{
 "metadata": {
  "name": "02-coinflips"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "See http://ivory.idyll.org/blog/2013-pycon-awesome-big-data-algorithms-talk.html"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Flip a lot of coins;\n",
      "# Use the distribution of longest run of zeros to infer how many\n",
      "# coinflips were done, ex post facto.\n",
      "import random\n",
      "def generate_coinflips(num):\n",
      "    return [ random.choice([0,1]) for i in range(num) ]\n",
      "\n",
      "def longest_run_zero(x):\n",
      "    i = 0\n",
      "    count = 0\n",
      "    max_count = 0\n",
      "    while i < len(x):\n",
      "        if x[i] == 0:\n",
      "            count += 1\n",
      "        else:\n",
      "            if count > max_count:\n",
      "                max_count = count\n",
      "            count = 0\n",
      "        i += 1\n",
      "        \n",
      "    return max_count"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def longest_run_mc(runsize, num):\n",
      "    z = []\n",
      "    for i in range(num):\n",
      "        x = generate_coinflips(runsize)\n",
      "        count = longest_run_zero(x)\n",
      "        z.append(count)\n",
      "        \n",
      "    return z"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# do 100 runs of 1000 coinflips, and plot the distribution\n",
      "d = longest_run_mc(100, 1000)\n",
      "hist(d, bins=max(d), range=(0, max(d)))\n",
      "\n",
      "# we expect a peak right around...\n",
      "print math.log(100, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "6.64385618977\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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sca/vcVJJ5XvYunWrioqKdPToUe3cuVOBQEB/+9vf9NJLL+mNN94YvlGPJ6U/Bkgfj8cj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\nABjq/wDPZlPBG+ezbQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b82c510>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# if we do 500 coinflips, the peak shifts right, to... \n",
      "d = longest_run_mc(500, 1000)\n",
      "hist(d, bins=max(d), range=(0, max(d)))\n",
      "print math.log(500, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "8.96578428466\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b886250>"
       ]
      }
     ],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}