8, 14, 18]\n", "[1, 3, 4, 8, 9, 11, 12]\n", "[1, 3, 4, 6, 7, 15, 17]\n", "[1, 3, 5, 6, 7, 15, 16]\n", "[1, 3, 5, 6, 10, 13, 16]\n", "[1, 3, 5, 7, 8, 15, 16]\n", "[1, 3, 4, 5, 8, 14, 20]\n", "[1, 3, 5, 6, 10, 11, 13]\n", "[1, 2, 5, 8, 9, 12, 14]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 3.31 ms\n", "24\n", "new smallest = 7\n", "[1, 2, 4, 5, 11, 13, 19]\n", "[1, 3, 5, 6, 10, 11, 18]\n", "[1, 3, 5, 7, 8, 17, 18]\n", "[1, 3, 4, 9, 10, 11, 13]\n", "[1, 3, 5, 6, 8, 15, 16]\n", "[1, 2, 5, 8, 11, 13, 15]\n", "[1, 3, 4, 5, 10, 12, 18]\n", "[1, 3, 4, 9, 11, 12, 16]\n", "[1, 3, 4, 9, 11, 16, 20]\n", "[1, 2, 5, 8, 11, 12, 13]\n", "[1, 2, 5, 6, 7, 15, 17]\n", "[1, 3, 4, 9, 10, 12, 14]\n", "[1, 3, 5, 7, 8, 16, 17]\n", "[1, 3, 4, 6, 11, 13, 17]\n", "[1, 3, 4, 9, 10, 12, 13]\n", "[1, 2, 5, 7, 10, 11, 12]\n", "[1, 2, 4, 7, 10, 11, 12]\n", "[1, 2, 5, 6, 7, 15, 18]\n", "[1, 3, 4, 8, 10, 11, 13]\n", "[1, 2, 5, 8, 10, 11, 12]\n", "[1, 3, 5, 7, 9, 11, 12]\n", "[1, 2, 5, 6, 7, 14, 17]\n", "[1, 3, 4, 8, 9, 11, 20]\n", "[1, 2, 5, 7, 10, 12, 16]\n", "[1, 3, 5, 6, 8, 14, 18]\n", "[1, 3, 4, 8, 9, 11, 12]\n", "[1, 3, 4, 6, 7, 15, 17]\n", "[1, 3, 5, 7, 8, 15, 16]\n", "[1, 3, 4, 5, 8, 14, 20]\n", "[1, 3, 5, 6, 10, 11, 13]\n", "[1, 2, 5, 8, 9, 12, 14]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 1 ms\n", "25\n", "new smallest = 8\n", "new smallest = 7\n", "[1, 3, 5, 7, 8, 16, 17]\n", "[1, 3, 4, 9, 10, 12, 13]\n", "[1, 3, 4, 9, 11, 12, 16]\n", "[1, 3, 4, 9, 11, 16, 20]\n", "[1, 2, 5, 6, 7, 15, 18]\n", "[1, 2, 5, 8, 11, 12, 13]\n", "[1, 3, 4, 5, 8, 14, 20]\n", "[1, 3, 5, 7, 8, 17, 18]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 828 µs\n" ] } ], "source": [ "for n in range(20, 25):\n", " print(n+1)\n", " %time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "26\n", "new smallest = 8\n", "new smallest = 7\n", "[1, 2, 5, 8, 11, 12, 13]\n", "[1, 3, 4, 9, 10, 12, 13]\n", "[1, 3, 5, 7, 8, 17, 18]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 332 µs\n", "27\n", "new smallest = 8\n", "considering 1\n", "considering 2\n", "considering 3\n", "considering 4\n", "[1, 3, 4, 9, 11, 12, 16, 17]\n", "[1, 2, 5, 7, 8, 11, 16, 18]\n", "[1, 2, 5, 6, 7, 8, 17, 19]\n", "[1, 2, 5, 7, 10, 11, 14, 16]\n", "[1, 2, 3, 4, 9, 13, 18, 23]\n", "[1, 3, 4, 9, 11, 13, 16, 20]\n", "[1, 3, 4, 9, 11, 15, 16, 20]\n", "[1, 3, 5, 6, 10, 13, 16, 24]\n", "[1, 3, 4, 5, 11, 13, 14, 20]\n", "[1, 3, 5, 6, 8, 10, 17, 18]\n", "[1, 3, 5, 6, 8, 9, 18, 19]\n", "[1, 3, 4, 6, 9, 11, 16, 20]\n", "[1, 3, 4, 8, 10, 11, 17, 23]\n", "[1, 2, 4, 5, 9, 12, 15, 21]\n", "[1, 2, 4, 7, 8, 13, 18, 23]\n", "[1, 2, 5, 6, 7, 14, 17, 25]\n", "[1, 2, 3, 4, 9, 13, 18, 21]\n", "[1, 2, 5, 8, 11, 13, 14, 15]\n", "[1, 2, 5, 7, 10, 13, 14, 15]\n", "[1, 3, 4, 9, 10, 11, 16, 23]\n", "[1, 3, 4, 8, 9, 11, 13, 14]\n", "[1, 2, 5, 6, 8, 13, 17, 19]\n", "[1, 3, 4, 6, 11, 13, 14, 20]\n", "[1, 3, 5, 6, 7, 11, 12, 20]\n", "[1, 3, 4, 9, 11, 16, 20, 25]\n", "[1, 2, 4, 7, 9, 12, 13, 23]\n", "[1, 2, 5, 8, 9, 12, 14, 25]\n", "[1, 2, 4, 5, 10, 12, 13, 17]\n", "[1, 2, 5, 7, 10, 13, 14, 20]\n", "[1, 2, 4, 5, 6, 12, 14, 21]\n", "[1, 2, 5, 6, 8, 12, 13, 22]\n", "[1, 3, 5, 7, 8, 16, 17, 26]\n", "[1, 2, 4, 5, 9, 12, 13, 18]\n", "[1, 2, 4, 6, 7, 9, 17, 18]\n", "[1, 2, 4, 7, 9, 11, 17, 23]\n", "[1, 2, 4, 6, 8, 11, 18, 19]\n", "[1, 2, 5, 7, 11, 13, 16, 18]\n", "[1, 2, 3, 4, 9, 14, 19, 23]\n", "[1, 2, 4, 6, 7, 8, 16, 19]\n", "[1, 3, 4, 9, 10, 12, 13, 23]\n", "[1, 2, 5, 8, 11, 14, 15, 16]\n", "[1, 3, 4, 8, 9, 12, 13, 15]\n", "[1, 3, 4, 5, 11, 12, 14, 16]\n", "[1, 3, 5, 7, 8, 10, 18, 19]\n", "[1, 2, 5, 6, 9, 11, 19, 21]\n", "[1, 3, 4, 8, 10, 11, 16, 22]\n", "[1, 2, 5, 6, 7, 15, 18, 20]\n", "[1, 2, 5, 7, 11, 12, 14, 15]\n", "[1, 2, 5, 7, 8, 10, 15, 19]\n", "[1, 3, 4, 5, 9, 11, 16, 23]\n", "[1, 2, 4, 6, 8, 9, 19, 20]\n", "[1, 3, 4, 5, 10, 12, 18, 22]\n", "[1, 2, 5, 7, 9, 12, 13, 14]\n", "[1, 3, 4, 9, 11, 12, 13, 16]\n", "[1, 3, 5, 6, 7, 12, 16, 20]\n", "[1, 2, 4, 7, 8, 11, 13, 23]\n", "[1, 3, 5, 6, 10, 14, 17, 20]\n", "[1, 3, 5, 7, 9, 10, 20, 21]\n", "[1, 2, 5, 6, 9, 13, 16, 18]\n", "[1, 3, 4, 5, 11, 12, 13, 16]\n", "[1, 3, 5, 6, 8, 10, 16, 22]\n", "[1, 3, 4, 9, 10, 12, 14, 15]\n", "[1, 3, 5, 7, 8, 13, 16, 22]\n", "[1, 2, 5, 8, 11, 12, 13, 25]\n", "[1, 2, 4, 5, 9, 10, 16, 22]\n", "[1, 3, 4, 9, 11, 13, 18, 22]\n", "[1, 3, 4, 9, 10, 12, 13, 17]\n", "[1, 2, 3, 4, 9, 13, 19, 24]\n", "[1, 3, 4, 9, 11, 12, 16, 25]\n", "[1, 3, 4, 5, 8, 14, 20, 26]\n", "[1, 2, 5, 6, 7, 14, 17, 20]\n", "[1, 3, 4, 9, 11, 14, 15, 18]\n", "[1, 2, 5, 8, 9, 10, 16, 22]\n", "[1, 2, 4, 7, 9, 11, 16, 17]\n", "[1, 2, 3, 4, 5, 11, 17, 22]\n", "[1, 3, 4, 9, 10, 11, 12, 16]\n", "[1, 3, 4, 6, 10, 12, 13, 17]\n", "[1, 3, 4, 5, 6, 9, 16, 23]\n", "[1, 3, 4, 5, 7, 8, 17, 19]\n", "[1, 3, 4, 6, 8, 12, 13, 19]\n", "[1, 3, 5, 6, 12, 14, 15, 22]\n", "[1, 2, 3, 5, 6, 13, 15, 22]\n", "[1, 3, 4, 9, 10, 13, 14, 21]\n", "[1, 2, 5, 7, 10, 12, 16, 25]\n", "[1, 3, 4, 5, 7, 12, 17, 22]\n", "[1, 2, 4, 6, 8, 9, 18, 19]\n", "[1, 2, 4, 5, 6, 9, 15, 21]\n", "[1, 2, 3, 4, 5, 11, 16, 21]\n", "[1, 3, 5, 7, 8, 14, 18, 19]\n", "[1, 2, 4, 6, 8, 9, 19, 22]\n", "[1, 2, 5, 6, 7, 15, 18, 21]\n", "[1, 3, 4, 9, 11, 16, 17, 23]\n", "[1, 3, 5, 7, 8, 16, 18, 19]\n", "[1, 3, 5, 7, 8, 17, 18, 20]\n", "[1, 2, 5, 7, 8, 10, 17, 21]\n", "[1, 2, 4, 7, 10, 12, 14, 23]\n", "[1, 2, 5, 7, 11, 13, 14, 16]\n", "[1, 3, 5, 6, 11, 12, 14, 21]\n", "[1, 3, 4, 5, 8, 13, 14, 20]\n", "[1, 2, 4, 7, 8, 11, 17, 19]\n", "[1, 2, 3, 4, 9, 14, 18, 22]\n", "[1, 2, 5, 8, 10, 13, 14, 15]\n", "[1, 3, 4, 9, 11, 12, 16, 23]\n", "[1, 3, 4, 5, 8, 11, 17, 23]\n", "[1, 3, 4, 7, 8, 13, 15, 24]\n", "[1, 3, 4, 8, 9, 11, 17, 23]\n", "[1, 3, 4, 6, 8, 9, 17, 18]\n", "[1, 3, 4, 5, 11, 13, 16, 20]\n", "[1, 3, 4, 7, 9, 12, 13, 20]\n", "[1, 3, 4, 9, 11, 13, 14, 18]\n", "[1, 2, 5, 6, 7, 15, 17, 20]\n", "[1, 3, 4, 9, 10, 11, 13, 16]\n", "[1, 2, 5, 8, 9, 12, 13, 18]\n", "[1, 2, 5, 8, 11, 14, 16, 18]\n", "[1, 3, 4, 6, 7, 10, 15, 23]\n", "[1, 3, 5, 6, 10, 12, 13, 15]\n", "[1, 3, 4, 9, 10, 12, 13, 26]\n", "[1, 2, 5, 8, 10, 13, 17, 22]\n", "[1, 2, 5, 8, 10, 13, 17, 19]\n", "[1, 3, 5, 6, 7, 12, 15, 20]\n", "[1, 3, 5, 6, 13, 15, 17, 24]\n", "[1, 3, 5, 7, 8, 9, 18, 19]\n", "[1, 3, 5, 7, 9, 10, 17, 18]\n", "[1, 3, 4, 6, 11, 12, 15, 19]\n", "[1, 2, 5, 6, 7, 8, 17, 20]\n", "[1, 2, 5, 6, 8, 9, 17, 19]\n", "[1, 2, 5, 7, 9, 12, 14, 20]\n", "[1, 3, 4, 8, 10, 11, 15, 16]\n", "[1, 3, 5, 6, 8, 10, 16, 17]\n", "[1, 3, 4, 7, 8, 12, 13, 15]\n", "[1, 3, 5, 7, 8, 10, 19, 20]\n", "[1, 2, 5, 7, 11, 12, 13, 20]\n", "[1, 2, 4, 5, 11, 13, 19, 23]\n", "[1, 2, 4, 5, 11, 13, 14, 19]\n", "[1, 2, 4, 7, 10, 12, 13, 14]\n", "[1, 2, 5, 6, 8, 9, 18, 20]\n", "[1, 3, 4, 8, 9, 14, 16, 18]\n", "[1, 3, 5, 6, 8, 12, 18, 22]\n", "[1, 3, 4, 9, 11, 16, 20, 23]\n", "[1, 2, 4, 5, 10, 13, 14, 21]\n", "[1, 3, 4, 5, 11, 12, 15, 20]\n", "[1, 3, 5, 6, 13, 14, 20, 21]\n", "[1, 3, 4, 5, 6, 10, 13, 21]\n", "[1, 2, 4, 6, 8, 11, 18, 21]\n", "[1, 3, 5, 6, 10, 11, 13, 24]\n", "[1, 3, 4, 7, 8, 9, 16, 18]\n", "[1, 3, 5, 7, 9, 10, 16, 17]\n", "[1, 2, 5, 8, 11, 13, 15, 25]\n", "[1, 3, 4, 9, 10, 15, 17, 22]\n", "[1, 3, 4, 7, 9, 11, 16, 17]\n", "[1, 3, 5, 6, 8, 9, 19, 20]\n", "[1, 3, 4, 5, 8, 14, 20, 22]\n", "[1, 3, 5, 6, 10, 11, 13, 22]\n", "[1, 2, 5, 8, 11, 12, 13, 16]\n", "[1, 3, 5, 7, 8, 12, 18, 22]\n", "[1, 3, 5, 7, 8, 17, 18, 19]\n", "[1, 2, 5, 8, 10, 11, 12, 25]\n", "[1, 2, 5, 8, 9, 12, 13, 14]\n", "[1, 3, 4, 9, 10, 12, 13, 15]\n", "[1, 3, 5, 6, 12, 13, 20, 22]\n", "[1, 2, 5, 8, 10, 11, 13, 17]\n", "[1, 2, 5, 8, 9, 11, 15, 16]\n", "[1, 2, 5, 8, 9, 12, 15, 17]\n", "[1, 3, 5, 6, 11, 13, 14, 20]\n", "[1, 2, 5, 8, 11, 12, 13, 26]\n", "[1, 2, 5, 8, 9, 11, 13, 14]\n", "[1, 2, 4, 7, 10, 13, 14, 15]\n", "[1, 3, 4, 8, 10, 12, 13, 19]\n", "[1, 3, 4, 7, 8, 13, 17, 19]\n", "[1, 3, 4, 9, 11, 12, 16, 26]\n", "[1, 2, 5, 7, 11, 12, 14, 20]\n", "[1, 3, 4, 6, 9, 10, 17, 21]\n", "[1, 3, 4, 9, 11, 16, 21, 22]\n", "[1, 3, 5, 6, 12, 13, 20, 21]\n", "[1, 3, 5, 6, 13, 14, 21, 22]\n", "[1, 3, 5, 7, 8, 17, 18, 24]\n", "[1, 3, 4, 9, 10, 15, 17, 19]\n", "[1, 3, 5, 6, 12, 13, 15, 22]\n", "[1, 3, 4, 8, 9, 13, 14, 16]\n", "[1, 3, 5, 6, 8, 14, 18, 22]\n", "[1, 3, 4, 9, 10, 12, 16, 23]\n", "[1, 3, 5, 6, 10, 12, 13, 21]\n", "[1, 2, 5, 8, 10, 12, 13, 17]\n", "[1, 3, 4, 5, 10, 11, 12, 15]\n", "[1, 3, 4, 5, 7, 13, 15, 20]\n", "[1, 3, 5, 7, 8, 16, 17, 19]\n", "[1, 2, 5, 8, 10, 12, 13, 19]\n", "[1, 2, 5, 6, 8, 9, 19, 21]\n", "[1, 2, 4, 7, 10, 11, 12, 25]\n", "[1, 3, 4, 6, 7, 10, 15, 20]\n", "[1, 3, 5, 6, 8, 12, 13, 22]\n", "[1, 3, 4, 8, 9, 11, 21, 23]\n", "[1, 3, 5, 7, 8, 17, 19, 20]\n", "[1, 2, 4, 5, 6, 12, 15, 21]\n", "[1, 3, 4, 5, 9, 10, 12, 22]\n", "[1, 2, 3, 4, 5, 11, 17, 23]\n", "[1, 3, 4, 7, 9, 12, 13, 23]\n", "[1, 2, 3, 4, 5, 11, 16, 23]\n", "[1, 3, 4, 9, 11, 12, 13, 15]\n", "[1, 3, 5, 6, 8, 14, 17, 21]\n", "[1, 3, 4, 6, 11, 13, 14, 17]\n", "[1, 2, 5, 7, 9, 12, 13, 18]\n", "[1, 2, 3, 5, 9, 12, 13, 18]\n", "[1, 2, 4, 7, 10, 11, 12, 15]\n", "[1, 2, 5, 6, 7, 15, 17, 25]\n", "[1, 3, 4, 8, 10, 12, 13, 15]\n", "[1, 3, 5, 6, 7, 10, 18, 21]\n", "[1, 2, 5, 7, 8, 10, 16, 17]\n", "[1, 3, 4, 6, 10, 15, 16, 23]\n", "[1, 3, 4, 9, 11, 16, 20, 26]\n", "[1, 3, 4, 9, 10, 13, 15, 18]\n", "[1, 3, 5, 6, 11, 12, 16, 20]\n", "[1, 3, 4, 7, 8, 12, 17, 19]\n", "[1, 3, 4, 9, 10, 14, 16, 18]\n", "[1, 3, 5, 6, 11, 13, 15, 22]\n", "[1, 3, 5, 6, 9, 12, 13, 14]\n", "[1, 3, 4, 9, 11, 16, 17, 20]\n", "[1, 2, 5, 6, 9, 12, 13, 14]\n", "[1, 3, 5, 6, 7, 9, 17, 18]\n", "[1, 2, 5, 8, 11, 12, 14, 16]\n", "[1, 3, 4, 8, 9, 10, 15, 18]\n", "[1, 3, 4, 9, 11, 12, 14, 15]\n", "[1, 2, 5, 8, 11, 12, 13, 15]\n", "[1, 2, 5, 7, 11, 14, 16, 19]\n", "[1, 3, 5, 7, 8, 17, 18, 26]\n", "[1, 3, 4, 5, 8, 14, 20, 23]\n", "[1, 3, 4, 9, 11, 12, 15, 16]\n", "[1, 2, 4, 5, 11, 12, 14, 16]\n", "[1, 2, 4, 7, 10, 13, 15, 17]\n", "[1, 2, 5, 8, 10, 13, 17, 24]\n", "[1, 2, 3, 4, 5, 10, 16, 22]\n", "[1, 2, 5, 7, 10, 12, 16, 20]\n", "[1, 3, 4, 6, 11, 12, 14, 15]\n", "[1, 3, 5, 7, 8, 9, 16, 19]\n", "[1, 3, 4, 9, 10, 11, 13, 14]\n", "[1, 2, 5, 7, 10, 12, 13, 14]\n", "[1, 3, 4, 6, 7, 9, 17, 18]\n", "[1, 3, 4, 5, 10, 11, 14, 22]\n", "[1, 2, 4, 6, 9, 12, 13, 14]\n", "[1, 2, 5, 7, 10, 12, 15, 16]\n", "[1, 3, 4, 7, 8, 9, 18, 20]\n", "[1, 3, 5, 7, 9, 10, 17, 20]\n", "[1, 2, 5, 8, 10, 12, 17, 21]\n", "[1, 2, 5, 6, 7, 8, 16, 19]\n", "[1, 3, 4, 6, 10, 11, 13, 14]\n", "[1, 3, 4, 8, 10, 11, 13, 24]\n", "[1, 2, 5, 6, 7, 10, 17, 20]\n", "[1, 3, 5, 6, 11, 12, 15, 19]\n", "[1, 2, 5, 7, 10, 11, 12, 15]\n", "[1, 2, 4, 6, 7, 12, 15, 19]\n", "[1, 3, 5, 6, 9, 10, 16, 18]\n", "[1, 3, 4, 6, 10, 13, 14, 21]\n", "[1, 2, 5, 7, 9, 12, 13, 22]\n", "[1, 3, 5, 6, 12, 13, 15, 17]\n", "[1, 2, 5, 7, 10, 11, 12, 25]\n", "[1, 3, 5, 6, 8, 12, 18, 19]\n", "[1, 2, 3, 4, 8, 13, 18, 23]\n", "[1, 3, 5, 7, 8, 12, 15, 18]\n", "[1, 3, 5, 7, 9, 10, 21, 22]\n", "[1, 3, 5, 6, 8, 12, 19, 20]\n", "[1, 2, 5, 6, 7, 10, 18, 21]\n", "[1, 2, 4, 5, 8, 10, 17, 22]\n", "[1, 3, 4, 6, 11, 13, 17, 21]\n", "[1, 2, 5, 8, 10, 14, 17, 21]\n", "[1, 3, 5, 6, 13, 14, 18, 22]\n", "[1, 2, 4, 6, 8, 9, 18, 21]\n", "[1, 3, 4, 5, 8, 14, 19, 21]\n", "[1, 3, 4, 9, 10, 11, 16, 20]\n", "[1, 2, 4, 5, 10, 11, 13, 14]\n", "[1, 2, 3, 4, 9, 13, 18, 22]\n", "[1, 2, 4, 5, 10, 13, 14, 20]\n", "[1, 3, 4, 8, 10, 13, 14, 15]\n", "[1, 3, 4, 9, 10, 11, 13, 24]\n", "[1, 3, 4, 8, 9, 10, 14, 17]\n", "[1, 3, 5, 6, 13, 14, 18, 19]\n", "[1, 3, 4, 6, 10, 11, 12, 15]\n", "[1, 2, 5, 6, 8, 10, 16, 17]\n", "[1, 2, 5, 7, 11, 12, 13, 16]\n", "[1, 2, 3, 4, 9, 14, 18, 24]\n", "[1, 2, 5, 7, 11, 12, 13, 14]\n", "[1, 2, 5, 6, 8, 9, 16, 18]\n", "[1, 3, 4, 7, 8, 10, 18, 20]\n", "[1, 3, 5, 6, 13, 14, 19, 20]\n", "[1, 3, 5, 7, 9, 10, 18, 21]\n", "[1, 2, 5, 7, 11, 14, 15, 22]\n", "[1, 2, 5, 7, 11, 12, 15, 20]\n", "[1, 3, 5, 6, 8, 14, 18, 24]\n", "[1, 3, 5, 7, 8, 12, 18, 19]\n", "[1, 2, 3, 4, 5, 11, 16, 22]\n", "[1, 3, 4, 6, 9, 10, 13, 21]\n", "[1, 2, 4, 5, 11, 14, 16, 22]\n", "[1, 3, 4, 7, 8, 13, 18, 20]\n", "[1, 2, 3, 5, 9, 10, 16, 22]\n", "[1, 2, 4, 7, 10, 11, 15, 23]\n", "[1, 3, 4, 9, 10, 12, 13, 14]\n", "[1, 2, 3, 5, 8, 12, 18, 22]\n", "[1, 3, 4, 8, 10, 11, 13, 17]\n", "[1, 3, 4, 8, 9, 12, 13, 19]\n", "[1, 3, 4, 9, 10, 12, 17, 22]\n", "[1, 3, 5, 6, 9, 10, 15, 17]\n", "[1, 2, 4, 5, 10, 12, 17, 21]\n", "[1, 2, 3, 4, 9, 14, 19, 24]\n", "[1, 2, 5, 6, 9, 11, 18, 20]\n", "[1, 2, 4, 7, 9, 12, 13, 14]\n", "[1, 3, 4, 9, 10, 12, 14, 24]\n", "[1, 3, 4, 5, 10, 11, 14, 23]\n", "[1, 3, 4, 9, 10, 12, 13, 24]\n", "[1, 3, 5, 7, 9, 10, 19, 20]\n", "[1, 2, 5, 8, 10, 13, 14, 17]\n", "[1, 3, 5, 6, 8, 11, 15, 19]\n", "[1, 2, 5, 8, 10, 11, 12, 15]\n", "[1, 3, 4, 5, 8, 12, 13, 19]\n", "[1, 3, 4, 6, 7, 8, 17, 19]\n", "[1, 3, 4, 7, 9, 12, 13, 14]\n", "[1, 3, 5, 7, 8, 12, 13, 15]\n", "[1, 3, 4, 9, 11, 16, 21, 23]\n", "[1, 3, 5, 6, 11, 13, 14, 18]\n", "[1, 2, 4, 6, 7, 12, 13, 21]\n", "[1, 3, 5, 7, 8, 10, 17, 18]\n", "[1, 2, 5, 8, 10, 12, 13, 14]\n", "[1, 2, 5, 6, 7, 9, 17, 20]\n", "[1, 3, 5, 7, 8, 9, 17, 18]\n", "[1, 3, 4, 6, 7, 9, 16, 20]\n", "[1, 2, 3, 4, 8, 11, 17, 23]\n", "[1, 3, 5, 6, 12, 13, 17, 21]\n", "[1, 3, 4, 6, 10, 12, 13, 21]\n", "[1, 3, 5, 6, 7, 10, 12, 20]\n", "[1, 2, 5, 8, 11, 12, 13, 19]\n", "[1, 2, 5, 6, 7, 10, 17, 19]\n", "[1, 3, 4, 7, 8, 9, 19, 21]\n", "[1, 3, 4, 6, 10, 12, 13, 15]\n", "[1, 2, 3, 4, 9, 13, 17, 23]\n", "[1, 2, 4, 5, 7, 8, 17, 19]\n", "[1, 3, 5, 6, 12, 14, 16, 22]\n", "[1, 2, 3, 4, 9, 13, 19, 23]\n", "[1, 3, 5, 7, 9, 11, 13, 14]\n", "[1, 2, 4, 5, 11, 13, 19, 25]\n", "[1, 3, 5, 6, 8, 9, 17, 18]\n", "[1, 3, 4, 6, 8, 9, 18, 19]\n", "[1, 3, 4, 9, 10, 11, 14, 16]\n", "[1, 2, 5, 6, 8, 12, 13, 21]\n", "[1, 3, 4, 5, 8, 14, 17, 23]\n", "[1, 3, 5, 7, 8, 12, 13, 22]\n", "[1, 2, 5, 8, 10, 13, 17, 23]\n", "[1, 3, 4, 9, 11, 12, 13, 18]\n", "[1, 3, 4, 9, 11, 12, 14, 18]\n", "[1, 3, 4, 7, 9, 14, 19, 24]\n", "[1, 3, 4, 9, 11, 12, 14, 16]\n", "[1, 3, 4, 9, 11, 16, 20, 22]\n", "[1, 3, 5, 6, 10, 11, 13, 14]\n", "[1, 2, 5, 7, 10, 11, 13, 14]\n", "[1, 2, 5, 8, 11, 12, 13, 14]\n", "[1, 2, 5, 6, 7, 15, 18, 25]\n", "[1, 2, 5, 6, 7, 15, 18, 26]\n", "[1, 2, 4, 6, 8, 9, 17, 18]\n", "[1, 3, 5, 7, 8, 17, 18, 22]\n", "[1, 2, 5, 7, 8, 10, 13, 17]\n", "[1, 3, 4, 5, 8, 10, 16, 22]\n", "[1, 3, 4, 8, 10, 11, 13, 14]\n", "[1, 2, 3, 5, 7, 10, 16, 22]\n", "[1, 3, 5, 7, 8, 10, 16, 17]\n", "[1, 3, 4, 8, 10, 11, 14, 23]\n", "[1, 3, 5, 6, 11, 12, 14, 15]\n", "[1, 3, 4, 6, 8, 9, 19, 20]\n", "[1, 3, 4, 6, 10, 13, 15, 21]\n", "[1, 3, 4, 5, 11, 13, 16, 22]\n", "[1, 3, 4, 6, 10, 11, 15, 23]\n", "[1, 3, 4, 6, 11, 13, 17, 24]\n", "[1, 3, 5, 6, 8, 11, 15, 24]\n", "[1, 3, 4, 9, 11, 16, 18, 23]\n", "[1, 3, 4, 5, 10, 11, 13, 14]\n", "[1, 2, 5, 8, 10, 13, 16, 17]\n", "[1, 3, 4, 9, 10, 13, 15, 17]\n", "[1, 2, 4, 5, 6, 13, 16, 23]\n", "[1, 3, 4, 7, 8, 10, 19, 21]\n", "[1, 3, 5, 7, 8, 9, 19, 20]\n", "[1, 3, 4, 9, 11, 12, 16, 22]\n", "[1, 2, 4, 5, 9, 11, 17, 23]\n", "[1, 2, 3, 4, 9, 14, 18, 23]\n", "[1, 3, 4, 5, 11, 12, 15, 21]\n", "[1, 3, 5, 6, 11, 12, 19, 21]\n", "[1, 2, 5, 8, 11, 12, 13, 22]\n", "[1, 2, 4, 7, 10, 12, 13, 17]\n", "[1, 3, 4, 7, 8, 13, 18, 23]\n", "[1, 2, 5, 6, 7, 10, 18, 20]\n", "[1, 2, 4, 6, 7, 8, 17, 20]\n", "[1, 2, 4, 7, 10, 13, 14, 18]\n", "[1, 3, 4, 5, 8, 14, 16, 22]\n", "[1, 3, 4, 7, 8, 10, 17, 19]\n", "[1, 3, 5, 7, 8, 10, 16, 22]\n", "[1, 3, 4, 7, 8, 9, 17, 19]\n", "[1, 3, 5, 7, 9, 10, 18, 19]\n", "[1, 3, 5, 7, 8, 9, 15, 18]\n", "[1, 3, 4, 9, 10, 12, 13, 18]\n", "[1, 3, 5, 6, 8, 14, 18, 19]\n", "[1, 3, 4, 7, 9, 14, 17, 18]\n", "[1, 3, 5, 6, 11, 12, 13, 15]\n", "[1, 3, 4, 7, 8, 10, 18, 23]\n", "[1, 3, 5, 6, 11, 12, 14, 16]\n", "CPU times: user 6.02 s, sys: 44 ms, total: 6.06 s\n", "Wall time: 6.06 s\n", "28\n", "new smallest = 8\n", "[1, 3, 4, 9, 11, 12, 16, 17]\n", "[1, 3, 4, 5, 10, 11, 14, 23]\n", "[1, 3, 4, 9, 10, 12, 13, 24]\n", "[1, 3, 4, 9, 10, 14, 16, 18]\n", "[1, 3, 5, 6, 11, 13, 15, 22]\n", "[1, 3, 5, 6, 9, 12, 13, 14]\n", "[1, 3, 5, 7, 9, 10, 19, 20]\n", "[1, 3, 4, 9, 11, 16, 17, 20]\n", "[1, 2, 5, 6, 9, 12, 13, 14]\n", "[1, 2, 5, 8, 10, 13, 14, 17]\n", "[1, 3, 4, 7, 9, 12, 13, 14]\n", "[1, 3, 5, 7, 8, 12, 13, 15]\n", "[1, 2, 5, 8, 11, 12, 14, 16]\n", "[1, 2, 5, 7, 10, 11, 14, 16]\n", "[1, 3, 4, 8, 9, 10, 15, 18]\n", "[1, 3, 4, 9, 11, 12, 14, 15]\n", "[1, 3, 5, 6, 13, 15, 17, 24]\n", "[1, 2, 5, 8, 11, 12, 13, 15]\n", "[1, 2, 5, 7, 11, 14, 16, 19]\n", "[1, 3, 4, 5, 8, 14, 20, 23]\n", "[1, 3, 5, 6, 11, 13, 14, 18]\n", "[1, 2, 4, 6, 7, 12, 13, 21]\n", "[1, 3, 4, 9, 11, 12, 15, 16]\n", "[1, 3, 5, 7, 8, 9, 18, 19]\n", "[1, 3, 5, 7, 8, 10, 17, 18]\n", "[1, 3, 4, 5, 11, 13, 14, 20]\n", "[1, 2, 5, 8, 10, 12, 13, 14]\n", "[1, 3, 5, 6, 8, 10, 17, 18]\n", "[1, 3, 5, 6, 8, 9, 18, 19]\n", "[1, 2, 4, 5, 11, 12, 14, 16]\n", "[1, 3, 5, 7, 9, 10, 17, 18]\n", "[1, 3, 4, 8, 10, 11, 17, 23]\n", "[1, 2, 4, 7, 10, 13, 15, 17]\n", "[1, 2, 5, 6, 7, 8, 17, 20]\n", "[1, 2, 5, 6, 8, 9, 17, 19]\n", "[1, 2, 5, 6, 7, 14, 17, 25]\n", "[1, 2, 5, 8, 11, 13, 14, 15]\n", "[1, 2, 5, 7, 10, 13, 14, 15]\n", "[1, 2, 5, 7, 10, 12, 16, 20]\n", "[1, 3, 4, 6, 11, 12, 14, 15]\n", "[1, 3, 4, 8, 9, 11, 13, 14]\n", "[1, 2, 3, 4, 8, 11, 17, 23]\n", "[1, 2, 5, 7, 9, 12, 14, 20]\n", "[1, 3, 4, 6, 11, 13, 14, 20]\n", "[1, 3, 5, 7, 8, 9, 16, 19]\n", "[1, 3, 4, 9, 10, 11, 13, 14]\n", "[1, 3, 4, 9, 11, 16, 20, 25]\n", "[1, 2, 5, 7, 10, 12, 13, 14]\n", "[1, 3, 4, 5, 10, 11, 14, 22]\n", "[1, 3, 4, 7, 8, 12, 13, 15]\n", "[1, 2, 5, 8, 9, 12, 14, 25]\n", "[1, 3, 5, 7, 8, 10, 19, 20]\n", "[1, 2, 4, 6, 9, 12, 13, 14]\n", "[1, 2, 5, 7, 10, 13, 14, 20]\n", "[1, 2, 5, 7, 10, 12, 15, 16]\n", "[1, 3, 4, 7, 8, 9, 19, 21]\n", "[1, 2, 4, 5, 6, 12, 14, 21]\n", "[1, 2, 4, 5, 11, 13, 19, 23]\n", "[1, 2, 4, 5, 11, 13, 14, 19]\n", "[1, 3, 4, 7, 8, 9, 18, 20]\n", "[1, 2, 5, 6, 8, 12, 13, 22]\n", "[1, 3, 4, 6, 10, 12, 13, 15]\n", "[1, 2, 4, 7, 10, 12, 13, 14]\n", "[1, 3, 4, 8, 9, 14, 16, 18]\n", "[1, 2, 5, 6, 8, 9, 18, 20]\n", "[1, 3, 5, 6, 8, 12, 18, 22]\n", "[1, 2, 4, 7, 9, 11, 17, 23]\n", "[1, 2, 4, 5, 10, 13, 14, 21]\n", "[1, 3, 4, 6, 10, 11, 13, 14]\n", "[1, 2, 3, 4, 9, 14, 19, 23]\n", "[1, 3, 5, 6, 12, 14, 16, 22]\n", "[1, 2, 3, 4, 9, 13, 19, 23]\n", "[1, 3, 5, 7, 9, 11, 13, 14]\n", "[1, 3, 4, 8, 10, 11, 13, 24]\n", "[1, 2, 5, 8, 11, 14, 15, 16]\n", "[1, 3, 4, 8, 9, 12, 13, 15]\n", "[1, 3, 5, 6, 13, 14, 20, 21]\n", "[1, 3, 4, 6, 8, 9, 18, 19]\n", "[1, 3, 4, 5, 11, 12, 14, 16]\n", "[1, 3, 5, 7, 8, 10, 18, 19]\n", "[1, 2, 5, 6, 9, 11, 19, 21]\n", "[1, 3, 4, 9, 10, 11, 14, 16]\n", "[1, 2, 5, 7, 11, 12, 14, 15]\n", "[1, 3, 4, 5, 8, 14, 17, 23]\n", "[1, 3, 5, 6, 9, 10, 16, 18]\n", "[1, 2, 5, 8, 11, 13, 15, 25]\n", "[1, 3, 4, 5, 9, 11, 16, 23]\n", "[1, 3, 4, 6, 10, 13, 14, 21]\n", "[1, 2, 4, 6, 8, 9, 19, 20]\n", "[1, 2, 5, 8, 10, 13, 17, 23]\n", "[1, 3, 4, 7, 9, 11, 16, 17]\n", "[1, 3, 5, 6, 8, 9, 19, 20]\n", "[1, 3, 5, 6, 12, 13, 15, 17]\n", "[1, 3, 4, 5, 10, 12, 18, 22]\n", "[1, 2, 5, 7, 9, 12, 13, 14]\n", "[1, 3, 4, 9, 11, 12, 14, 18]\n", "[1, 3, 4, 7, 9, 14, 19, 24]\n", "[1, 3, 4, 9, 11, 12, 13, 16]\n", "[1, 3, 4, 5, 8, 14, 20, 22]\n", "[1, 3, 5, 6, 10, 11, 13, 22]\n", "[1, 3, 5, 6, 7, 12, 16, 20]\n", "[1, 3, 4, 9, 11, 12, 14, 16]\n", "[1, 2, 5, 8, 11, 12, 13, 16]\n", "[1, 3, 5, 6, 10, 11, 13, 14]\n", "[1, 2, 5, 7, 10, 11, 13, 14]\n", "[1, 3, 5, 6, 10, 14, 17, 20]\n", "[1, 2, 5, 8, 11, 12, 13, 14]\n", "[1, 3, 5, 7, 9, 10, 21, 22]\n", "[1, 3, 5, 6, 8, 12, 19, 20]\n", "[1, 2, 5, 6, 7, 10, 18, 21]\n", "[1, 2, 5, 6, 7, 15, 18, 26]\n", "[1, 3, 5, 7, 9, 10, 20, 21]\n", "[1, 2, 5, 8, 9, 12, 13, 14]\n", "[1, 3, 4, 6, 11, 13, 17, 21]\n", "[1, 3, 4, 9, 10, 12, 13, 15]\n", "[1, 3, 4, 5, 11, 12, 13, 16]\n", "[1, 3, 5, 6, 8, 10, 16, 22]\n", "[1, 3, 5, 6, 12, 13, 20, 22]\n", "[1, 3, 4, 9, 10, 12, 14, 15]\n", "[1, 2, 5, 8, 10, 11, 13, 17]\n", "[1, 3, 5, 6, 11, 13, 14, 20]\n", "[1, 2, 5, 8, 11, 12, 13, 26]\n", "[1, 2, 5, 8, 9, 11, 13, 14]\n", "[1, 2, 5, 8, 10, 14, 17, 21]\n", "[1, 3, 5, 6, 13, 14, 18, 22]\n", "[1, 2, 3, 4, 9, 13, 19, 24]\n", "[1, 2, 4, 7, 9, 12, 13, 14]\n", "[1, 3, 4, 9, 11, 12, 16, 25]\n", "[1, 2, 4, 7, 10, 13, 14, 15]\n", "[1, 3, 4, 5, 8, 14, 20, 26]\n", "[1, 2, 5, 6, 7, 14, 17, 20]\n", "[1, 3, 4, 8, 10, 11, 13, 14]\n", "[1, 3, 4, 9, 11, 12, 16, 26]\n", "[1, 3, 4, 9, 11, 14, 15, 18]\n", "[1, 2, 5, 7, 11, 12, 14, 20]\n", "[1, 3, 4, 8, 10, 11, 14, 23]\n", "[1, 3, 5, 6, 11, 12, 14, 15]\n", "[1, 2, 4, 7, 9, 11, 16, 17]\n", "[1, 3, 4, 6, 8, 9, 19, 20]\n", "[1, 2, 3, 4, 5, 11, 17, 22]\n", "[1, 3, 4, 9, 10, 11, 12, 16]\n", "[1, 3, 4, 5, 8, 14, 19, 21]\n", "[1, 3, 4, 6, 10, 13, 15, 21]\n", "[1, 2, 4, 5, 10, 11, 13, 14]\n", "[1, 3, 5, 6, 13, 14, 21, 22]\n", "[1, 3, 4, 5, 6, 9, 16, 23]\n", "[1, 2, 4, 5, 10, 13, 14, 20]\n", "[1, 3, 4, 8, 10, 13, 14, 15]\n", "[1, 3, 4, 9, 10, 11, 13, 24]\n", "[1, 3, 4, 9, 10, 15, 17, 19]\n", "[1, 3, 5, 6, 12, 13, 15, 22]\n", "[1, 3, 4, 8, 9, 13, 14, 16]\n", "[1, 3, 5, 6, 12, 14, 15, 22]\n", "[1, 3, 4, 8, 9, 10, 14, 17]\n", "[1, 2, 3, 5, 6, 13, 15, 22]\n", "[1, 3, 4, 9, 10, 13, 14, 21]\n", "[1, 2, 5, 7, 10, 12, 16, 25]\n", "[1, 2, 4, 6, 8, 9, 18, 19]\n", "[1, 3, 5, 6, 13, 14, 18, 19]\n", "[1, 3, 5, 6, 8, 14, 18, 22]\n", "[1, 3, 4, 9, 10, 12, 16, 23]\n", "[1, 3, 5, 7, 8, 14, 18, 19]\n", "[1, 2, 5, 7, 11, 12, 13, 16]\n", "[1, 2, 4, 6, 8, 9, 19, 22]\n", "[1, 2, 5, 6, 7, 15, 18, 21]\n", "[1, 3, 4, 6, 11, 13, 17, 24]\n", "[1, 2, 3, 4, 9, 14, 18, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 23]\n", "[1, 2, 5, 7, 11, 12, 13, 14]\n", "[1, 3, 4, 9, 10, 13, 15, 18]\n", "[1, 3, 4, 5, 7, 13, 15, 20]\n", "[1, 2, 5, 6, 8, 9, 19, 21]\n", "[1, 3, 4, 5, 10, 11, 13, 14]\n", "[1, 3, 5, 7, 8, 17, 18, 20]\n", "[1, 3, 4, 7, 8, 10, 18, 20]\n", "[1, 3, 5, 6, 8, 12, 13, 22]\n", "[1, 2, 5, 7, 8, 10, 17, 21]\n", "[1, 3, 4, 9, 10, 13, 15, 17]\n", "[1, 2, 4, 7, 10, 12, 14, 23]\n", "[1, 3, 5, 6, 13, 14, 19, 20]\n", "[1, 3, 5, 7, 8, 17, 19, 20]\n", "[1, 2, 4, 5, 6, 13, 16, 23]\n", "[1, 3, 5, 7, 9, 10, 18, 21]\n", "[1, 2, 5, 7, 11, 13, 14, 16]\n", "[1, 2, 5, 7, 11, 14, 15, 22]\n", "[1, 3, 5, 6, 8, 14, 18, 24]\n", "[1, 2, 3, 4, 5, 11, 17, 23]\n", "[1, 3, 5, 6, 11, 12, 14, 21]\n", "[1, 3, 4, 7, 8, 10, 19, 21]\n", "[1, 3, 5, 7, 8, 9, 19, 20]\n", "[1, 3, 5, 6, 11, 12, 14, 16]\n", "[1, 2, 3, 4, 5, 11, 16, 23]\n", "[1, 3, 4, 9, 11, 12, 13, 15]\n", "[1, 3, 5, 6, 8, 14, 17, 21]\n", "[1, 3, 4, 5, 8, 13, 14, 20]\n", "[1, 2, 4, 7, 8, 11, 17, 19]\n", "[1, 3, 4, 6, 11, 13, 14, 17]\n", "[1, 2, 3, 4, 9, 14, 18, 22]\n", "[1, 2, 5, 8, 10, 13, 14, 15]\n", "[1, 3, 4, 9, 11, 12, 16, 23]\n", "[1, 3, 4, 9, 11, 12, 16, 22]\n", "[1, 2, 4, 5, 9, 11, 17, 23]\n", "[1, 2, 3, 4, 9, 14, 18, 23]\n", "[1, 2, 4, 5, 11, 14, 16, 22]\n", "[1, 3, 4, 5, 8, 11, 17, 23]\n", "[1, 3, 4, 7, 8, 13, 15, 24]\n", "[1, 3, 4, 7, 8, 13, 18, 20]\n", "[1, 3, 4, 9, 10, 12, 13, 14]\n", "[1, 3, 4, 8, 9, 11, 17, 23]\n", "[1, 2, 5, 6, 7, 10, 18, 20]\n", "[1, 2, 4, 6, 7, 8, 17, 20]\n", "[1, 2, 4, 7, 10, 13, 14, 18]\n", "[1, 3, 4, 5, 8, 14, 16, 22]\n", "[1, 3, 4, 7, 8, 9, 17, 19]\n", "[1, 3, 5, 7, 9, 10, 18, 19]\n", "[1, 3, 4, 8, 10, 12, 13, 15]\n", "[1, 3, 5, 6, 7, 10, 18, 21]\n", "[1, 3, 4, 8, 10, 11, 13, 17]\n", "[1, 3, 4, 9, 11, 13, 14, 18]\n", "[1, 3, 4, 8, 9, 12, 13, 19]\n", "[1, 3, 4, 9, 10, 12, 13, 18]\n", "[1, 3, 5, 6, 8, 14, 18, 19]\n", "[1, 3, 4, 7, 9, 14, 17, 18]\n", "[1, 3, 5, 6, 11, 12, 13, 15]\n", "[1, 2, 5, 8, 11, 14, 16, 18]\n", "[1, 3, 4, 7, 8, 10, 18, 23]\n", "[1, 2, 3, 4, 9, 14, 19, 24]\n", "[1, 3, 5, 6, 10, 12, 13, 15]\n", "[1, 3, 5, 6, 11, 12, 16, 20]\n", "[1, 3, 4, 9, 10, 12, 14, 24]\n", "CPU times: user 12 ms, sys: 0 ns, total: 12 ms\n", "Wall time: 9.31 ms\n", "29\n", "new smallest = 8\n", "[1, 3, 4, 9, 11, 12, 16, 17]\n", "[1, 3, 5, 7, 9, 10, 19, 20]\n", "[1, 3, 5, 7, 9, 10, 20, 21]\n", "[1, 3, 4, 9, 11, 16, 17, 20]\n", "[1, 3, 4, 7, 8, 10, 19, 21]\n", "[1, 3, 4, 5, 11, 12, 13, 16]\n", "[1, 3, 4, 9, 10, 12, 14, 15]\n", "[1, 2, 5, 6, 8, 9, 19, 21]\n", "[1, 2, 5, 8, 11, 14, 15, 16]\n", "[1, 3, 4, 9, 11, 12, 14, 15]\n", "[1, 3, 5, 6, 13, 15, 17, 24]\n", "[1, 2, 5, 7, 8, 10, 17, 21]\n", "[1, 2, 5, 8, 10, 14, 17, 21]\n", "[1, 2, 4, 5, 6, 13, 16, 23]\n", "[1, 3, 5, 6, 11, 13, 14, 18]\n", "[1, 3, 4, 9, 11, 12, 16, 25]\n", "[1, 2, 4, 7, 10, 13, 14, 15]\n", "[1, 3, 5, 7, 8, 10, 18, 19]\n", "[1, 3, 4, 5, 8, 14, 20, 26]\n", "[1, 2, 5, 7, 11, 13, 14, 16]\n", "[1, 3, 4, 9, 11, 12, 16, 26]\n", "[1, 3, 4, 9, 11, 14, 15, 18]\n", "[1, 3, 5, 6, 11, 12, 14, 15]\n", "[1, 2, 5, 7, 11, 14, 15, 22]\n", "[1, 3, 5, 6, 8, 14, 18, 24]\n", "[1, 3, 5, 7, 8, 9, 19, 20]\n", "[1, 3, 5, 6, 8, 14, 17, 21]\n", "[1, 2, 5, 7, 11, 12, 14, 15]\n", "[1, 2, 5, 8, 10, 13, 14, 15]\n", "[1, 3, 4, 6, 8, 9, 19, 20]\n", "[1, 3, 4, 5, 8, 14, 19, 21]\n", "[1, 2, 5, 8, 11, 13, 14, 15]\n", "[1, 2, 5, 7, 10, 13, 14, 15]\n", "[1, 3, 4, 6, 11, 12, 14, 15]\n", "[1, 3, 4, 5, 6, 9, 16, 23]\n", "[1, 3, 4, 8, 10, 13, 14, 15]\n", "[1, 2, 5, 7, 9, 12, 14, 20]\n", "[1, 2, 4, 6, 8, 9, 19, 20]\n", "[1, 3, 4, 9, 10, 15, 17, 19]\n", "[1, 3, 5, 6, 12, 13, 15, 17]\n", "[1, 3, 5, 6, 8, 9, 19, 20]\n", "[1, 3, 4, 8, 9, 13, 14, 16]\n", "[1, 3, 5, 7, 9, 10, 18, 19]\n", "[1, 3, 5, 6, 12, 14, 15, 22]\n", "[1, 3, 4, 9, 11, 12, 14, 18]\n", "[1, 3, 4, 9, 11, 16, 20, 25]\n", "[1, 3, 4, 9, 11, 12, 13, 16]\n", "[1, 3, 4, 9, 11, 13, 14, 18]\n", "[1, 3, 5, 7, 8, 10, 19, 20]\n", "[1, 2, 5, 8, 11, 12, 13, 16]\n", "[1, 3, 4, 7, 8, 9, 19, 21]\n", "[1, 3, 4, 7, 8, 9, 18, 20]\n", "[1, 2, 5, 8, 11, 14, 16, 18]\n", "[1, 2, 5, 6, 8, 9, 18, 20]\n", "[1, 3, 5, 7, 9, 10, 21, 22]\n", "[1, 2, 5, 7, 11, 12, 13, 16]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 5.6 ms\n", "30\n", "new smallest = 9\n", "new smallest = 8\n", "[1, 3, 5, 7, 9, 10, 19, 20]\n", "[1, 3, 5, 7, 9, 10, 20, 21]\n", "[1, 3, 4, 9, 10, 12, 14, 15]\n", "[1, 2, 5, 6, 8, 9, 19, 21]\n", "[1, 2, 5, 8, 11, 14, 15, 16]\n", "[1, 3, 4, 9, 11, 12, 14, 15]\n", "[1, 3, 5, 6, 13, 15, 17, 24]\n", "[1, 2, 5, 7, 11, 13, 14, 16]\n", "[1, 2, 4, 7, 10, 13, 14, 15]\n", "[1, 3, 4, 5, 8, 14, 20, 26]\n", "[1, 2, 5, 7, 11, 14, 15, 22]\n", "[1, 3, 5, 6, 8, 14, 18, 24]\n", "[1, 3, 4, 9, 11, 12, 16, 26]\n", "[1, 3, 4, 9, 11, 14, 15, 18]\n", "[1, 3, 5, 6, 11, 12, 14, 15]\n", "[1, 2, 5, 7, 11, 12, 14, 15]\n", "[1, 2, 5, 8, 10, 13, 14, 15]\n", "[1, 2, 5, 8, 11, 13, 14, 15]\n", "[1, 2, 5, 7, 10, 13, 14, 15]\n", "[1, 3, 4, 6, 11, 12, 14, 15]\n", "[1, 3, 4, 8, 10, 13, 14, 15]\n", "[1, 3, 4, 9, 10, 15, 17, 19]\n", "[1, 3, 5, 6, 12, 13, 15, 17]\n", "[1, 3, 4, 8, 9, 13, 14, 16]\n", "[1, 3, 5, 6, 12, 14, 15, 22]\n", "[1, 3, 4, 9, 11, 12, 14, 18]\n", "[1, 3, 5, 7, 8, 10, 19, 20]\n", "[1, 3, 4, 7, 8, 9, 19, 21]\n", "[1, 2, 5, 8, 11, 14, 16, 18]\n", "[1, 3, 5, 7, 9, 10, 21, 22]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 1.36 ms\n" ] } ], "source": [ "for n in range(25, 30):\n", " print(n+1)\n", " %time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "31\n", "new smallest = 9\n", "new smallest = 8\n", "[1, 2, 5, 8, 11, 14, 15, 16]\n", "[1, 3, 4, 5, 8, 14, 20, 26]\n", "[1, 3, 5, 7, 9, 10, 21, 22]\n", "[1, 3, 5, 7, 9, 10, 20, 21]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 811 µs\n" ] } ], "source": [ "n = 30\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "32\n", "new smallest = 8\n", "[1, 2, 5, 8, 11, 14, 15, 16]\n", "[1, 3, 5, 7, 9, 10, 21, 22]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 190 µs\n" ] } ], "source": [ "n = 31\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "33\n", "new smallest = 9\n", "considering 1\n", "considering 2\n", "considering 3\n", "considering 4\n", "[1, 2, 5, 8, 9, 10, 18, 20, 23]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21]\n", "[1, 3, 5, 6, 13, 14, 16, 17, 19]\n", "[1, 3, 4, 5, 8, 14, 17, 23, 29]\n", "[1, 2, 4, 6, 8, 10, 11, 22, 25]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26]\n", "[1, 3, 4, 6, 10, 14, 15, 16, 17]\n", "[1, 3, 4, 6, 8, 9, 11, 21, 22]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 32]\n", "[1, 2, 5, 7, 10, 13, 15, 19, 26]\n", "[1, 3, 5, 6, 11, 12, 17, 19, 21]\n", "[1, 2, 5, 6, 7, 11, 15, 18, 26]\n", "[1, 3, 4, 9, 11, 12, 14, 16, 17]\n", "[1, 3, 4, 5, 8, 14, 20, 23, 29]\n", "[1, 3, 4, 5, 11, 13, 18, 20, 27]\n", "[1, 3, 5, 6, 8, 11, 15, 21, 25]\n", "[1, 3, 5, 6, 8, 14, 16, 17, 26]\n", "[1, 3, 5, 6, 10, 11, 18, 20, 27]\n", "[1, 2, 4, 5, 6, 11, 13, 19, 27]\n", "[1, 2, 5, 8, 10, 14, 16, 19, 23]\n", "[1, 2, 5, 8, 10, 13, 14, 15, 31]\n", "[1, 3, 4, 6, 10, 13, 15, 18, 26]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22]\n", "[1, 3, 4, 8, 9, 14, 15, 17, 19]\n", "[1, 3, 4, 9, 10, 13, 15, 18, 29]\n", "[1, 3, 4, 9, 11, 12, 14, 18, 19]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 29]\n", "[1, 3, 4, 7, 8, 13, 15, 23, 25]\n", "[1, 2, 5, 6, 8, 14, 16, 17, 21]\n", "[1, 3, 4, 9, 10, 14, 16, 17, 19]\n", "[1, 3, 4, 5, 6, 9, 16, 20, 27]\n", "[1, 2, 4, 5, 11, 13, 14, 19, 29]\n", "[1, 3, 5, 7, 9, 10, 20, 22, 23]\n", "[1, 3, 5, 7, 9, 10, 12, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 23]\n", "[1, 2, 5, 6, 7, 14, 15, 18, 25]\n", "[1, 3, 4, 7, 9, 12, 15, 16, 26]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 30]\n", "[1, 3, 4, 8, 9, 14, 16, 17, 26]\n", "[1, 3, 5, 6, 10, 14, 15, 16, 17]\n", "[1, 3, 4, 6, 10, 15, 16, 18, 23]\n", "[1, 3, 4, 9, 10, 14, 15, 21, 23]\n", "[1, 2, 5, 6, 9, 10, 12, 22, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 27]\n", "[1, 2, 4, 5, 10, 12, 17, 21, 28]\n", "[1, 2, 4, 7, 10, 13, 14, 18, 29]\n", "[1, 3, 4, 5, 7, 13, 15, 20, 28]\n", "[1, 2, 5, 8, 10, 14, 15, 16, 25]\n", "[1, 3, 4, 7, 8, 11, 13, 23, 25]\n", "[1, 3, 4, 7, 9, 14, 15, 17, 18]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19]\n", "[1, 3, 5, 7, 8, 14, 15, 24, 26]\n", "[1, 2, 3, 4, 9, 13, 16, 20, 27]\n", "[1, 3, 4, 9, 10, 13, 14, 16, 17]\n", "[1, 3, 4, 8, 9, 11, 20, 22, 23]\n", "[1, 3, 4, 9, 11, 12, 15, 16, 17]\n", "[1, 2, 5, 7, 10, 12, 15, 16, 28]\n", "[1, 3, 4, 7, 8, 13, 18, 23, 25]\n", "[1, 3, 5, 6, 8, 10, 16, 23, 24]\n", "[1, 3, 5, 7, 8, 14, 16, 17, 26]\n", "[1, 3, 4, 9, 11, 12, 15, 16, 18]\n", "[1, 3, 4, 6, 10, 14, 16, 19, 21]\n", "[1, 2, 5, 6, 7, 15, 17, 25, 27]\n", "[1, 2, 5, 7, 8, 10, 12, 20, 21]\n", "[1, 3, 4, 6, 7, 9, 16, 20, 24]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 26]\n", "[1, 3, 4, 6, 7, 12, 14, 19, 26]\n", "[1, 3, 4, 9, 11, 12, 16, 17, 30]\n", "[1, 3, 4, 9, 11, 14, 15, 17, 24]\n", "[1, 3, 5, 7, 9, 11, 12, 21, 22]\n", "[1, 2, 5, 7, 10, 13, 14, 15, 18]\n", "[1, 3, 4, 5, 8, 12, 13, 19, 25]\n", "[1, 2, 5, 8, 11, 13, 15, 20, 27]\n", "[1, 2, 5, 8, 11, 14, 15, 17, 19]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 31]\n", "[1, 3, 5, 6, 12, 13, 15, 16, 20]\n", "[1, 3, 4, 5, 11, 13, 14, 20, 29]\n", "[1, 3, 4, 6, 10, 15, 16, 23, 28]\n", "[1, 3, 4, 5, 6, 9, 16, 22, 24]\n", "[1, 3, 4, 7, 8, 11, 13, 22, 24]\n", "[1, 2, 3, 5, 7, 10, 16, 22, 28]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 28]\n", "[1, 3, 5, 7, 8, 16, 17, 26, 27]\n", "[1, 2, 5, 8, 9, 10, 19, 22, 25]\n", "[1, 3, 4, 5, 10, 11, 12, 15, 28]\n", "[1, 3, 4, 6, 10, 13, 15, 16, 23]\n", "[1, 3, 4, 7, 9, 12, 13, 19, 26]\n", "[1, 2, 5, 6, 9, 10, 12, 23, 25]\n", "[1, 3, 4, 8, 9, 13, 15, 16, 18]\n", "[1, 2, 5, 7, 11, 14, 15, 16, 22]\n", "[1, 2, 3, 5, 6, 11, 13, 20, 27]\n", "[1, 2, 5, 8, 10, 13, 14, 16, 17]\n", "[1, 2, 5, 7, 11, 12, 14, 18, 26]\n", "[1, 3, 5, 6, 11, 12, 16, 17, 25]\n", "[1, 3, 4, 6, 7, 13, 15, 20, 25]\n", "[1, 3, 4, 5, 8, 11, 17, 23, 29]\n", "[1, 3, 4, 8, 9, 12, 13, 19, 21]\n", "[1, 3, 5, 6, 7, 10, 12, 20, 28]\n", "[1, 2, 5, 6, 7, 14, 16, 24, 27]\n", "[1, 3, 4, 7, 8, 13, 15, 24, 29]\n", "[1, 3, 5, 7, 8, 14, 15, 19, 24]\n", "[1, 3, 4, 8, 10, 15, 17, 21, 25]\n", "[1, 2, 5, 8, 10, 13, 17, 19, 23]\n", "[1, 2, 4, 7, 10, 13, 16, 18, 20]\n", "[1, 2, 5, 7, 11, 14, 15, 22, 31]\n", "[1, 2, 4, 5, 11, 13, 19, 23, 29]\n", "[1, 3, 4, 6, 11, 13, 14, 16, 17]\n", "[1, 3, 4, 6, 10, 11, 15, 23, 28]\n", "[1, 3, 4, 5, 11, 12, 14, 16, 28]\n", "[1, 2, 3, 4, 5, 11, 16, 22, 27]\n", "[1, 2, 4, 6, 8, 10, 13, 22, 23]\n", "[1, 2, 5, 6, 9, 13, 15, 16, 18]\n", "[1, 3, 5, 7, 8, 13, 14, 16, 17]\n", "[1, 2, 4, 5, 10, 13, 14, 20, 27]\n", "[1, 3, 5, 7, 9, 11, 12, 25, 26]\n", "[1, 2, 5, 7, 8, 10, 19, 21, 25]\n", "[1, 2, 5, 8, 9, 10, 17, 21, 23]\n", "[1, 2, 3, 5, 6, 7, 15, 18, 26]\n", "[1, 3, 4, 9, 10, 12, 13, 20, 27]\n", "[1, 3, 5, 7, 9, 11, 12, 24, 25]\n", "[1, 3, 4, 6, 8, 10, 11, 23, 24]\n", "[1, 3, 4, 7, 8, 10, 11, 22, 24]\n", "[1, 2, 5, 7, 10, 13, 15, 16, 17]\n", "[1, 3, 5, 7, 8, 15, 16, 24, 25]\n", "[1, 2, 4, 6, 7, 15, 16, 23, 26]\n", "[1, 2, 5, 6, 7, 15, 18, 26, 29]\n", "[1, 3, 5, 6, 8, 11, 12, 21, 25]\n", "[1, 3, 5, 6, 7, 10, 15, 18, 26]\n", "[1, 2, 4, 5, 7, 13, 15, 16, 20]\n", "[1, 3, 5, 6, 8, 14, 18, 21, 25]\n", "[1, 3, 5, 7, 8, 9, 12, 22, 25]\n", "[1, 3, 5, 7, 8, 12, 14, 18, 26]\n", "[1, 2, 5, 6, 7, 15, 18, 24, 26]\n", "[1, 3, 4, 9, 10, 14, 15, 18, 22]\n", "[1, 2, 3, 4, 5, 11, 17, 23, 28]\n", "[1, 3, 5, 6, 7, 12, 15, 22, 26]\n", "[1, 2, 4, 6, 7, 15, 16, 24, 27]\n", "[1, 2, 4, 7, 10, 13, 15, 16, 20]\n", "[1, 3, 4, 8, 9, 13, 14, 16, 17]\n", "[1, 2, 4, 7, 9, 11, 16, 19, 22]\n", "[1, 3, 4, 8, 9, 10, 14, 17, 29]\n", "[1, 2, 5, 8, 11, 14, 15, 16, 25]\n", "[1, 3, 5, 6, 11, 13, 15, 16, 22]\n", "[1, 2, 4, 5, 8, 9, 10, 21, 23]\n", "[1, 2, 4, 5, 11, 14, 15, 16, 22]\n", "[1, 2, 5, 7, 11, 14, 15, 16, 17]\n", "[1, 3, 5, 6, 11, 13, 15, 20, 26]\n", "[1, 2, 5, 6, 7, 11, 14, 22, 25]\n", "[1, 2, 5, 6, 9, 12, 15, 16, 17]\n", "[1, 3, 4, 5, 11, 13, 16, 20, 27]\n", "[1, 3, 4, 5, 11, 13, 19, 20, 24]\n", "[1, 3, 4, 6, 10, 15, 16, 23, 24]\n", "[1, 2, 5, 8, 9, 10, 21, 23, 25]\n", "[1, 3, 4, 9, 11, 16, 20, 24, 26]\n", "[1, 2, 4, 7, 10, 12, 15, 16, 17]\n", "[1, 3, 4, 8, 10, 14, 16, 17, 19]\n", "[1, 2, 4, 7, 8, 13, 14, 16, 17]\n", "[1, 3, 5, 6, 13, 15, 16, 17, 24]\n", "[1, 2, 5, 7, 11, 13, 16, 17, 20]\n", "[1, 2, 4, 6, 9, 13, 15, 18, 23]\n", "[1, 2, 4, 7, 9, 10, 14, 22, 23]\n", "[1, 2, 5, 7, 9, 13, 14, 16, 17]\n", "[1, 3, 5, 6, 7, 14, 15, 18, 26]\n", "[1, 3, 4, 9, 11, 16, 20, 25, 29]\n", "[1, 2, 3, 4, 9, 14, 19, 24, 29]\n", "[1, 3, 5, 6, 11, 13, 15, 22, 26]\n", "[1, 3, 4, 6, 10, 13, 14, 17, 19]\n", "[1, 2, 5, 6, 7, 13, 15, 23, 26]\n", "[1, 2, 5, 8, 9, 10, 19, 22, 24]\n", "[1, 3, 4, 5, 11, 12, 13, 16, 30]\n", "[1, 2, 5, 8, 11, 13, 14, 15, 31]\n", "[1, 3, 4, 6, 8, 10, 11, 21, 22]\n", "[1, 3, 4, 7, 8, 10, 11, 21, 23]\n", "[1, 3, 5, 7, 8, 17, 18, 25, 26]\n", "[1, 3, 5, 6, 8, 10, 11, 21, 22]\n", "[1, 3, 4, 9, 11, 15, 16, 20, 24]\n", "[1, 3, 4, 7, 8, 9, 10, 21, 23]\n", "[1, 3, 5, 6, 11, 13, 14, 18, 19]\n", "[1, 2, 5, 6, 8, 14, 15, 18, 25]\n", "[1, 2, 5, 6, 8, 9, 10, 21, 23]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 27]\n", "[1, 2, 5, 8, 11, 12, 15, 16, 17]\n", "[1, 2, 4, 6, 9, 14, 15, 18, 25]\n", "[1, 3, 4, 9, 11, 12, 13, 16, 30]\n", "[1, 2, 3, 4, 9, 13, 19, 24, 27]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 24]\n", "[1, 2, 5, 7, 10, 12, 15, 16, 17]\n", "[1, 2, 5, 8, 10, 13, 14, 17, 19]\n", "[1, 2, 4, 7, 8, 13, 15, 16, 25]\n", "[1, 3, 4, 8, 10, 15, 16, 18, 19]\n", "[1, 3, 5, 6, 12, 14, 16, 22, 28]\n", "[1, 3, 5, 7, 8, 12, 15, 21, 24]\n", "[1, 2, 5, 6, 7, 15, 17, 24, 27]\n", "[1, 3, 5, 7, 8, 10, 15, 18, 24]\n", "[1, 3, 4, 7, 8, 10, 16, 21, 23]\n", "[1, 2, 5, 7, 8, 9, 19, 22, 24]\n", "[1, 2, 4, 7, 10, 13, 14, 15, 31]\n", "[1, 3, 4, 6, 11, 12, 14, 16, 17]\n", "[1, 3, 5, 6, 8, 14, 18, 24, 25]\n", "[1, 3, 5, 6, 12, 13, 17, 18, 27]\n", "[1, 3, 4, 5, 10, 11, 14, 22, 26]\n", "[1, 2, 5, 6, 7, 8, 12, 21, 25]\n", "[1, 2, 5, 6, 7, 15, 18, 26, 28]\n", "[1, 3, 4, 9, 11, 15, 16, 18, 19]\n", "[1, 2, 4, 6, 8, 9, 10, 21, 24]\n", "[1, 3, 5, 6, 11, 12, 18, 20, 27]\n", "[1, 3, 4, 7, 9, 10, 15, 18, 22]\n", "[1, 2, 5, 8, 10, 12, 13, 19, 28]\n", "[1, 2, 4, 7, 8, 9, 15, 20, 24]\n", "[1, 2, 5, 7, 8, 10, 14, 21, 25]\n", "[1, 3, 4, 7, 8, 9, 12, 22, 24]\n", "[1, 3, 4, 5, 11, 13, 16, 17, 20]\n", "[1, 3, 5, 6, 12, 13, 15, 16, 17]\n", "[1, 3, 4, 6, 10, 12, 15, 16, 23]\n", "[1, 3, 4, 6, 10, 14, 15, 22, 27]\n", "[1, 2, 5, 6, 8, 15, 17, 23, 25]\n", "[1, 3, 4, 8, 10, 12, 13, 19, 20]\n", "[1, 3, 4, 9, 11, 12, 15, 17, 22]\n", "[1, 3, 5, 6, 12, 13, 15, 16, 18]\n", "[1, 2, 5, 8, 11, 12, 14, 16, 17]\n", "[1, 2, 4, 5, 9, 10, 12, 21, 27]\n", "[1, 3, 4, 5, 6, 9, 16, 23, 30]\n", "[1, 3, 4, 8, 10, 13, 15, 19, 23]\n", "[1, 3, 4, 9, 10, 12, 13, 18, 20]\n", "[1, 2, 5, 7, 11, 13, 16, 18, 28]\n", "[1, 3, 4, 5, 6, 10, 15, 16, 23]\n", "[1, 3, 4, 8, 10, 11, 17, 21, 22]\n", "[1, 2, 4, 6, 7, 15, 18, 21, 25]\n", "[1, 3, 5, 6, 11, 13, 14, 16, 17]\n", "[1, 3, 4, 8, 9, 10, 15, 18, 28]\n", "[1, 2, 3, 4, 5, 11, 16, 22, 28]\n", "[1, 2, 5, 7, 11, 13, 14, 16, 17]\n", "[1, 2, 5, 8, 9, 10, 20, 22, 25]\n", "[1, 3, 4, 6, 8, 9, 11, 20, 24]\n", "[1, 3, 4, 6, 10, 14, 17, 19, 26]\n", "[1, 3, 4, 7, 8, 10, 11, 20, 25]\n", "[1, 3, 4, 9, 11, 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24]\n", "[1, 2, 4, 6, 9, 13, 15, 19, 27]\n", "[1, 3, 4, 5, 11, 12, 15, 21, 28]\n", "[1, 3, 4, 9, 10, 11, 16, 17, 20]\n", "[1, 3, 5, 7, 8, 12, 15, 20, 26]\n", "[1, 3, 4, 7, 9, 15, 16, 21, 26]\n", "[1, 3, 4, 6, 7, 9, 10, 21, 23]\n", "[1, 2, 4, 6, 8, 10, 11, 23, 24]\n", "[1, 3, 5, 6, 8, 13, 14, 16, 17]\n", "[1, 2, 3, 4, 9, 14, 18, 24, 29]\n", "[1, 2, 5, 6, 9, 13, 15, 18, 23]\n", "[1, 2, 4, 6, 7, 14, 16, 17, 25]\n", "[1, 3, 4, 8, 10, 14, 15, 17, 25]\n", "[1, 3, 4, 9, 11, 13, 14, 18, 19]\n", "[1, 2, 5, 6, 7, 15, 17, 25, 28]\n", "[1, 3, 5, 6, 11, 13, 14, 18, 27]\n", "[1, 3, 5, 6, 9, 10, 15, 17, 28]\n", "[1, 2, 4, 5, 11, 12, 18, 21, 27]\n", "[1, 3, 4, 8, 9, 13, 15, 16, 24]\n", "[1, 2, 5, 7, 11, 15, 16, 17, 24]\n", "[1, 3, 5, 7, 9, 10, 11, 20, 23]\n", "[1, 2, 5, 8, 11, 14, 15, 16, 32]\n", "[1, 3, 4, 6, 11, 13, 18, 19, 27]\n", "[1, 2, 4, 5, 11, 13, 14, 19, 27]\n", "[1, 3, 5, 7, 9, 10, 21, 23, 24]\n", "[1, 3, 4, 6, 11, 13, 15, 16, 22]\n", "[1, 3, 4, 9, 11, 13, 16, 17, 20]\n", "[1, 2, 5, 8, 9, 10, 18, 21, 24]\n", "[1, 2, 5, 7, 11, 12, 13, 20, 28]\n", "[1, 2, 5, 8, 10, 13, 16, 17, 18]\n", "[1, 2, 4, 5, 6, 10, 13, 20, 27]\n", "[1, 2, 4, 7, 9, 11, 16, 17, 29]\n", "[1, 2, 5, 8, 11, 14, 17, 19, 21]\n", "[1, 3, 4, 5, 11, 13, 15, 16, 22]\n", "[1, 3, 5, 6, 8, 11, 15, 24, 25]\n", "[1, 2, 4, 7, 9, 11, 17, 23, 29]\n", "[1, 2, 5, 7, 11, 13, 14, 16, 26]\n", "[1, 3, 4, 9, 11, 12, 16, 26, 30]\n", "[1, 3, 4, 8, 9, 12, 13, 19, 29]\n", "[1, 2, 5, 6, 7, 14, 15, 18, 26]\n", "[1, 2, 5, 6, 7, 15, 18, 23, 26]\n", "[1, 2, 5, 6, 7, 8, 12, 21, 24]\n", "[1, 3, 5, 6, 12, 14, 16, 17, 24]\n", "[1, 3, 4, 5, 8, 14, 16, 22, 28]\n", "[1, 3, 4, 7, 8, 13, 14, 16, 17]\n", "[1, 3, 5, 7, 9, 10, 16, 21, 24]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 28]\n", "[1, 3, 4, 8, 9, 14, 19, 21, 23]\n", "[1, 2, 5, 8, 11, 14, 15, 16, 17]\n", "[1, 2, 5, 7, 8, 10, 19, 22, 23]\n", "[1, 3, 5, 7, 8, 17, 18, 24, 25]\n", "[1, 2, 5, 8, 10, 12, 19, 20, 21]\n", "[1, 3, 5, 7, 8, 17, 18, 27, 28]\n", "[1, 3, 5, 6, 10, 11, 15, 16, 18]\n", "[1, 3, 4, 8, 9, 11, 16, 20, 22]\n", "[1, 2, 3, 4, 5, 6, 13, 20, 27]\n", "[1, 3, 4, 9, 11, 14, 16, 17, 20]\n", "[1, 3, 5, 6, 7, 10, 12, 18, 26]\n", "[1, 2, 5, 6, 8, 13, 17, 18, 27]\n", "[1, 3, 4, 7, 9, 14, 15, 17, 24]\n", "[1, 3, 4, 9, 10, 13, 15, 16, 18]\n", "[1, 3, 4, 9, 11, 12, 14, 18, 22]\n", "[1, 3, 4, 9, 10, 13, 15, 16, 17]\n", "[1, 3, 5, 6, 11, 13, 14, 15, 18]\n", "[1, 3, 4, 6, 11, 13, 14, 20, 26]\n", "[1, 2, 4, 7, 9, 12, 15, 16, 17]\n", "[1, 3, 4, 5, 6, 9, 13, 20, 27]\n", "[1, 2, 3, 5, 9, 13, 15, 16, 18]\n", "[1, 2, 4, 7, 8, 9, 19, 22, 25]\n", "[1, 3, 4, 7, 9, 14, 16, 22, 24]\n", "[1, 2, 5, 8, 9, 10, 21, 23, 26]\n", "[1, 3, 5, 7, 9, 10, 12, 22, 23]\n", "[1, 3, 5, 7, 8, 16, 17, 22, 23]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 29]\n", "[1, 3, 4, 6, 10, 13, 14, 15, 18]\n", "[1, 2, 4, 5, 10, 13, 15, 20, 27]\n", "[1, 3, 4, 7, 9, 13, 14, 16, 17]\n", "[1, 2, 5, 8, 11, 13, 16, 17, 18]\n", "[1, 3, 4, 8, 9, 11, 21, 22, 24]\n", "[1, 2, 5, 6, 9, 10, 12, 21, 23]\n", "[1, 3, 5, 6, 10, 11, 18, 22, 25]\n", "[1, 2, 4, 7, 10, 13, 14, 15, 18]\n", "[1, 2, 5, 6, 9, 10, 11, 22, 24]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22]\n", "[1, 3, 4, 7, 9, 12, 16, 22, 26]\n", "[1, 3, 5, 7, 8, 10, 18, 22, 23]\n", "[1, 3, 5, 6, 10, 14, 16, 17, 19]\n", "[1, 2, 4, 5, 11, 14, 15, 19, 27]\n", "[1, 3, 5, 6, 13, 14, 18, 19, 29]\n", "[1, 3, 4, 6, 11, 12, 19, 21, 25]\n", "[1, 3, 5, 7, 9, 10, 11, 21, 22]\n", "[1, 3, 5, 6, 10, 11, 18, 20, 22]\n", "[1, 2, 4, 5, 6, 12, 15, 21, 27]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22]\n", "[1, 2, 4, 5, 6, 7, 11, 19, 27]\n", "[1, 3, 4, 6, 10, 15, 16, 22, 23]\n", "[1, 3, 4, 8, 10, 13, 14, 16, 17]\n", "[1, 3, 4, 8, 9, 11, 18, 22, 24]\n", "[1, 3, 4, 8, 9, 12, 13, 18, 20]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29]\n", "[1, 2, 3, 4, 9, 14, 19, 23, 29]\n", "[1, 3, 5, 7, 9, 11, 12, 22, 25]\n", "[1, 2, 4, 7, 10, 13, 16, 17, 21]\n", "[1, 3, 5, 6, 10, 14, 15, 18, 21]\n", "[1, 3, 5, 6, 12, 14, 15, 17, 19]\n", "[1, 3, 4, 6, 7, 15, 16, 24, 26]\n", "[1, 3, 4, 9, 11, 12, 16, 17, 19]\n", "[1, 2, 4, 5, 10, 13, 14, 21, 28]\n", "[1, 2, 4, 5, 6, 13, 16, 23, 29]\n", "[1, 2, 5, 6, 7, 15, 18, 24, 27]\n", "[1, 3, 4, 9, 11, 16, 20, 22, 27]\n", "CPU times: user 1min 54s, sys: 624 ms, total: 1min 54s\n", "Wall time: 1min 54s\n" ] } ], "source": [ "n = 32\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "34\n", "new smallest = 10\n", "new smallest = 9\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21]\n", "[1, 3, 5, 6, 13, 14, 16, 17, 19]\n", "[1, 3, 4, 5, 8, 14, 17, 23, 29]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26]\n", "[1, 3, 4, 6, 10, 14, 15, 16, 17]\n", "[1, 2, 5, 7, 10, 13, 15, 19, 26]\n", "[1, 3, 5, 6, 11, 12, 17, 19, 21]\n", "[1, 3, 4, 9, 11, 12, 14, 16, 17]\n", "[1, 3, 4, 5, 8, 14, 20, 23, 29]\n", "[1, 3, 5, 6, 8, 14, 16, 17, 26]\n", "[1, 3, 4, 8, 9, 14, 15, 17, 19]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 29]\n", "[1, 2, 5, 6, 8, 14, 16, 17, 21]\n", "[1, 3, 4, 9, 10, 14, 16, 17, 19]\n", "[1, 2, 4, 5, 11, 13, 14, 19, 29]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 30]\n", "[1, 3, 4, 8, 9, 14, 16, 17, 26]\n", "[1, 3, 5, 6, 10, 14, 15, 16, 17]\n", "[1, 3, 4, 6, 10, 15, 16, 18, 23]\n", "[1, 2, 5, 6, 9, 10, 12, 22, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 27]\n", "[1, 2, 4, 5, 10, 12, 17, 21, 28]\n", "[1, 3, 4, 7, 8, 11, 13, 23, 25]\n", "[1, 3, 4, 7, 9, 14, 15, 17, 18]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19]\n", "[1, 3, 5, 7, 8, 14, 15, 24, 26]\n", "[1, 3, 4, 9, 10, 13, 14, 16, 17]\n", "[1, 3, 4, 8, 9, 11, 20, 22, 23]\n", "[1, 3, 4, 9, 11, 12, 15, 16, 17]\n", "[1, 3, 5, 6, 8, 10, 16, 23, 24]\n", "[1, 3, 5, 7, 8, 14, 16, 17, 26]\n", "[1, 3, 4, 9, 11, 12, 15, 16, 18]\n", "[1, 2, 5, 6, 7, 15, 17, 25, 27]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 26]\n", "[1, 3, 4, 9, 11, 12, 16, 17, 30]\n", "[1, 3, 4, 9, 11, 14, 15, 17, 24]\n", "[1, 3, 5, 7, 9, 11, 12, 21, 22]\n", "[1, 2, 5, 8, 11, 14, 15, 17, 19]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 31]\n", "[1, 3, 4, 5, 11, 13, 14, 20, 29]\n", 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5, 8, 9, 10, 21, 23, 26]\n", "[1, 3, 5, 7, 9, 10, 12, 22, 23]\n", "[1, 3, 5, 7, 8, 16, 17, 22, 23]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 29]\n", "[1, 3, 4, 7, 9, 13, 14, 16, 17]\n", "[1, 2, 5, 8, 11, 13, 16, 17, 18]\n", "[1, 2, 5, 6, 9, 10, 11, 22, 24]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22]\n", "[1, 3, 4, 7, 9, 12, 16, 22, 26]\n", "[1, 3, 5, 6, 10, 14, 16, 17, 19]\n", "[1, 2, 4, 5, 11, 14, 15, 19, 27]\n", "[1, 3, 5, 6, 13, 14, 18, 19, 29]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22]\n", "[1, 2, 4, 5, 6, 7, 11, 19, 27]\n", "[1, 3, 4, 8, 10, 13, 14, 16, 17]\n", "[1, 3, 5, 7, 9, 11, 12, 22, 25]\n", "[1, 2, 4, 7, 10, 13, 16, 17, 21]\n", "[1, 3, 5, 6, 12, 14, 15, 17, 19]\n", "[1, 3, 4, 9, 11, 12, 16, 17, 19]\n", "[1, 2, 4, 5, 10, 13, 14, 21, 28]\n", "[1, 2, 4, 5, 6, 13, 16, 23, 29]\n", "[1, 2, 5, 6, 7, 15, 18, 24, 27]\n", "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n", "Wall time: 21.4 ms\n" ] } ], "source": [ "n = 33\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "35\n", "new smallest = 9\n", "[1, 3, 4, 7, 8, 10, 11, 23, 25]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 32]\n", "[1, 3, 5, 6, 12, 13, 17, 18, 27]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21]\n", "[1, 3, 5, 6, 13, 14, 16, 17, 19]\n", "[1, 3, 4, 6, 11, 13, 14, 20, 29]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26]\n", "[1, 2, 5, 6, 7, 15, 18, 26, 28]\n", "[1, 3, 4, 9, 11, 15, 16, 18, 19]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 24]\n", "[1, 2, 5, 8, 11, 14, 15, 16, 19]\n", "[1, 3, 4, 6, 7, 10, 15, 23, 28]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 30]\n", "[1, 3, 4, 5, 6, 9, 16, 23, 30]\n", "[1, 3, 4, 9, 10, 14, 15, 17, 18]\n", "[1, 2, 5, 7, 11, 13, 16, 18, 28]\n", "[1, 2, 5, 6, 8, 14, 16, 17, 21]\n", "[1, 3, 4, 9, 11, 15, 17, 22, 26]\n", "[1, 3, 4, 9, 10, 14, 16, 17, 19]\n", "[1, 3, 5, 6, 12, 13, 15, 17, 18]\n", "[1, 3, 5, 6, 7, 12, 15, 20, 28]\n", "[1, 2, 5, 8, 9, 10, 20, 22, 25]\n", "[1, 2, 5, 8, 9, 10, 21, 24, 27]\n", "[1, 3, 4, 9, 10, 13, 14, 20, 22]\n", "[1, 3, 4, 8, 9, 14, 16, 17, 26]\n", "[1, 2, 5, 6, 9, 10, 11, 23, 25]\n", "[1, 3, 5, 7, 8, 17, 18, 26, 27]\n", "[1, 3, 5, 6, 11, 13, 14, 20, 29]\n", "[1, 3, 5, 6, 13, 14, 16, 18, 19]\n", "[1, 3, 4, 8, 10, 15, 17, 18, 21]\n", "[1, 3, 5, 7, 8, 15, 16, 20, 26]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20]\n", "[1, 2, 5, 6, 7, 15, 16, 19, 27]\n", "[1, 2, 4, 7, 10, 13, 16, 17, 18]\n", "[1, 3, 4, 7, 9, 14, 15, 17, 18]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19]\n", "[1, 2, 5, 8, 10, 13, 17, 23, 27]\n", "[1, 3, 4, 9, 10, 13, 14, 19, 21]\n", "[1, 3, 5, 6, 8, 11, 15, 24, 28]\n", "[1, 2, 5, 8, 10, 14, 15, 16, 19]\n", "[1, 3, 4, 6, 11, 13, 14, 17, 29]\n", "[1, 3, 4, 8, 9, 11, 20, 24, 26]\n", "[1, 2, 5, 7, 11, 15, 16, 17, 18]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24]\n", "[1, 3, 5, 7, 9, 11, 12, 23, 24]\n", "[1, 2, 5, 7, 11, 12, 14, 20, 28]\n", "[1, 3, 4, 9, 11, 15, 16, 17, 20]\n", "[1, 3, 4, 8, 10, 14, 15, 17, 18]\n", "[1, 3, 5, 6, 8, 14, 16, 17, 21]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 26]\n", "[1, 3, 4, 9, 11, 14, 15, 17, 24]\n", "[1, 3, 5, 7, 8, 12, 15, 20, 26]\n", "[1, 2, 4, 6, 8, 10, 11, 23, 24]\n", "[1, 3, 5, 7, 8, 10, 11, 23, 24]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 31]\n", "[1, 3, 5, 6, 8, 14, 17, 21, 27]\n", "[1, 3, 4, 8, 10, 14, 15, 17, 25]\n", "[1, 2, 5, 7, 8, 10, 17, 21, 25]\n", "[1, 2, 5, 6, 7, 15, 17, 25, 28]\n", "[1, 2, 5, 7, 11, 15, 16, 17, 24]\n", "[1, 2, 5, 7, 10, 13, 16, 17, 18]\n", "[1, 2, 5, 7, 11, 13, 16, 17, 24]\n", "[1, 3, 5, 7, 8, 16, 17, 26, 27]\n", "[1, 2, 5, 8, 9, 10, 19, 22, 25]\n", "[1, 2, 5, 8, 10, 14, 16, 17, 21]\n", "[1, 2, 5, 6, 9, 10, 12, 23, 25]\n", "[1, 2, 5, 8, 9, 10, 21, 24, 26]\n", "[1, 2, 5, 7, 11, 14, 16, 19, 29]\n", "[1, 3, 5, 6, 7, 10, 12, 20, 28]\n", "[1, 3, 4, 6, 10, 14, 16, 17, 25]\n", "[1, 2, 5, 7, 11, 13, 16, 17, 18]\n", "[1, 3, 4, 8, 10, 15, 17, 21, 25]\n", "[1, 2, 5, 8, 10, 13, 16, 17, 18]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 19]\n", "[1, 3, 5, 6, 11, 12, 19, 21, 23]\n", "[1, 2, 5, 8, 11, 14, 17, 19, 21]\n", "[1, 3, 4, 8, 9, 14, 15, 17, 18]\n", "[1, 2, 5, 8, 9, 10, 20, 23, 25]\n", "[1, 2, 5, 8, 9, 10, 20, 23, 26]\n", "[1, 3, 4, 9, 11, 12, 16, 26, 30]\n", "[1, 3, 4, 9, 11, 15, 17, 20, 24]\n", "[1, 3, 5, 7, 9, 10, 11, 23, 24]\n", "[1, 3, 5, 7, 9, 11, 12, 25, 26]\n", "[1, 2, 5, 6, 7, 14, 17, 25, 28]\n", "[1, 2, 5, 6, 7, 15, 18, 25, 28]\n", "[1, 3, 5, 7, 9, 11, 12, 24, 25]\n", "[1, 3, 4, 6, 8, 10, 11, 23, 24]\n", "[1, 3, 4, 7, 8, 10, 11, 22, 24]\n", "[1, 3, 4, 8, 9, 11, 21, 23, 24]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 20]\n", "[1, 2, 5, 6, 7, 15, 18, 26, 29]\n", "[1, 3, 5, 7, 8, 17, 18, 24, 25]\n", "[1, 3, 4, 9, 11, 13, 16, 17, 22]\n", "[1, 3, 4, 9, 11, 12, 16, 22, 26]\n", "[1, 3, 5, 6, 12, 14, 15, 19, 20]\n", "[1, 3, 4, 6, 10, 14, 16, 17, 19]\n", "[1, 3, 5, 7, 9, 10, 12, 23, 24]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 20]\n", "[1, 3, 5, 7, 8, 17, 18, 27, 28]\n", "[1, 2, 5, 6, 8, 13, 17, 18, 27]\n", "[1, 3, 4, 5, 8, 14, 20, 25, 27]\n", "[1, 3, 4, 9, 10, 15, 16, 17, 19]\n", "[1, 3, 4, 6, 10, 13, 14, 21, 29]\n", "[1, 3, 5, 6, 12, 13, 15, 17, 30]\n", "[1, 2, 5, 8, 9, 10, 21, 23, 26]\n", "[1, 2, 5, 8, 9, 10, 21, 23, 25]\n", "[1, 3, 5, 7, 9, 10, 12, 22, 23]\n", "[1, 3, 4, 8, 10, 14, 16, 17, 19]\n", "[1, 3, 4, 6, 10, 13, 15, 21, 29]\n", "[1, 2, 5, 7, 11, 14, 15, 16, 19]\n", "[1, 3, 5, 6, 8, 10, 11, 23, 24]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 22]\n", "[1, 3, 5, 7, 9, 11, 12, 22, 23]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 29]\n", "[1, 3, 4, 9, 10, 11, 16, 20, 24]\n", "[1, 3, 4, 9, 11, 14, 15, 17, 18]\n", "[1, 2, 5, 8, 11, 13, 16, 17, 18]\n", "[1, 2, 5, 8, 11, 14, 16, 17, 18]\n", "[1, 2, 5, 6, 9, 10, 11, 22, 24]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22]\n", "[1, 3, 4, 7, 9, 12, 16, 22, 26]\n", "[1, 3, 4, 9, 10, 13, 14, 21, 29]\n", "[1, 3, 4, 5, 11, 12, 13, 16, 30]\n", "[1, 3, 5, 6, 10, 14, 16, 17, 19]\n", "[1, 3, 5, 6, 13, 14, 18, 19, 29]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22]\n", "[1, 3, 5, 7, 8, 17, 18, 25, 26]\n", "[1, 2, 5, 7, 9, 13, 16, 17, 26]\n", "[1, 2, 4, 5, 11, 14, 15, 16, 19]\n", "[1, 3, 4, 8, 10, 15, 16, 18, 19]\n", "[1, 3, 4, 9, 11, 12, 16, 17, 19]\n", "[1, 2, 4, 5, 10, 13, 14, 21, 28]\n", "[1, 3, 4, 6, 10, 15, 17, 18, 25]\n", "[1, 2, 4, 5, 6, 13, 16, 23, 29]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20]\n", "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n", "Wall time: 23.5 ms\n" ] } ], "source": [ "n = 34\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "36\n", "new smallest = 9\n", "[1, 3, 4, 7, 8, 10, 11, 23, 25]\n", "[1, 3, 4, 9, 10, 15, 16, 17, 19]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 32]\n", "[1, 3, 5, 6, 12, 13, 17, 18, 27]\n", "[1, 3, 5, 6, 12, 13, 15, 17, 30]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20]\n", "[1, 2, 5, 7, 11, 14, 16, 19, 29]\n", "[1, 3, 4, 8, 10, 15, 17, 18, 21]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21]\n", "[1, 3, 5, 6, 13, 14, 16, 17, 19]\n", "[1, 2, 4, 7, 10, 13, 16, 17, 18]\n", "[1, 3, 4, 7, 9, 14, 15, 17, 18]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26]\n", "[1, 2, 5, 6, 7, 15, 18, 26, 28]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19]\n", "[1, 3, 4, 9, 11, 15, 16, 18, 19]\n", "[1, 2, 5, 8, 10, 13, 17, 23, 27]\n", "[1, 3, 5, 6, 8, 11, 15, 24, 28]\n", "[1, 2, 5, 7, 11, 13, 16, 17, 18]\n", "[1, 3, 4, 8, 10, 15, 17, 21, 25]\n", "[1, 3, 4, 8, 10, 14, 16, 17, 19]\n", "[1, 3, 4, 6, 10, 13, 15, 21, 29]\n", "[1, 2, 5, 7, 11, 15, 16, 17, 18]\n", "[1, 2, 5, 8, 10, 13, 16, 17, 18]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24]\n", "[1, 3, 5, 7, 9, 11, 12, 23, 24]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 19]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 29]\n", "[1, 2, 5, 8, 11, 14, 17, 19, 21]\n", "[1, 3, 4, 8, 9, 14, 15, 17, 18]\n", "[1, 3, 4, 9, 10, 11, 16, 20, 24]\n", "[1, 3, 4, 9, 11, 14, 15, 17, 18]\n", "[1, 2, 5, 8, 11, 13, 16, 17, 18]\n", "[1, 2, 5, 8, 11, 14, 16, 17, 18]\n", "[1, 3, 4, 9, 11, 15, 16, 17, 20]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22]\n", "[1, 2, 5, 8, 9, 10, 20, 23, 26]\n", "[1, 3, 5, 6, 10, 14, 16, 17, 19]\n", "[1, 3, 5, 7, 9, 11, 12, 25, 26]\n", "[1, 3, 4, 8, 10, 14, 15, 17, 18]\n", "[1, 3, 5, 6, 13, 14, 18, 19, 29]\n", "[1, 2, 5, 6, 7, 15, 18, 25, 28]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22]\n", "[1, 3, 5, 7, 8, 17, 18, 25, 26]\n", "[1, 3, 5, 7, 9, 11, 12, 24, 25]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 30]\n", "[1, 3, 4, 5, 6, 9, 16, 23, 30]\n", "[1, 3, 4, 7, 9, 14, 17, 18, 26]\n", "[1, 2, 5, 8, 9, 10, 21, 23, 26]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 20]\n", "[1, 3, 4, 9, 10, 14, 15, 17, 18]\n", "[1, 2, 5, 7, 11, 13, 16, 18, 28]\n", "[1, 2, 5, 6, 7, 15, 18, 26, 29]\n", "[1, 3, 5, 7, 8, 17, 18, 24, 25]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 31]\n", "[1, 3, 4, 9, 10, 14, 16, 17, 19]\n", "[1, 3, 5, 6, 12, 13, 15, 17, 18]\n", "[1, 3, 4, 6, 10, 14, 16, 17, 19]\n", "[1, 3, 5, 7, 9, 10, 12, 23, 24]\n", "[1, 2, 5, 8, 9, 10, 21, 24, 27]\n", "[1, 3, 4, 9, 10, 13, 14, 20, 22]\n", "[1, 3, 4, 9, 11, 14, 15, 18, 20]\n", "[1, 2, 5, 6, 9, 10, 11, 23, 25]\n", "[1, 3, 5, 7, 8, 17, 18, 26, 27]\n", "[1, 3, 5, 7, 8, 17, 18, 27, 28]\n", "[1, 3, 4, 8, 10, 15, 16, 18, 19]\n", "[1, 2, 5, 7, 10, 13, 16, 17, 18]\n", "[1, 2, 5, 6, 8, 13, 17, 18, 27]\n", "[1, 3, 4, 9, 11, 12, 16, 17, 19]\n", "[1, 3, 4, 6, 10, 15, 17, 18, 25]\n", "[1, 2, 4, 5, 6, 13, 16, 23, 29]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20]\n", "[1, 3, 5, 6, 13, 14, 16, 18, 19]\n", "[1, 3, 5, 7, 8, 15, 16, 20, 26]\n", "[1, 2, 5, 8, 9, 10, 21, 24, 26]\n", "CPU times: user 8 ms, sys: 0 ns, total: 8 ms\n", "Wall time: 7.78 ms\n" ] } ], "source": [ "n = 35\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "37\n", "new smallest = 10\n", "new smallest = 9\n", "[1, 3, 5, 7, 9, 11, 12, 24, 25]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 30]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 32]\n", "[1, 2, 5, 8, 9, 10, 21, 24, 27]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20]\n", "[1, 3, 4, 8, 10, 15, 16, 18, 19]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21]\n", "[1, 3, 4, 9, 11, 15, 16, 17, 20]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19]\n", "[1, 2, 5, 8, 10, 13, 17, 23, 27]\n", "[1, 3, 4, 9, 11, 15, 16, 18, 19]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20]\n", "[1, 3, 5, 7, 9, 11, 12, 25, 26]\n", "[1, 3, 5, 6, 13, 14, 18, 19, 29]\n", "[1, 3, 5, 6, 13, 14, 16, 18, 19]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 19]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 2.88 ms\n" ] } ], "source": [ "n = 36\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "38\n", "new smallest = 10\n", "new smallest = 9\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20]\n", "[1, 3, 4, 8, 10, 15, 16, 18, 19]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 19]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19]\n", "[1, 3, 4, 9, 11, 15, 16, 18, 19]\n", "[1, 3, 5, 6, 13, 14, 18, 19, 29]\n", "[1, 3, 5, 7, 9, 11, 12, 25, 26]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20]\n", "[1, 3, 5, 6, 13, 14, 16, 18, 19]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 2.88 ms\n" ] } ], "source": [ "n = 37\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "39\n", "new smallest = 10\n", "new smallest = 9\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 3.24 ms\n" ] } ], "source": [ "n = 38\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "40\n", "new smallest = 9\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20]\n", "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n", "Wall time: 140 µs\n" ] } ], "source": [ "n = 39\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "41\n", "new smallest = 10\n", "considering 1\n", "considering 2\n", "considering 3\n", "considering 4\n", "[1, 3, 4, 9, 11, 16, 18, 19, 21, 22]\n", "[1, 2, 5, 8, 11, 12, 13, 24, 26, 28]\n", "[1, 3, 5, 6, 11, 12, 19, 21, 23, 36]\n", "[1, 2, 4, 5, 6, 7, 11, 19, 27, 35]\n", "[1, 3, 5, 7, 9, 10, 19, 20, 28, 31]\n", "[1, 3, 4, 8, 10, 14, 18, 19, 22, 31]\n", "[1, 3, 4, 8, 10, 14, 19, 20, 22, 27]\n", "[1, 3, 5, 6, 11, 12, 16, 19, 25, 28]\n", "[1, 2, 5, 7, 11, 13, 17, 18, 20, 21]\n", "[1, 3, 4, 7, 8, 10, 19, 21, 29, 31]\n", "[1, 3, 5, 6, 12, 14, 15, 19, 20, 36]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 34]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 32, 33]\n", "[1, 3, 4, 9, 11, 15, 17, 20, 21, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 22]\n", "[1, 3, 5, 6, 13, 14, 15, 19, 22, 26]\n", "[1, 3, 4, 7, 8, 11, 12, 14, 27, 29]\n", "[1, 3, 5, 6, 9, 13, 17, 19, 20, 22]\n", "[1, 2, 5, 8, 10, 11, 13, 17, 27, 31]\n", "[1, 2, 3, 5, 9, 13, 17, 19, 20, 22]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 20, 26]\n", "[1, 3, 4, 8, 9, 11, 16, 20, 26, 30]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 22, 36]\n", "[1, 3, 5, 6, 7, 10, 12, 18, 26, 34]\n", "[1, 2, 5, 7, 10, 13, 15, 19, 26, 30]\n", "[1, 2, 5, 7, 11, 13, 17, 18, 19, 22]\n", "[1, 2, 4, 7, 8, 13, 18, 19, 22, 26]\n", "[1, 3, 5, 6, 13, 14, 18, 21, 24, 27]\n", "[1, 3, 4, 6, 10, 14, 17, 19, 20, 31]\n", "[1, 3, 4, 9, 11, 16, 20, 25, 30, 34]\n", "[1, 3, 4, 7, 8, 11, 12, 13, 26, 28]\n", "[1, 3, 5, 6, 13, 15, 16, 19, 20, 22]\n", "[1, 3, 4, 9, 11, 15, 17, 20, 24, 35]\n", "[1, 3, 4, 8, 10, 15, 17, 18, 23, 29]\n", "[1, 3, 5, 6, 7, 10, 12, 20, 28, 36]\n", "[1, 3, 4, 5, 11, 13, 17, 18, 19, 22]\n", "[1, 3, 5, 6, 10, 11, 13, 25, 27, 28]\n", "[1, 3, 4, 7, 8, 9, 19, 21, 30, 32]\n", "[1, 3, 4, 9, 11, 16, 19, 21, 25, 30]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 24]\n", "[1, 3, 5, 6, 13, 15, 16, 17, 24, 35]\n", "[1, 2, 5, 8, 11, 13, 16, 19, 20, 21]\n", "[1, 2, 5, 7, 10, 13, 15, 19, 26, 35]\n", "[1, 3, 5, 7, 8, 10, 12, 20, 26, 34]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 31, 32]\n", "[1, 2, 4, 7, 10, 13, 16, 19, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 31, 32]\n", "[1, 2, 5, 8, 10, 14, 17, 20, 21, 31]\n", "[1, 3, 5, 6, 13, 14, 16, 17, 22, 24]\n", "[1, 3, 4, 7, 8, 13, 17, 19, 20, 28]\n", "[1, 3, 5, 6, 13, 15, 16, 17, 19, 24]\n", "[1, 3, 5, 6, 11, 13, 14, 18, 27, 34]\n", "[1, 2, 5, 8, 10, 12, 17, 18, 20, 31]\n", "[1, 2, 5, 7, 11, 13, 17, 19, 20, 22]\n", "[1, 3, 4, 6, 10, 14, 18, 19, 20, 21]\n", "[1, 2, 5, 7, 10, 11, 12, 25, 26, 29]\n", "[1, 3, 5, 7, 9, 10, 18, 19, 30, 31]\n", "[1, 3, 5, 7, 8, 15, 17, 19, 20, 26]\n", "[1, 3, 4, 7, 9, 11, 16, 19, 20, 30]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 30, 35]\n", "[1, 2, 5, 8, 11, 13, 15, 25, 26, 27]\n", "[1, 3, 4, 9, 11, 16, 18, 19, 20, 22]\n", "[1, 2, 4, 5, 11, 14, 15, 19, 27, 35]\n", "[1, 2, 5, 6, 8, 10, 15, 19, 20, 31]\n", "[1, 3, 4, 8, 9, 10, 15, 18, 29, 31]\n", "[1, 3, 5, 6, 13, 14, 15, 19, 22, 25]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 21, 35]\n", "[1, 3, 4, 6, 10, 14, 18, 20, 25, 27]\n", "[1, 3, 4, 7, 8, 11, 12, 13, 27, 29]\n", "[1, 3, 4, 9, 11, 16, 17, 18, 20, 30]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 32]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 23, 24]\n", "[1, 3, 4, 6, 11, 13, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 11, 12, 16, 24, 26, 30]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 28, 29]\n", "[1, 3, 4, 8, 9, 10, 15, 18, 28, 31]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 30]\n", "[1, 3, 5, 6, 8, 12, 19, 20, 28, 29]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 25]\n", "[1, 2, 5, 6, 9, 10, 12, 13, 27, 29]\n", "[1, 2, 5, 8, 11, 12, 13, 27, 28, 29]\n", "[1, 3, 5, 6, 11, 13, 15, 20, 26, 33]\n", "[1, 3, 4, 6, 10, 14, 19, 20, 27, 32]\n", "[1, 3, 5, 7, 8, 10, 18, 19, 30, 31]\n", "[1, 2, 5, 8, 11, 14, 17, 19, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 29, 30]\n", "[1, 3, 4, 9, 10, 11, 13, 24, 27, 28]\n", "[1, 3, 4, 9, 11, 12, 16, 20, 26, 30]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 32, 33]\n", "[1, 2, 5, 7, 10, 11, 12, 25, 28, 29]\n", "[1, 3, 5, 7, 8, 12, 14, 18, 26, 34]\n", "[1, 3, 4, 7, 8, 10, 18, 20, 29, 31]\n", "[1, 3, 4, 5, 11, 13, 17, 19, 20, 24]\n", "[1, 3, 4, 9, 10, 13, 14, 21, 27, 29]\n", "[1, 3, 5, 7, 8, 13, 17, 19, 20, 28]\n", "[1, 3, 5, 7, 9, 10, 19, 20, 31, 32]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 25, 33]\n", "[1, 3, 4, 6, 10, 12, 17, 18, 20, 21]\n", "[1, 2, 4, 5, 7, 13, 16, 18, 23, 33]\n", "[1, 3, 4, 9, 10, 12, 13, 23, 28, 30]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 20, 24]\n", "[1, 2, 5, 7, 10, 13, 16, 19, 20, 21]\n", "[1, 3, 4, 9, 11, 12, 16, 26, 30, 36]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22, 23]\n", "[1, 2, 5, 6, 7, 10, 18, 20, 29, 31]\n", "[1, 3, 4, 7, 9, 15, 17, 19, 20, 24]\n", "[1, 3, 4, 9, 11, 12, 16, 24, 25, 27]\n", "[1, 3, 4, 5, 11, 13, 16, 20, 25, 34]\n", "[1, 3, 4, 6, 8, 12, 17, 19, 20, 29]\n", "[1, 2, 5, 6, 9, 11, 19, 21, 28, 30]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 22, 23]\n", "[1, 3, 5, 6, 12, 13, 15, 18, 22, 26]\n", "[1, 2, 5, 8, 9, 12, 14, 25, 26, 27]\n", "[1, 3, 5, 6, 8, 12, 19, 20, 29, 33]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 21, 28]\n", "[1, 3, 5, 6, 10, 13, 16, 24, 25, 33]\n", "[1, 3, 4, 9, 11, 14, 15, 17, 24, 36]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 38]\n", "[1, 2, 4, 6, 9, 10, 17, 19, 20, 31]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 21, 24]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 21, 32]\n", "[1, 2, 5, 7, 8, 11, 17, 20, 21, 28]\n", "[1, 3, 4, 5, 6, 9, 16, 23, 30, 37]\n", "[1, 3, 5, 6, 10, 11, 12, 16, 25, 28]\n", "[1, 3, 4, 9, 10, 12, 13, 22, 27, 29]\n", "[1, 2, 5, 8, 11, 13, 17, 19, 22, 29]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 28, 29]\n", "[1, 3, 4, 7, 8, 9, 19, 21, 31, 33]\n", "[1, 3, 4, 9, 11, 13, 17, 18, 19, 22]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 19, 22]\n", "[1, 2, 4, 5, 10, 13, 14, 21, 28, 35]\n", "[1, 3, 5, 6, 13, 14, 16, 18, 20, 21]\n", "[1, 3, 5, 6, 10, 13, 16, 23, 24, 25]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 35]\n", "[1, 2, 5, 8, 11, 14, 17, 20, 22, 24]\n", "[1, 2, 5, 8, 10, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 21, 22]\n", "[1, 3, 4, 9, 11, 16, 20, 26, 27, 30]\n", "[1, 3, 4, 7, 8, 9, 18, 20, 30, 32]\n", "[1, 3, 5, 6, 13, 14, 16, 20, 21, 25]\n", "[1, 3, 5, 6, 13, 14, 21, 23, 25, 27]\n", "[1, 3, 4, 8, 10, 11, 13, 24, 28, 30]\n", "[1, 3, 4, 6, 10, 15, 16, 18, 23, 34]\n", "[1, 2, 5, 8, 11, 13, 17, 18, 19, 22]\n", "[1, 3, 4, 6, 11, 12, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 10, 12, 13, 21, 26, 28]\n", "[1, 3, 4, 6, 11, 13, 18, 20, 21, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 30, 34]\n", "[1, 2, 5, 8, 11, 14, 16, 19, 20, 21]\n", "[1, 2, 5, 8, 10, 12, 18, 19, 20, 33]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 30, 35]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 20, 21]\n", "[1, 2, 5, 8, 10, 12, 13, 18, 27, 33]\n", "[1, 3, 4, 9, 11, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 8, 10, 12, 15, 18, 20, 29]\n", "[1, 3, 4, 8, 9, 10, 14, 17, 29, 32]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22, 26]\n", "[1, 3, 4, 5, 11, 12, 18, 19, 21, 23]\n", "[1, 3, 4, 8, 10, 15, 17, 18, 20, 21]\n", "[1, 3, 5, 6, 10, 14, 15, 19, 22, 25]\n", "[1, 3, 4, 9, 11, 12, 17, 19, 20, 24]\n", "[1, 3, 5, 6, 11, 12, 18, 19, 21, 23]\n", "[1, 2, 4, 7, 10, 11, 14, 19, 25, 30]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 38]\n", "[1, 2, 4, 5, 7, 12, 14, 18, 27, 33]\n", "[1, 3, 4, 7, 8, 10, 19, 21, 29, 34]\n", "[1, 3, 4, 8, 10, 14, 18, 20, 25, 27]\n", "[1, 3, 5, 6, 12, 14, 16, 17, 23, 24]\n", "[1, 3, 5, 6, 13, 15, 17, 20, 21, 26]\n", "[1, 3, 4, 6, 9, 10, 17, 20, 22, 32]\n", "[1, 3, 4, 9, 10, 15, 17, 18, 20, 21]\n", "[1, 2, 5, 7, 11, 15, 19, 20, 21, 22]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 33, 34]\n", "[1, 3, 5, 7, 8, 12, 15, 20, 26, 36]\n", "[1, 2, 5, 8, 10, 14, 16, 19, 20, 21]\n", "[1, 2, 5, 8, 11, 13, 15, 24, 25, 26]\n", "[1, 2, 4, 5, 10, 13, 14, 20, 27, 34]\n", "[1, 3, 5, 7, 8, 10, 19, 20, 30, 31]\n", "[1, 3, 4, 9, 11, 12, 17, 19, 24, 28]\n", "[1, 2, 5, 7, 11, 15, 16, 17, 24, 36]\n", "[1, 2, 5, 7, 11, 15, 17, 19, 20, 22]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 20, 24]\n", "[1, 2, 5, 8, 11, 14, 17, 20, 21, 22]\n", "[1, 3, 4, 9, 11, 13, 17, 19, 20, 24]\n", "[1, 2, 4, 6, 9, 13, 15, 19, 27, 35]\n", "[1, 3, 4, 9, 11, 16, 17, 18, 20, 21]\n", "[1, 3, 5, 7, 8, 10, 12, 13, 27, 28]\n", "[1, 3, 4, 9, 11, 16, 18, 19, 22, 23]\n", "[1, 3, 4, 8, 9, 11, 17, 19, 20, 32]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 21, 22]\n", "[1, 2, 4, 5, 11, 14, 17, 18, 19, 22]\n", "[1, 2, 5, 8, 10, 13, 16, 19, 20, 21]\n", "[1, 2, 5, 6, 8, 9, 19, 21, 30, 32]\n", "[1, 2, 4, 5, 10, 12, 18, 20, 25, 29]\n", "[1, 3, 4, 9, 10, 14, 16, 19, 20, 27]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 26, 27]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19, 22]\n", "[1, 3, 5, 6, 8, 15, 17, 18, 22, 23]\n", "[1, 2, 5, 8, 10, 12, 18, 20, 25, 29]\n", "[1, 3, 4, 5, 6, 7, 10, 18, 26, 34]\n", "[1, 2, 4, 5, 8, 10, 17, 20, 21, 31]\n", "[1, 3, 4, 8, 10, 11, 13, 24, 26, 30]\n", "[1, 2, 5, 6, 9, 11, 18, 20, 28, 30]\n", "[1, 2, 4, 7, 10, 11, 12, 25, 27, 29]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 21]\n", "[1, 3, 4, 9, 10, 12, 13, 24, 26, 28]\n", "[1, 2, 5, 8, 11, 14, 17, 18, 19, 39]\n", "[1, 2, 4, 6, 8, 10, 12, 13, 27, 28]\n", "[1, 3, 5, 7, 8, 10, 18, 21, 27, 33]\n", "[1, 3, 4, 8, 9, 10, 15, 18, 19, 31]\n", "[1, 3, 5, 6, 13, 15, 17, 23, 24, 30]\n", "[1, 2, 5, 8, 10, 13, 17, 19, 27, 31]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 26, 30]\n", "[1, 3, 5, 6, 13, 15, 17, 19, 20, 26]\n", "[1, 3, 4, 6, 11, 13, 14, 20, 26, 35]\n", "[1, 2, 5, 7, 9, 13, 14, 16, 24, 34]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 28, 35]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22, 36]\n", "[1, 3, 5, 7, 8, 17, 19, 20, 24, 30]\n", "[1, 3, 5, 7, 8, 15, 17, 18, 22, 23]\n", "[1, 3, 4, 8, 10, 12, 13, 19, 27, 33]\n", "[1, 3, 5, 7, 8, 14, 17, 19, 22, 32]\n", "[1, 3, 4, 5, 8, 14, 20, 25, 27, 33]\n", "[1, 3, 4, 8, 10, 11, 13, 20, 24, 28]\n", "[1, 3, 5, 6, 12, 13, 18, 19, 21, 23]\n", "[1, 3, 4, 8, 9, 11, 17, 19, 20, 24]\n", "[1, 3, 4, 6, 10, 13, 15, 18, 26, 34]\n", "[1, 3, 4, 9, 10, 15, 17, 20, 21, 24]\n", "[1, 2, 5, 8, 11, 12, 13, 26, 28, 30]\n", "[1, 3, 4, 8, 10, 12, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 11, 13, 16, 20, 25, 26]\n", "[1, 3, 4, 5, 8, 11, 15, 16, 25, 34]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20, 21]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 33]\n", "[1, 2, 5, 8, 11, 12, 13, 26, 27, 28]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 31, 33]\n", "[1, 3, 5, 6, 13, 15, 17, 22, 23, 28]\n", "[1, 3, 4, 6, 11, 12, 14, 18, 27, 34]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 25]\n", "[1, 3, 4, 8, 10, 15, 17, 18, 21, 37]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 24, 29]\n", "[1, 2, 5, 8, 11, 12, 13, 27, 29, 31]\n", "[1, 3, 5, 6, 8, 15, 16, 20, 21, 33]\n", "[1, 3, 5, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 4, 9, 10, 12, 13, 26, 28, 30]\n", "[1, 3, 4, 5, 10, 12, 17, 18, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 18, 21, 28, 31]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 30, 31]\n", "[1, 2, 5, 8, 10, 11, 12, 25, 27, 29]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 22, 24]\n", "[1, 2, 4, 5, 11, 13, 18, 20, 26, 30]\n", "[1, 3, 4, 5, 8, 14, 17, 22, 24, 32]\n", "[1, 3, 4, 9, 10, 11, 12, 16, 26, 30]\n", "[1, 3, 5, 7, 8, 16, 18, 20, 21, 30]\n", "[1, 3, 4, 8, 10, 11, 13, 25, 27, 31]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 20, 21]\n", "[1, 3, 5, 6, 12, 14, 15, 19, 20, 22]\n", "[1, 3, 5, 6, 11, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 7, 10, 11, 13, 18, 27, 28]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 22, 30]\n", "[1, 2, 5, 7, 11, 12, 14, 18, 26, 34]\n", "[1, 3, 4, 7, 9, 12, 13, 20, 27, 34]\n", "[1, 3, 4, 9, 10, 12, 13, 25, 27, 29]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 27, 28]\n", "[1, 3, 5, 6, 8, 10, 12, 13, 27, 28]\n", "[1, 2, 4, 5, 11, 12, 18, 19, 21, 23]\n", "[1, 3, 4, 8, 10, 14, 18, 19, 20, 21]\n", "[1, 3, 4, 8, 10, 11, 14, 19, 26, 31]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 37]\n", "[1, 3, 5, 6, 12, 14, 16, 17, 24, 34]\n", "[1, 2, 5, 8, 10, 14, 17, 18, 19, 22]\n", "[1, 3, 4, 8, 10, 14, 18, 23, 25, 30]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 32, 38]\n", "[1, 3, 4, 6, 11, 13, 18, 19, 21, 22]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 24, 35]\n", "[1, 3, 5, 6, 8, 12, 19, 20, 29, 30]\n", "[1, 3, 4, 6, 10, 14, 16, 19, 20, 21]\n", "[1, 3, 4, 8, 9, 11, 12, 22, 27, 29]\n", "[1, 3, 5, 6, 8, 15, 16, 18, 20, 21]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 23]\n", "[1, 3, 4, 7, 9, 15, 17, 18, 20, 24]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22, 37]\n", "[1, 2, 5, 6, 8, 15, 16, 18, 20, 21]\n", "[1, 3, 4, 7, 9, 15, 17, 18, 19, 22]\n", "[1, 3, 4, 9, 10, 12, 13, 25, 27, 32]\n", "[1, 3, 5, 7, 9, 10, 12, 13, 27, 28]\n", "[1, 3, 5, 6, 7, 15, 16, 19, 22, 33]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 24, 35]\n", "[1, 3, 4, 6, 10, 13, 15, 21, 29, 37]\n", "[1, 3, 4, 9, 10, 12, 13, 24, 29, 31]\n", "[1, 3, 4, 8, 10, 11, 13, 24, 28, 29]\n", "[1, 2, 5, 7, 10, 12, 16, 25, 28, 29]\n", "[1, 2, 5, 7, 11, 15, 18, 20, 23, 32]\n", "[1, 3, 4, 9, 11, 15, 17, 19, 20, 24]\n", "[1, 3, 5, 6, 12, 13, 18, 19, 27, 29]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22, 23]\n", "[1, 3, 4, 9, 10, 12, 16, 18, 23, 28]\n", "[1, 3, 5, 6, 13, 15, 16, 19, 20, 21]\n", "[1, 3, 4, 6, 10, 14, 19, 20, 26, 31]\n", "[1, 3, 4, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 2, 5, 6, 7, 11, 15, 18, 26, 33]\n", "[1, 2, 5, 7, 11, 14, 17, 18, 19, 22]\n", "[1, 2, 4, 7, 8, 13, 15, 16, 23, 33]\n", "[1, 3, 4, 8, 10, 15, 16, 19, 20, 33]\n", "[1, 2, 4, 5, 6, 13, 16, 23, 29, 36]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20, 24]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 29, 30]\n", "[1, 3, 4, 9, 11, 13, 18, 20, 21, 24]\n", "[1, 2, 5, 6, 7, 15, 18, 22, 26, 33]\n", "[1, 2, 5, 7, 11, 15, 18, 19, 20, 21]\n", "[1, 3, 4, 6, 10, 14, 18, 20, 23, 25]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 21, 30]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20, 39]\n", "[1, 3, 4, 9, 10, 12, 17, 18, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 30, 31]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 24, 26]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22, 34]\n", "[1, 3, 4, 9, 11, 15, 16, 17, 20, 38]\n", "[1, 3, 4, 8, 10, 14, 18, 20, 23, 25]\n", "[1, 2, 5, 7, 10, 12, 16, 25, 29, 33]\n", "[1, 2, 5, 8, 11, 12, 13, 25, 27, 29]\n", "[1, 3, 5, 6, 12, 13, 19, 20, 22, 24]\n", "[1, 3, 4, 8, 10, 14, 18, 20, 21, 23]\n", "[1, 2, 5, 7, 9, 13, 15, 18, 20, 32]\n", "[1, 3, 4, 9, 10, 15, 16, 21, 23, 25]\n", "[1, 2, 5, 6, 8, 9, 18, 20, 30, 32]\n", "[1, 2, 5, 7, 8, 10, 17, 21, 30, 31]\n", "[1, 2, 4, 6, 8, 9, 19, 20, 29, 32]\n", "[1, 3, 4, 8, 10, 14, 17, 18, 19, 22]\n", "[1, 2, 5, 7, 9, 13, 17, 19, 20, 22]\n", "[1, 3, 5, 7, 9, 11, 12, 14, 26, 27]\n", "[1, 3, 5, 6, 10, 14, 18, 19, 20, 21]\n", "[1, 3, 4, 9, 11, 12, 14, 18, 26, 30]\n", "[1, 3, 4, 8, 9, 11, 12, 17, 27, 29]\n", "[1, 3, 4, 9, 11, 13, 16, 19, 20, 21]\n", "[1, 2, 4, 6, 8, 9, 19, 20, 30, 33]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 40]\n", "[1, 3, 4, 8, 10, 14, 18, 21, 23, 30]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22, 33]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22, 38]\n", "[1, 3, 4, 9, 10, 12, 13, 26, 28, 33]\n", "[1, 3, 5, 6, 13, 14, 18, 20, 21, 24]\n", "[1, 2, 5, 8, 10, 12, 17, 20, 21, 34]\n", "[1, 3, 5, 7, 9, 11, 12, 14, 27, 28]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20, 34]\n", "[1, 3, 4, 5, 7, 13, 15, 16, 20, 34]\n", "[1, 3, 5, 7, 9, 11, 12, 13, 27, 28]\n", "[1, 2, 5, 7, 8, 10, 13, 17, 27, 31]\n", "[1, 3, 4, 5, 8, 11, 15, 16, 24, 33]\n", "[1, 3, 4, 8, 10, 14, 16, 19, 20, 21]\n", "[1, 3, 4, 9, 10, 15, 17, 18, 19, 22]\n", "[1, 3, 4, 8, 9, 11, 12, 25, 27, 32]\n", "[1, 2, 5, 8, 9, 11, 13, 23, 27, 28]\n", "[1, 2, 5, 7, 11, 12, 14, 20, 28, 36]\n", "[1, 3, 4, 9, 11, 15, 16, 19, 20, 22]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 30, 37]\n", "[1, 3, 4, 8, 9, 11, 12, 25, 27, 29]\n", "[1, 2, 5, 6, 8, 9, 19, 21, 31, 33]\n", "[1, 2, 5, 7, 11, 12, 14, 19, 27, 35]\n", "[1, 2, 5, 6, 9, 10, 12, 13, 26, 28]\n", "[1, 3, 4, 6, 10, 15, 16, 23, 25, 33]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 29, 32]\n", "[1, 3, 5, 7, 8, 15, 16, 18, 20, 21]\n", "[1, 3, 4, 6, 8, 10, 12, 13, 27, 28]\n", "[1, 3, 5, 7, 8, 15, 17, 18, 20, 24]\n", "[1, 2, 4, 5, 9, 12, 13, 18, 28, 34]\n", "[1, 3, 5, 6, 13, 15, 17, 20, 23, 26]\n", "[1, 2, 4, 6, 8, 9, 19, 22, 28, 31]\n", "[1, 3, 4, 6, 10, 14, 16, 19, 20, 27]\n", "[1, 3, 5, 7, 8, 14, 17, 18, 19, 22]\n", "[1, 3, 5, 6, 12, 13, 17, 19, 20, 22]\n", "[1, 3, 4, 9, 11, 15, 17, 20, 24, 27]\n", "[1, 2, 5, 7, 11, 13, 16, 19, 20, 21]\n", "[1, 2, 4, 5, 10, 12, 17, 18, 20, 21]\n", "[1, 3, 5, 6, 11, 13, 15, 20, 23, 26]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 24, 28]\n", "[1, 2, 5, 7, 11, 15, 16, 17, 21, 24]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 37]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 20, 21]\n", "[1, 2, 4, 7, 8, 12, 14, 15, 24, 33]\n", "[1, 2, 4, 7, 9, 10, 15, 19, 26, 30]\n", "[1, 3, 4, 6, 11, 13, 18, 20, 24, 28]\n", "[1, 3, 5, 7, 9, 10, 19, 20, 30, 31]\n", "[1, 3, 5, 7, 8, 10, 19, 20, 31, 32]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22, 38]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26, 38]\n", "[1, 2, 5, 7, 11, 15, 16, 18, 23, 35]\n", "[1, 2, 5, 6, 8, 15, 17, 18, 22, 23]\n", "[1, 3, 4, 9, 10, 12, 13, 24, 26, 31]\n", "[1, 3, 5, 7, 8, 14, 18, 20, 21, 30]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 25, 30]\n", "[1, 3, 4, 9, 11, 13, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 31]\n", "CPU times: user 9h 56min 8s, sys: 57.9 s, total: 9h 57min 6s\n", "Wall time: 9h 56min 49s\n" ] } ], "source": [ "n = 40\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "42\n", "new smallest = 10\n", "[1, 3, 4, 9, 11, 16, 18, 19, 21, 22]\n", "[1, 3, 5, 6, 11, 12, 19, 21, 23, 36]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 32, 33]\n", "[1, 3, 4, 6, 10, 13, 15, 21, 29, 37]\n", "[1, 2, 4, 5, 6, 7, 11, 19, 27, 35]\n", "[1, 3, 5, 7, 8, 12, 14, 18, 26, 34]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 21, 22]\n", "[1, 3, 4, 9, 10, 12, 13, 24, 29, 31]\n", "[1, 3, 4, 8, 10, 14, 19, 20, 22, 27]\n", "[1, 2, 5, 8, 10, 13, 16, 19, 20, 21]\n", "[1, 3, 4, 9, 10, 13, 14, 21, 27, 29]\n", "[1, 2, 5, 6, 8, 9, 19, 21, 30, 32]\n", "[1, 3, 5, 7, 9, 10, 19, 20, 31, 32]\n", "[1, 3, 4, 8, 10, 11, 13, 24, 28, 29]\n", "[1, 2, 5, 7, 11, 13, 17, 18, 20, 21]\n", "[1, 3, 4, 7, 8, 10, 19, 21, 29, 31]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 25, 33]\n", "[1, 3, 4, 6, 10, 12, 17, 18, 20, 21]\n", "[1, 3, 5, 6, 12, 13, 18, 19, 27, 29]\n", "[1, 3, 4, 9, 10, 12, 13, 23, 28, 30]\n", "[1, 3, 5, 6, 13, 15, 16, 19, 20, 21]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 20, 24]\n", "[1, 3, 5, 6, 12, 14, 15, 19, 20, 36]\n", "[1, 2, 5, 7, 10, 13, 16, 19, 20, 21]\n", "[1, 2, 4, 5, 8, 10, 17, 20, 21, 31]\n", "[1, 3, 4, 9, 11, 12, 16, 26, 30, 36]\n", "[1, 3, 4, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 34]\n", "[1, 2, 5, 6, 9, 11, 19, 21, 28, 30]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 32, 33]\n", "[1, 3, 5, 7, 8, 10, 18, 21, 27, 33]\n", "[1, 3, 4, 9, 11, 15, 17, 20, 21, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 22]\n", "[1, 2, 4, 5, 6, 13, 16, 23, 29, 36]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 21, 28]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20, 24]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 29, 30]\n", "[1, 3, 4, 9, 11, 13, 18, 20, 21, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 38]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 21, 24]\n", "[1, 3, 5, 6, 9, 13, 17, 19, 20, 22]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 21, 32]\n", "[1, 2, 5, 7, 8, 11, 17, 20, 21, 28]\n", "[1, 3, 4, 5, 6, 9, 16, 23, 30, 37]\n", "[1, 2, 5, 8, 10, 11, 13, 17, 27, 31]\n", "[1, 3, 4, 9, 10, 12, 13, 22, 27, 29]\n", "[1, 2, 5, 7, 11, 15, 18, 19, 20, 21]\n", "[1, 2, 3, 5, 9, 13, 17, 19, 20, 22]\n", "[1, 2, 5, 8, 11, 13, 17, 19, 22, 29]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 28, 29]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 26, 30]\n", "[1, 3, 4, 7, 8, 9, 19, 21, 31, 33]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 21, 30]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22, 36]\n", "[1, 3, 4, 8, 9, 11, 16, 20, 26, 30]\n", "[1, 2, 4, 5, 10, 13, 14, 21, 28, 35]\n", "[1, 3, 5, 6, 13, 14, 16, 18, 20, 21]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 22, 36]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 35]\n", "[1, 2, 5, 8, 11, 14, 17, 20, 22, 24]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 31]\n", "[1, 3, 5, 6, 12, 13, 18, 19, 21, 23]\n", "[1, 3, 4, 9, 10, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 8, 10, 12, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 10, 15, 17, 20, 21, 24]\n", "[1, 2, 5, 8, 11, 12, 13, 26, 28, 30]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 30, 31]\n", "[1, 3, 4, 8, 10, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 24, 26]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22, 34]\n", "[1, 3, 4, 9, 11, 15, 16, 17, 20, 38]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 21, 22]\n", "[1, 3, 5, 6, 13, 14, 18, 21, 24, 27]\n", "[1, 2, 5, 8, 11, 12, 13, 25, 27, 29]\n", "[1, 3, 5, 6, 12, 13, 19, 20, 22, 24]\n", "[1, 3, 4, 9, 11, 13, 16, 20, 25, 26]\n", "[1, 3, 4, 9, 11, 16, 20, 26, 27, 30]\n", "[1, 3, 4, 5, 8, 11, 15, 16, 25, 34]\n", "[1, 3, 5, 6, 13, 15, 16, 19, 20, 22]\n", "[1, 3, 5, 6, 13, 14, 16, 20, 21, 25]\n", "[1, 3, 5, 6, 13, 14, 21, 23, 25, 27]\n", "[1, 2, 5, 7, 11, 15, 17, 18, 20, 21]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 33]\n", "[1, 3, 4, 8, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 4, 9, 10, 15, 16, 21, 23, 25]\n", "[1, 3, 5, 6, 7, 10, 12, 20, 28, 36]\n", "[1, 2, 5, 7, 8, 10, 17, 21, 30, 31]\n", "[1, 3, 4, 7, 8, 9, 19, 21, 30, 32]\n", "[1, 2, 5, 7, 9, 13, 17, 19, 20, 22]\n", "[1, 3, 4, 9, 11, 16, 19, 21, 25, 30]\n", "[1, 3, 4, 6, 11, 12, 17, 18, 20, 21]\n", "[1, 3, 5, 6, 10, 14, 18, 19, 20, 21]\n", "[1, 3, 4, 9, 11, 12, 14, 18, 26, 30]\n", "[1, 3, 4, 9, 10, 12, 13, 21, 26, 28]\n", "[1, 3, 4, 6, 11, 13, 18, 20, 21, 24]\n", "[1, 3, 4, 9, 11, 13, 16, 19, 20, 21]\n", "[1, 2, 5, 8, 11, 14, 16, 19, 20, 21]\n", "[1, 2, 4, 6, 8, 9, 19, 20, 30, 33]\n", "[1, 2, 5, 8, 11, 13, 16, 19, 20, 21]\n", "[1, 3, 4, 8, 10, 14, 18, 21, 23, 30]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22, 33]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 25]\n", "[1, 2, 5, 7, 10, 13, 15, 19, 26, 35]\n", "[1, 3, 5, 7, 8, 10, 12, 20, 26, 34]\n", "[1, 3, 4, 9, 10, 12, 13, 26, 28, 33]\n", "[1, 3, 4, 8, 10, 15, 17, 18, 21, 37]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 31, 32]\n", "[1, 2, 4, 7, 10, 13, 16, 19, 20, 21]\n", "[1, 2, 5, 8, 11, 12, 13, 27, 29, 31]\n", "[1, 3, 5, 6, 8, 15, 16, 20, 21, 33]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 31, 32]\n", "[1, 3, 5, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 5, 6, 13, 14, 18, 20, 21, 24]\n", "[1, 3, 4, 9, 11, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 8, 10, 12, 17, 20, 21, 34]\n", "[1, 3, 4, 9, 10, 12, 13, 26, 28, 30]\n", "[1, 3, 5, 7, 9, 11, 12, 14, 27, 28]\n", "[1, 3, 4, 5, 10, 12, 17, 18, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 18, 21, 28, 31]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 30, 31]\n", "[1, 3, 4, 8, 9, 10, 14, 17, 29, 32]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 22, 26]\n", "[1, 3, 4, 5, 11, 12, 18, 19, 21, 23]\n", "[1, 2, 5, 8, 10, 14, 17, 20, 21, 31]\n", "[1, 3, 4, 8, 10, 15, 17, 18, 20, 21]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 22, 24]\n", "[1, 3, 4, 8, 10, 14, 16, 19, 20, 21]\n", "[1, 2, 5, 7, 11, 12, 14, 20, 28, 36]\n", "[1, 3, 5, 6, 11, 12, 18, 19, 21, 23]\n", "[1, 3, 4, 9, 11, 15, 16, 19, 20, 22]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 30, 37]\n", "[1, 2, 5, 6, 8, 9, 19, 21, 31, 33]\n", "[1, 3, 4, 9, 10, 11, 12, 16, 26, 30]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 38]\n", "[1, 3, 5, 7, 8, 16, 18, 20, 21, 30]\n", "[1, 3, 4, 8, 10, 11, 13, 25, 27, 31]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 20, 21]\n", "[1, 3, 5, 6, 12, 14, 15, 19, 20, 22]\n", "[1, 3, 4, 7, 8, 10, 19, 21, 29, 34]\n", "[1, 2, 5, 7, 11, 13, 17, 19, 20, 22]\n", "[1, 3, 4, 6, 10, 14, 18, 19, 20, 21]\n", "[1, 3, 5, 6, 11, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 7, 11, 12, 14, 19, 27, 35]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 29, 32]\n", "[1, 3, 5, 7, 8, 15, 16, 18, 20, 21]\n", "[1, 3, 5, 7, 8, 15, 17, 18, 20, 24]\n", "[1, 3, 4, 9, 10, 12, 13, 25, 27, 29]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 27, 28]\n", "[1, 3, 5, 6, 12, 13, 17, 19, 20, 22]\n", "[1, 3, 5, 6, 13, 15, 17, 20, 21, 26]\n", "[1, 2, 5, 8, 11, 13, 15, 25, 26, 27]\n", "[1, 3, 4, 9, 11, 16, 18, 19, 20, 22]\n", "[1, 3, 4, 6, 9, 10, 17, 20, 22, 32]\n", "[1, 2, 4, 5, 11, 12, 18, 19, 21, 23]\n", "[1, 2, 4, 5, 11, 14, 15, 19, 27, 35]\n", "[1, 3, 4, 9, 11, 15, 17, 20, 24, 27]\n", "[1, 3, 4, 8, 10, 14, 18, 19, 20, 21]\n", "[1, 3, 4, 8, 10, 11, 14, 19, 26, 31]\n", "[1, 3, 4, 9, 10, 15, 17, 18, 20, 21]\n", "[1, 2, 5, 7, 11, 15, 19, 20, 21, 22]\n", "[1, 2, 5, 7, 11, 13, 16, 19, 20, 21]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 21, 35]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 33, 34]\n", "[1, 2, 4, 5, 10, 12, 17, 18, 20, 21]\n", "[1, 2, 5, 8, 10, 14, 16, 19, 20, 21]\n", "[1, 2, 5, 7, 11, 15, 16, 17, 21, 24]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 37]\n", "[1, 3, 4, 9, 10, 15, 16, 18, 20, 21]\n", "[1, 3, 4, 7, 8, 11, 12, 13, 27, 29]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 23, 24]\n", "[1, 3, 4, 6, 11, 13, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 11, 12, 16, 24, 26, 30]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 28, 29]\n", "[1, 3, 4, 6, 11, 13, 18, 20, 24, 28]\n", "[1, 3, 5, 7, 8, 10, 19, 20, 31, 32]\n", "[1, 3, 4, 9, 11, 15, 17, 18, 22, 38]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26, 38]\n", "[1, 2, 5, 7, 11, 15, 16, 18, 23, 35]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 20, 24]\n", "[1, 2, 5, 7, 11, 15, 17, 19, 20, 22]\n", "[1, 2, 5, 8, 11, 14, 17, 20, 21, 22]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 32, 38]\n", "[1, 3, 4, 9, 11, 16, 17, 19, 20, 25]\n", "[1, 2, 5, 6, 9, 10, 12, 13, 27, 29]\n", "[1, 2, 4, 6, 9, 13, 15, 19, 27, 35]\n", "[1, 2, 5, 8, 11, 12, 13, 27, 28, 29]\n", "[1, 3, 4, 6, 11, 13, 18, 19, 21, 22]\n", "[1, 3, 4, 6, 10, 14, 19, 20, 27, 32]\n", "[1, 3, 5, 6, 13, 15, 16, 18, 24, 35]\n", "[1, 3, 5, 7, 8, 14, 18, 20, 21, 30]\n", "[1, 3, 5, 6, 8, 12, 19, 20, 29, 30]\n", "[1, 3, 4, 9, 11, 16, 17, 18, 20, 21]\n", "[1, 3, 4, 6, 10, 14, 16, 19, 20, 21]\n", "[1, 3, 5, 6, 8, 15, 16, 18, 20, 21]\n", "[1, 2, 5, 8, 11, 14, 17, 19, 20, 21]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 29, 30]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 23]\n", "[1, 3, 4, 7, 9, 15, 17, 18, 20, 24]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 25, 30]\n", "[1, 2, 5, 6, 8, 15, 16, 18, 20, 21]\n", "[1, 3, 4, 9, 10, 12, 13, 25, 27, 32]\n", "[1, 3, 4, 9, 11, 13, 17, 18, 20, 21]\n", "[1, 3, 4, 9, 11, 16, 18, 19, 22, 23]\n", "[1, 3, 4, 9, 11, 12, 16, 20, 26, 30]\n", "[1, 3, 4, 7, 9, 15, 17, 20, 24, 35]\n", "CPU times: user 20 ms, sys: 0 ns, total: 20 ms\n", "Wall time: 20.5 ms\n" ] } ], "source": [ "n = 41\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "43\n", "new smallest = 10\n", "[1, 3, 4, 9, 11, 16, 18, 19, 21, 22]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 21, 32]\n", "[1, 3, 5, 7, 9, 10, 20, 21, 32, 33]\n", "[1, 3, 4, 6, 10, 13, 15, 21, 29, 37]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 21, 22]\n", "[1, 3, 4, 5, 6, 9, 16, 23, 30, 37]\n", "[1, 3, 5, 6, 13, 15, 17, 20, 21, 26]\n", "[1, 3, 4, 9, 10, 12, 13, 24, 29, 31]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 25]\n", "[1, 3, 4, 9, 10, 13, 14, 21, 27, 29]\n", "[1, 3, 4, 9, 10, 12, 13, 26, 28, 33]\n", "[1, 2, 5, 7, 11, 15, 19, 20, 21, 22]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 33, 34]\n", "[1, 2, 5, 8, 11, 12, 13, 27, 29, 31]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 22, 36]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 31, 32]\n", "[1, 3, 5, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 5, 6, 13, 15, 17, 18, 24, 37]\n", "[1, 3, 4, 9, 10, 12, 13, 26, 28, 30]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 30, 31]\n", "[1, 3, 4, 9, 10, 12, 13, 23, 28, 30]\n", "[1, 3, 4, 8, 9, 10, 14, 17, 29, 32]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 28, 29]\n", "[1, 2, 5, 8, 11, 12, 13, 26, 28, 30]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 24, 26]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22, 34]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 22, 24]\n", "[1, 3, 4, 9, 11, 16, 17, 20, 26, 38]\n", "[1, 3, 4, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 21, 22]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 34]\n", "[1, 2, 5, 8, 11, 14, 17, 20, 21, 22]\n", "[1, 3, 4, 5, 8, 14, 20, 26, 32, 38]\n", "[1, 2, 5, 7, 11, 12, 14, 20, 28, 36]\n", "[1, 3, 4, 6, 11, 13, 18, 19, 21, 22]\n", "[1, 3, 5, 6, 12, 13, 19, 20, 22, 24]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 32, 33]\n", "[1, 3, 4, 9, 11, 16, 20, 26, 27, 30]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 30, 37]\n", "[1, 3, 4, 8, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 5, 7, 8, 10, 18, 21, 27, 33]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 38]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 23]\n", "[1, 3, 5, 6, 7, 10, 12, 20, 28, 36]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 21, 28]\n", "[1, 3, 5, 6, 13, 15, 17, 24, 25, 30]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 29, 30]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 31]\n", "CPU times: user 16 ms, sys: 0 ns, total: 16 ms\n", "Wall time: 13.6 ms\n" ] } ], "source": [ "n = 42\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "44\n", "new smallest = 10\n", "[1, 3, 4, 9, 11, 16, 18, 19, 21, 22]\n", "[1, 3, 4, 6, 10, 13, 15, 21, 29, 37]\n", "[1, 3, 4, 9, 11, 13, 18, 19, 21, 22]\n", "[1, 3, 4, 9, 10, 12, 13, 24, 29, 31]\n", "[1, 2, 5, 7, 11, 15, 19, 20, 21, 22]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 33, 34]\n", "[1, 2, 5, 8, 11, 12, 13, 27, 29, 31]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 22, 36]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 31, 32]\n", "[1, 3, 5, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 30, 31]\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22, 34]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 22, 24]\n", "[1, 3, 4, 6, 10, 14, 18, 20, 21, 23]\n", "[1, 2, 5, 7, 11, 15, 17, 20, 21, 22]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 34]\n", "[1, 2, 5, 8, 11, 14, 17, 20, 21, 22]\n", "[1, 3, 4, 6, 11, 13, 18, 19, 21, 22]\n", "[1, 3, 5, 7, 9, 10, 21, 22, 32, 33]\n", "[1, 3, 5, 6, 12, 13, 19, 20, 22, 24]\n", "[1, 3, 4, 8, 10, 14, 18, 20, 21, 23]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 38]\n", "[1, 3, 5, 6, 13, 15, 16, 20, 21, 23]\n", "[1, 3, 5, 7, 9, 11, 13, 14, 29, 30]\n", "[1, 3, 4, 9, 10, 12, 13, 27, 29, 31]\n", "CPU times: user 8 ms, sys: 0 ns, total: 8 ms\n", "Wall time: 5.12 ms\n" ] } ], "source": [ "n = 43\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "45\n", "new smallest = 11\n", "new smallest = 10\n", "[1, 3, 4, 9, 11, 16, 19, 20, 22, 34]\n", "[1, 2, 5, 7, 11, 15, 19, 21, 22, 24]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 6.3 ms\n" ] } ], "source": [ "n = 44\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "46\n", "new smallest = 11\n", "new smallest = 10\n", "[1, 2, 5, 7, 11, 15, 19, 21, 22, 24]\n", "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n", "Wall time: 726 µs\n" ] } ], "source": [ "n = 45\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n = 46\n", "print(n+1)\n", "%time upgrade(cmap, n, n+1)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pickle.dump(cmap, open( \"coins.p\", \"wb\" ) )" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{10: <__main__.Combinator at 0x7fd57c8802b0>,\n", " 11: <__main__.Combinator at 0x7fd57c880390>,\n", " 12: <__main__.Combinator at 0x7fd57c8803c8>,\n", " 13: <__main__.Combinator at 0x7fd57c880400>,\n", " 14: <__main__.Combinator at 0x7fd57c880438>,\n", " 15: <__main__.Combinator at 0x7fd57c880470>,\n", " 16: <__main__.Combinator at 0x7fd57c8804a8>,\n", " 17: <__main__.Combinator at 0x7fd57c8804e0>,\n", " 18: <__main__.Combinator at 0x7fd57c880518>,\n", " 19: <__main__.Combinator at 0x7fd57c880550>,\n", " 20: <__main__.Combinator at 0x7fd57c880588>,\n", " 21: <__main__.Combinator at 0x7fd57c8805c0>,\n", " 22: <__main__.Combinator at 0x7fd57c880630>,\n", " 23: <__main__.Combinator at 0x7fd57c880668>,\n", " 24: <__main__.Combinator at 0x7fd57c8806a0>,\n", " 25: <__main__.Combinator at 0x7fd57c8806d8>,\n", " 26: <__main__.Combinator at 0x7fd57c880128>,\n", " 27: <__main__.Combinator at 0x7fd57c880710>,\n", " 28: <__main__.Combinator at 0x7fd57c880748>,\n", " 29: <__main__.Combinator at 0x7fd57c880780>,\n", " 30: <__main__.Combinator at 0x7fd57c8807b8>,\n", " 31: <__main__.Combinator at 0x7fd57c8807f0>,\n", " 32: <__main__.Combinator at 0x7fd57c880860>,\n", " 33: <__main__.Combinator at 0x7fd57c880898>,\n", " 34: <__main__.Combinator at 0x7fd57c8808d0>,\n", " 35: <__main__.Combinator at 0x7fd57c880940>,\n", " 36: <__main__.Combinator at 0x7fd57c880978>,\n", " 37: <__main__.Combinator at 0x7fd57c8809b0>,\n", " 38: <__main__.Combinator at 0x7fd57c8809e8>,\n", " 39: <__main__.Combinator at 0x7fd57c880a20>,\n", " 40: <__main__.Combinator at 0x7fd57c880a58>,\n", " 41: <__main__.Combinator at 0x7fd57c880a90>,\n", " 42: <__main__.Combinator at 0x7fd5776aeb00>,\n", " 43: <__main__.Combinator at 0x7fd5776ae9b0>,\n", " 44: <__main__.Combinator at 0x7fd5776aec50>,\n", " 45: <__main__.Combinator at 0x7fd57c86cb38>,\n", " 46: <__main__.Combinator at 0x7fd57c86cc88>,\n", " 47: <__main__.Combinator at 0x7fd57c86cd68>}" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pickle.load( open( \"coins.p\", \"rb\" ) )" ] }, { "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }