euler-020-factorial-digit-sum-20130808.ipynb

{
 "metadata": {
  "name": "euler-020-factorial-digit-sum-20130808"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "n! means n \u00d7 (n \u2212 1) \u00d7 ... \u00d7 3 \u00d7 2 \u00d7 1  \n",
      "\n",
      "For example, 10! = 10 \u00d7 9 \u00d7 ... \u00d7 3 \u00d7 2 \u00d7 1 = 3628800,\n",
      "and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.  \n",
      "\n",
      "Find the sum of the digits in the number 100!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import operator"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def foo(n):\n",
      "    return reduce((lambda x, y: int(x) + int(y)), str(reduce(operator.mul, range(1, 100 + 1))))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 100\n",
      "%timeit foo(n)\n",
      "foo(n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 240 us per loop\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "648"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def foo(n):\n",
      "    return sum(map(int, str(reduce(operator.mul, range(1, 100 + 1)))))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 100\n",
      "%timeit foo(n)\n",
      "foo(n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 160 us per loop\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "648"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}