report.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def formatSums(weights):\n",
    "    sums = [ weights[0] ]\n",
    "    for i in xrange(1, len(weights)):\n",
    "        sums.append(sums[-1] + weights[i])\n",
    "    return sums\n",
    "\n",
    "def binSearch(sums, l, r, S):\n",
    "    start = l;\n",
    "    if start > 0:\n",
    "        S += sums[start - 1]\n",
    "    while True:\n",
    "        mid = l + (r - l) / 2\n",
    "        if sums[mid] > S:\n",
    "            if l >= mid:\n",
    "                return start\n",
    "            r = mid\n",
    "        else:\n",
    "            if mid == r - 1 or sums[mid + 1] > S:\n",
    "                return mid + 1\n",
    "            l = mid\n",
    "            \n",
    "def bucketsCount(sums, start, end, S):\n",
    "    partsCount = 0\n",
    "    while start < end:\n",
    "        pos = binSearch(sums, start, end, S)\n",
    "        if pos == start:\n",
    "            return -1\n",
    "        start = pos\n",
    "        partsCount += 1\n",
    "    return partsCount\n",
    "\n",
    "def buckets(sums, start, end, S, parts):\n",
    "    while start < end:\n",
    "        pos = binSearch(sums, start, end, S)\n",
    "        parts.append(pos - start)\n",
    "        start = pos\n",
    "\n",
    "def partition(weights, count):\n",
    "    size = len(weights)\n",
    "    \n",
    "    i = 0\n",
    "    j = 0\n",
    "    iB = 0\n",
    "    jB = 0\n",
    "    SB = 2 * sum(weights)\n",
    "\n",
    "    sums = formatSums(weights)\n",
    "\n",
    "    while i < size and j < size:\n",
    "        S = sums[j]\n",
    "        if i > 0:\n",
    "            S -= sums[i - 1]\n",
    "        leftParts = bucketsCount(sums, 0, i, S)\n",
    "        rigthParts = bucketsCount(sums, j + 1, size, S)\n",
    "        if leftParts < 0 or rigthParts < 0 or leftParts + rigthParts > count - 1:\n",
    "            j += 1\n",
    "        else:\n",
    "            if S < SB:\n",
    "                iB = i\n",
    "                jB = j\n",
    "                SB = S\n",
    "            i += 1\n",
    "            if i == j:\n",
    "                j += 1\n",
    "            \n",
    "    parts = []\n",
    "    buckets(sums, 0, iB, SB, parts);\n",
    "    parts.append(jB - iB + 1)\n",
    "    buckets(sums, jB + 1, size, SB, parts)\n",
    "\n",
    "    return parts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def printParts(weights, parts):\n",
    "    begin = 0\n",
    "    for part in parts:\n",
    "        weightsPart = weights[begin:begin+part]\n",
    "        begin += part\n",
    "        print weightsPart, '=', sum(weightsPart)\n",
    "\n",
    "def costParts(weights, parts):\n",
    "    SB = 0\n",
    "    begin = 0\n",
    "    for part in parts:\n",
    "        weightsPart = weights[begin:begin+part]\n",
    "        begin += part\n",
    "        S = sum(weightsPart)\n",
    "        if S > SB:\n",
    "            SB = S\n",
    "    return SB\n",
    "\n",
    "def predefinedSample(foo):\n",
    "    ww = [\n",
    "        3.0, 40.0, 17.0,\n",
    "        10.0, 5.0, 17.0, 11.0, 11.0, 3.0, 1.0, \n",
    "        15.0, 17.0, 23.0, 6.0, 5.0, \n",
    "        66, \n",
    "        1.0, 1.0, 1.0, 1.0, 1.0, 62 \n",
    "    ]\n",
    "    parts = foo(ww, 5)\n",
    "    printParts(ww, parts)\n",
    "    \n",
    "def randomSample(foo):\n",
    "    ww = np.random.rand(20)\n",
    "    parts = foo(ww, 5)\n",
    "    printParts(ww, parts)\n",
    "    \n",
    "def scoreAlg(alg, baseline = partition, repeats = 10000, size = 100, count = 5):\n",
    "    scores = []\n",
    "    for i in xrange(repeats):\n",
    "        weights = np.random.rand(size)\n",
    "        baseParts = baseline(weights, count)\n",
    "        parts = alg(weights, count)\n",
    "        score = (costParts(weights, parts) - costParts(weights, baseParts)) / costParts(weights, baseParts)\n",
    "        scores.append(score)\n",
    "    return sum(scores) / count                                                 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.0, 40.0, 17.0] = 60.0\n",
      "[10.0, 5.0, 17.0, 11.0, 11.0, 3.0] = 57.0\n",
      "[1.0, 15.0, 17.0, 23.0, 6.0, 5.0] = 67.0\n",
      "[66, 1.0] = 67.0\n",
      "[1.0, 1.0, 1.0, 1.0, 62] = 66.0\n"
     ]
    }
   ],
   "source": [
    "predefinedSample(partition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def allParts(size, count):\n",
    "    if count == 1:\n",
    "        return [[size]]\n",
    "    parts = []\n",
    "    for i in xrange(size + 1):\n",
    "        for nextParts in allParts(size - i, count - 1):\n",
    "            parts.append([i] + nextParts)\n",
    "    return parts\n",
    "\n",
    "def minimax(weights, count):\n",
    "    SB = sum(weights)\n",
    "    partsB = []\n",
    "    for parts in allParts(len(weights), count):\n",
    "        SSB = costParts(weights, parts)\n",
    "        if SSB < SB:\n",
    "            SB = SSB\n",
    "            partsB = parts\n",
    "    return partsB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.0, 40.0, 17.0] = 60.0\n",
      "[10.0, 5.0, 17.0, 11.0, 11.0, 3.0] = 57.0\n",
      "[1.0, 15.0, 17.0, 23.0, 6.0, 5.0] = 67.0\n",
      "[66] = 66\n",
      "[1.0, 1.0, 1.0, 1.0, 1.0, 62] = 67.0\n"
     ]
    }
   ],
   "source": [
    "predefinedSample(minimax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.63077597  0.41953264  0.16958134  0.39744007  0.8537009 ] = 2.47103091977\n",
      "[ 0.8993891   0.10200362  0.55251368  0.06772391  0.59323951] = 2.21486982565\n",
      "[ 0.74550317  0.35104538  0.05680016  0.08895249  0.51637994  0.29083562\n",
      "  0.87398526] = 2.92350201522\n",
      "[ 0.29500139  0.20228135  0.63769679  0.07619964  0.17620645  0.04761826\n",
      "  0.68169842  0.6781675 ] = 2.79486979163\n",
      "[ 0.78497384  0.48993738  0.26107191  0.7220026   0.57841041] = 2.8363961451\n"
     ]
    }
   ],
   "source": [
    "ww = np.random.rand(30)\n",
    "parts = partition(ww, 5)\n",
    "printParts(ww, parts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "count = 5\n",
    "size = 20\n",
    "repeats = 11\n",
    "\n",
    "fp = 0\n",
    "for i in xrange(repeats):\n",
    "    ww = np.random.rand(size)\n",
    "    partsP = partition(ww, count)\n",
    "    costP = costParts(ww, partsP)\n",
    "    partsB = minimax(ww, count)\n",
    "    costB = costParts(ww, partsB)\n",
    "    if costP != costB:\n",
    "        fp += 1\n",
    "        \n",
    "print fp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fastPartition(weights, count):\n",
    "    sums = formatSums(weights)\n",
    "    SB = sums[-1] / count\n",
    "    parts = [0]\n",
    "    \n",
    "    lastDelta = SB\n",
    "    S = SB\n",
    "    for i in xrange(len(sums)):\n",
    "        delta = abs(S - sums[i])\n",
    "        if delta < lastDelta:\n",
    "            parts[-1] += 1\n",
    "            lastDelta = delta\n",
    "        if sums[i] > S:\n",
    "            parts += [0]\n",
    "            S += SB\n",
    "            lastDelta = SB\n",
    "        #print S, sums[i], delta, parts\\\n",
    "    \n",
    "    #for k in xrange(count):\n",
    "    its = 0\n",
    "    SB = 0\n",
    "    while True:\n",
    "        newSB = costParts(weights, parts)\n",
    "        if abs(newSB - SB) < 0.000001:\n",
    "            break\n",
    "        its += 1\n",
    "        SB = newSB\n",
    "        S = 0\n",
    "        idx = 0\n",
    "        #printParts(weights, parts)\n",
    "        for i in xrange(count - 1):\n",
    "            s1 = sums[idx + parts[i] - 1] - S\n",
    "            s2 = sums[idx + parts[i] + parts[i + 1] - 1] - sums[idx + parts[i] - 1]\n",
    "            z1 = weights[idx + parts[i] - 1]\n",
    "            z2 = weights[idx + parts[i]]\n",
    "            #print i,\n",
    "            if s1 + z2 < SB and s1 < s2:\n",
    "                parts[i] += 1\n",
    "                parts[i + 1] -= 1\n",
    "                #print '+',\n",
    "            elif s2 + z1 < SB and s2 > s1:\n",
    "                parts[i + 1] += 1\n",
    "                parts[i] -= 1\n",
    "                #print '-',\n",
    "            S = sums[idx + parts[i] - 1]\n",
    "            idx += parts[i]\n",
    "            #print SB, s1, s2, z1, z2\n",
    "        #print\n",
    "    #print its\n",
    "    return parts, its\n",
    "    \n",
    "#predefinedSample(fastPartition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "count = 30\n",
    "size = 5000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.08 s, sys: 18 ms, total: 1.1 s\n",
      "Wall time: 1.15 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "84.008990703019151"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ww = np.random.rand(size)\n",
    "parts = %time partition(ww, count)\n",
    "costParts(ww, parts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 20s, sys: 1.47 s, total: 1min 21s\n",
      "Wall time: 1min 25s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[8, 8, 9, 7, 9, 9]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time minimax(ww, count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.21 ms, sys: 2.33 ms, total: 7.54 ms\n",
      "Wall time: 5.84 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "84.868263055803155"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ww = np.random.rand(size)\n",
    "parts, its = %time fastPartition(ww, count)\n",
    "costParts(ww, parts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50000 15.6096404744\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([   1.,   21.,    0.,   90.,    0.,  232.,    0.,  284.,    0.,\n",
       "         185.,  102.,    0.,   53.,    0.,   24.,    0.,    6.,    0.,\n",
       "           0.,    2.]),\n",
       " array([  1.  ,   1.55,   2.1 ,   2.65,   3.2 ,   3.75,   4.3 ,   4.85,\n",
       "          5.4 ,   5.95,   6.5 ,   7.05,   7.6 ,   8.15,   8.7 ,   9.25,\n",
       "          9.8 ,  10.35,  10.9 ,  11.45,  12.  ]),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b29c290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count = 30\n",
    "size = 50000\n",
    "itss = []\n",
    "for i in xrange(1000):\n",
    "    ww = np.random.rand(size)\n",
    "    parts, its = fastPartition(ww, count)\n",
    "    itss += [its]\n",
    "print size, log(size)/log(2)\n",
    "hist(itss, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "500 8.96578428466\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([   1.,    1.,   11.,   28.,   88.,  123.,  126.,  127.,  127.,\n",
       "          94.,   81.,   46.,   45.,   41.,   18.,   20.,    9.,    6.,\n",
       "           5.,    3.]),\n",
       " array([-0.03324634, -0.02547507, -0.01770381, -0.00993254, -0.00216127,\n",
       "         0.00560999,  0.01338126,  0.02115253,  0.0289238 ,  0.03669506,\n",
       "         0.04446633,  0.0522376 ,  0.06000886,  0.06778013,  0.0755514 ,\n",
       "         0.08332266,  0.09109393,  0.0988652 ,  0.10663647,  0.11440773,\n",
       "         0.122179  ]),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEACAYAAABbMHZzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b08f290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count = 30\n",
    "size = 500\n",
    "costs = []\n",
    "for i in xrange(1000):\n",
    "    ww = np.random.rand(size)\n",
    "    parts, its = fastPartition(ww, count)\n",
    "    bestParts = partition(ww, count)\n",
    "    c = costParts(ww, parts)\n",
    "    bestC = costParts(ww, bestParts)\n",
    "    costs += [(c - bestC) / bestC]\n",
    "print size, log(size)/log(2)\n",
    "hist(costs, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def histParts(weights, parts):\n",
    "    SB = 0\n",
    "    begin = 0\n",
    "    wParts = []\n",
    "    for part in parts:\n",
    "        weightsPart = weights[begin:begin+part]\n",
    "        begin += part\n",
    "        S = sum(weightsPart)\n",
    "        wParts += [weightsPart]\n",
    "    df = pd.DataFrame(wParts)\n",
    "    df.plot(kind='bar', stacked=True, legend=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+ + + + + - - + + + - - + + + + + - - - + +\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWcAAAD8CAYAAACrbmW5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZwDIEOEMABn6fzL55kIyG010AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1157ede10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histParts(ww, fastPartition(ww, count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWcAAAD8CAYAAACrbmW5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAADxhJREFUeJzt3VGMHdddx/Hf7zrYazc0QhR5Q6zEqAWhViA3AVdVkJgF\ntTEtah8QEi1VpT6UF6oEgSokePD1A6hPlEjwgppagFqKalEIKIVUrQeUoLZunNA0dtSKNmkS1asi\nRQnB2Tjx/HnY67W73fWdvTvnzJl7vx9pld274z3/yZ37u+eeOXPGESEAQFlGfRcAAPhhhDMAFIhw\nBoACEc4AUCDCGQAKRDgDQIFahbPtm2x/1vZ520/YflvqwgBgkd3Qcrt7JT0QEb9p+wZJBxLWBAAL\nz9MuQrH9ekmPRsQb85QEAGgzrPFTkv7H9knbZ23/le39qQsDgEXWpud8h6QvS3p7RHzN9p9LeiEi\njm/ajuvAAWCHIsJbPd6m5/yspGci4muTn09Jun2bRrJ8HT9+PFtbfXyxf8P+Yv+G+5V7365najhH\nxKqkZ2z/zOShX5V0rkWoAwBm1Ha2xt2SPmX7RyR9W9KH0pUEAGgVzhHxX5J+MXEtrVVV1XcJSbF/\nw8b+DVdJ+zb1hGDrP2RHV38LABaBbcUuTggCADIjnAGgQIQzABSIcAaAAhHOAFAgwhkACkQ4A0CB\nCGcAKBDhDAAFIpwBoECEMwAUiHAGgAIRzgBQoN7DeXn5sGxn+VpePtz37gJAK70vGWpbUq6lRj31\n1jAAkAtLhgLAwBDOAFAgwhkACkQ4A0CBCGcAKBDhDGwj5zRPpnpiM6bSJbS8fFirq09na+/gwdt0\n4cJT2dqbd3mPTYmpnovnelPpCOeUrfHiHjSeP6TGPGcAGBjCGQAKRDgDQIEIZwAo0A1tNrL9lKQX\nJDWSXo2IoymLwjAsH1rW6nOr2do7eMtBXXj2Qrb2gD61mq1h+9uS7oiI56+zDbM1Nrc252f7bUvj\nbM1JY/H8Ya50MVvDO9gWALBLbQM3JH3B9hnbH05ZEACg5ZizpDsj4nu2f0LrIX0+Ih7avNF4PN74\nvqoqVVXVSZEAMA/qulZd16223fEVgraPS/rfiPizTY8z5ry5tTkfs2TMufMWGXNeMLsac7Z9wPaN\nk+9fJ+mdkr7RbYkAgGu1GdY4KOlztmOy/aci4sG0ZQHAYpsazhHxHUlHMtQCICPmqZet7QlBAHNm\n9bnVrOcMVsf53gjmAXOXAaBAhDMAFIhwBoACEc4AUCDCGQAKRDgDQIEIZwAoEOEMAAUinAGgQFwh\nmNBodEBNs+WCU8naQ3d4/tCn3sM55wsg98HfNBfnur15x/OHPvU+rJHzgOTgBzAUvYczAOCHEc4A\nUCDCGcBcWl4+LNtZvpaXD3def+8nBAH0Y7R3pGbcZG0vp9XVp5XrHpCrq91PaiCcgQXVXGqU8wa2\nzaV80xLnAcMaAFAgwhkACkQ4A0CBCGcAKBDhDAAFIpwBoECO6GYqje2Y5W/ZeafXdLW/beTeNynv\n/u3Zt2cyHSuP0d6RLr9yOVt78/78re9fvvYkz/H+zbZvthURWx5ozHPGzJgnC6TDsAYAFIhwBoAC\nEc4AUKDW4Wx7ZPus7ftTFgQA2FnP+R5J51IVAgC4qlU42z4k6V2SPpG2HACA1L7n/HFJH1XeSZEA\nsLCmznO2/W5JqxHxmO1K0raTTcfj8cb3VVWpqqrdVwgAc6Kua9V13WrbqVcI2v5TSR+Q9Jqk/ZJ+\nVNI/RMQHN23HFYKbcIVZ5y3y/HVoMZ6/4V4huKPLt23/sqQ/iIj3bPE7wnkTXtydt8jz16HFeP6G\nG87McwaAArHwUUL0vDpvkeevQ4vx/NFzBgB0iFXpgAU1Gh1Q0+T7dDAaHcjW1jyg5wwsqKa5ONft\nDR3hDAAFIpwBoECEc0KjUd7/vbnbA5BO7ycER6ORmibPfehyh1fTNDp9Ol97Kyv57ucHIK3ewzln\ngBFe2ImcHYcr7QFX9B7OQKn45IM+8VYNAAUinAGgQIQzABSIcAaAAnFCEFhQ8z4bJefaISnWDSGc\ngQU177NRcq7lkaIthjUAoECEMwAUiHAGgAIRzgBQIMIZAApEOANAgQhnACgQ4QwABeIiFMyMuzcD\n6dBzxsy4ezOQDuEMAAUinAGgQIQzABRo6glB2/sk/YekvZPtT0XEidSFAcAimxrOEfGK7ZWIuGh7\nj6SHbX8+Ir6aoT4AWEitptJFxJXT5Psm/ya6KmBpaZRtndelJUZxAAxDq3C2PZL0iKQ3SvrLiDjT\nVQFra41OK8+K3ytrK1nauSLnG8+V9gDMh7Y950bSW22/XtI/2n5zRJzbvN14PN74vqoqVVXVUZnD\nlPONR8r/5gNgZ+q6Vl3Xrbbd0RWCEfGi7dOSjkm6bjgDQJ9y3iOx7f0RN3daT5zYfm5Fm9kab5D0\nakS8YHu/pHdI+lirSgCgJznvkZhi+LJNz/lmSX89GXceSfr7iHig80oAABvaTKV7XNLtGWoBAExw\neh8ACkQ4A0CBCGcAKBCL7QMLioukykY4AwuKi6TKRjgD26BniT4RzsA26FmiT7xVA0CBCGfMrO16\nAkNtD+gTwxqYWc61C6Q06xcApaIrAgAFIpwBoEC9D2ssjZa00uQ5S700WsrSDgDsVu/hvNasKdfA\n5doKU5UADEPv4Yzh4iINIB3CGTPjIg0gHcIZwFzK+ckuxac6whnYRs6T1VfaQ3dyfrJL8amOcAa2\nkfNktcQJa/wgzrAAQIHoOSfEx2IAsyKcE+JjMYBZMawBAAUinAGgQIQzABSIcAaAAnFCEFhQzCYq\nG+EMLChmE5Vt6rCG7UO2v2T7CduP2747R2EAsMja9Jxfk/T7EfGY7RslPWL7wYh4MnFtgzdaWlKT\nsbcwWuJjIzAvpoZzRFyQdGHy/Uu2z0u6RRLhPEWztqbI2J7X1jK2BiClHY052z4s6Yikr6QoBkA+\nfLIrW+twngxpnJJ0T0S8tNU24/F44/uqqlRV1S7LA5AKn+zyq+tadV232tYR058e2zdI+hdJn4+I\ne7fZJtr8rS3+Xb4zxisrmqXGWdnOe/BL2fcv651QlPf527N/v5qMgTJaWtLll1/O1h7HZ3dmPTZt\nKyK81e/a9pw/KencdsEMzCN6luhTm6l0d0r6bUm/YvtR22dtH0tfGgAsrjazNR6WtCdDLQCACdbW\nAIACEc4AUCDCGQAKRDgDQIEIZwAoEOEMAAUinAGgQCy2j5lxJw2ULOfxmeLYJJwxM+6kgZLlPD5T\nHJsMawBAgeg5Y2asBwyk03s453yB8+LuFqu2Aen0Hs45X+C8uAEMRavF9lv9oV0stp8tnJV/se95\nX8yc/euwPbF/Xcp5s4RZb5TQxWL7AObMgdFIbpqs7eU09E/lhDOwjXkPr4tNI40ztjfO9/9yHhDO\nwDYIL/Sp93DO2TvJ3TMBgFn1Hs45eyf0TAAMBV1JACgQ4QwABSKcAaBAhDMAFIhwBoAC9T5bY57N\n+0UMANIhnBPiIgYAs6KrBQAFIpwBoEBTw9n2fbZXbX89R0EAgHY955OS7kpdCADgqqnhHBEPSXo+\nQy0AgAnGnAGgQJ1OpRuPxxvfV1Wlqqq6/PMA0FqJyxHXda26rlttmyycAaBPJS5HvLnTeuLEiW23\nbRvOnnwBG7gCEiUb7R2pyXRh1mhv98fm1HC2/WlJlaQft/1dSccj4mTnlWBw5v0KyJwv7ivtoTvN\npUbKdIvX5lL3fdep4RwR7++8VWAAcr6419vjwymu4q0aAApEOANAgQhnACgQ4QwABSKcAaBALLaP\nmTHVDEiHcMbMmGoGpENXBAAKRDgDQIEIZwAoEGPOwILihG7ZCGdgQXFCt2y8lQFAgQhnAChQ78Ma\nQ18QGwBScEQ3Y062Y5a/ZVv5xr2srva3jT379kzG9fIY7R3p8iuXs7WX97mTcj9/7F/nLc7x/s22\nb7YVEVsOxvfec55nnHABMCs+5wNAgQhnACgQ4QwABSKcAaBAhDMAFIhwBoACEc4AUCDCGQAKRDgD\nQIEIZwAoEOEMAAVqFc62j9l+0vY3bf9h6qKmq/suILG67wISq/suILG67wISq/suIKG67wI2TA1n\n2yNJfyHpLklvkfQ+2z+burDrq/ttPrm67wISq/suILG67wISq/suIKG67wI2tOk5H5X0rYh4OiJe\nlfQZSe9NWxYALLY24XyLpGeu+fnZyWMAgESmLrZv+zck3RURvzP5+QOSjkbE3Zu2y7lqNwDMhd0s\ntv+cpFuv+fnQ5LFWDQAAdq7NsMYZSW+yfZvtvZJ+S9L9acsCgMU2teccEZdtf0TSg1oP8/si4nzy\nygBggXV2g1cAQHe4QhAACkQ4A0CB2szW6N3kisT36ur86uck3c/Y9zBMnr9bJH0lIl665vFjEfGv\n/VXWDdtHJUVEnLH9ZknHJD0ZEQ/0XFrnbP9NRHyw7zpSsP1LWr/o7hsR8WDv9ZQ+5jxZy+N9Wr8y\n8dnJw4e0PmvkMxHxsb5qS832hyLiZN917IbtuyX9rqTzko5Iuici/mnyu7MRcXuf9e2W7eOSfk3r\nHZ0vSHqbpNOS3iHp3yLiT3osb1dsb56VZUkrkr4kSRHxnuxFdcj2VyPi6OT7D2v9OP2cpHdK+ue+\ns2UI4fxNSW+ZXDp+7eN7JT0RET/dT2Xp2f5uRNw6fcty2X5c0tsj4iXbhyWdkvS3EXGv7Ucj4q29\nFrhLk/07ImmfpAuSDkXEi7b3a/2Tws/3WuAu2D4r6ZykT0gKrYfz32m9Y6SI+Pf+qtu9a48/22ck\nvSsivm/7dZK+HBE/12d9QxjWaCT9pKSnNz1+8+R3g2b769v9StLBnLUkMroylBERT9muJJ2yfZvW\n93HoXouIy5Iu2v7viHhRkiLiZdtDPz5/QdI9kv5Y0kcj4jHbLw89lK8xsv1jWj/3ticivi9JEfF/\ntl/rt7RhhPPvSfqi7W/p6hoft0p6k6SP9FZVdw5qfcW/5zc9bkn/mb+czq3aPhIRj0nSpAf965I+\nKanXnklHLtk+EBEXJd1x5UHbN2ngnYeIaCR93PZnJ/9d1TAyo62bJD2i9dda2L45Ir5n+0YV0HEo\nflhD2li29Kh+8ITgmUmPZdBs3yfpZEQ8tMXvPh0R7++hrM7YPqT13uWFLX53Z0Q83ENZnbG9LyJe\n2eLxN0i6OSIe76GsJGy/W9KdEfFHfdeSku0Dkg5GxHd6rWMI4QwAi4Z5zgBQIMIZAApEOANAgQhn\nACjQ/wNZvhe5erRn1AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115422190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histParts(ww, partition(ww, count))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}