{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#voc = [1, 1, 1, 1, 1, 1, 1, 1] ## complete tree\n",
      "voc = [4, 3, 2, 1] ## single path tree\n",
      "voc_size = len(voc)\n",
      "\n",
      "count = voc + [1e5 for _ in range(voc_size + 1)]\n",
      "binary = [0 for _ in range(voc_size * 2 + 1)]\n",
      "parent_node = [0 for _ in range(voc_size * 2 + 1)]\n",
      "print count"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[4, 3, 2, 1, 100000.0, 100000.0, 100000.0, 100000.0, 100000.0]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pos1, pos2 = voc_size - 1, voc_size\n",
      "for i in range(0, voc_size-1):\n",
      "    if pos1 >= 0:\n",
      "        if count[pos1] < count[pos2]:\n",
      "            min1i = pos1\n",
      "            pos1 -= 1\n",
      "        else:\n",
      "            min1i = pos2\n",
      "            pos2 += 1\n",
      "    else:\n",
      "        min1i = pos2\n",
      "        pos2 += 1\n",
      "        \n",
      "    if pos1 >= 0:\n",
      "        if count[pos1] < count[pos2]:\n",
      "            min2i = pos1\n",
      "            pos1 -= 1\n",
      "        else:\n",
      "            min2i = pos2\n",
      "            pos2 += 1\n",
      "    else:\n",
      "        min2i = pos2\n",
      "        pos2 += 1\n",
      "    count[voc_size + i] = count[min1i] + count[min2i]\n",
      "    parent_node[min1i] = voc_size + i\n",
      "    parent_node[min2i] = voc_size + i\n",
      "    ## implicitly binary[min1i] = 0\n",
      "    binary[min2i] = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print count\n",
      "print binary"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[4, 3, 2, 1, 3, 6, 10, 100000.0, 100000.0]\n",
        "[0, 1, 1, 0, 0, 1, 0, 0, 0]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*So it proves that only 2 * voc_size - 1 nodes will be needed to construct a tree, even the tree is complete*"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "point = [0 for _ in range(40)]\n",
      "code = [0 for _ in range(40)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for a in range(voc_size):\n",
      "    b = a\n",
      "    i = 0\n",
      "    while True:\n",
      "        code[i] = binary[b]\n",
      "        point[i] = b\n",
      "        i += 1\n",
      "        b = parent_node[b]\n",
      "        if (b == voc_size * 2 - 2):\n",
      "            break"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print code\n",
      "print point"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
        "[3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}