doc/OpenAnalysis/02 - Sorting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sorting Analysis\n",
    "\n",
    "Consider a finite collection of orderable elements. Re-arranging that collection, so that the collection is completely ordered is called sorting. There are many techiniques to sort a collection. Following are some of the comparision based Sorting Algorithms.\n",
    "\n",
    "- Bubble Sort\n",
    "- Insertion Sort\n",
    "- Selection Sort\n",
    "- Merge Sort\n",
    "- Quick Sort\n",
    "- Heap Sort\n",
    "\n",
    "Before looking at the analysis part, we shall examine the Language in built methods to sorting\n",
    "\n",
    "## `sorted(collection,reverse = False[,key])`\n",
    "\n",
    "This function takes an iterable as argument, and returns it in sorted form based on `key`. If `key` is not given, sorting is done according to default comparision rules. Let's see the examples and understand the working of `sorted()`. If `reverse` is `True`, reversed collection is returned after sorting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = list(range(10))\n",
    "import random\n",
    "random.shuffle(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 7, 9, 0, 4, 5, 8, 2, 1, 3]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 4, 6, 0, 3, 9, 7, 1, 2, 8]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "y  = sorted(x,key = lambda x: math.sin(x))  # Sort elements of x in increasing order of their sines\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.9589242746631385,\n",
       " -0.7568024953079282,\n",
       " -0.27941549819892586,\n",
       " 0.0,\n",
       " 0.1411200080598672,\n",
       " 0.4121184852417566,\n",
       " 0.6569865987187891,\n",
       " 0.8414709848078965,\n",
       " 0.9092974268256817,\n",
       " 0.9893582466233818]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[math.sin(i) for i in y]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the elements of `sin(y)` are in increasing order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standard `import` statement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from openanalysis.sorting import SortingAlgorithm,SortAnalyzer\n",
    "import numpy as np   # for doing vstack()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`SortingAlgorithm` is the base class providing the standards to implement sorting algorithms, `SortAnalyzer` visualizes and analyses the algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `SortingAlgorithm` class\n",
    "\n",
    "Any sorting algorithm, which has to be implemented, has to be derived from this class. Now we shall see data members and member functions of this class.\n",
    "\n",
    "### Data Members\n",
    "\n",
    "- `name` -  Name of the Sorting Algorithm\n",
    "- `count` - Holds the number of basic operations performed\n",
    "- `hist_arr` - A 2D `numpy` array, holding the instances of array, as exchange is performed\n",
    "\n",
    "### Member Functions\n",
    "\n",
    "- `__init__(self, name):` - Initializes algorithm with a `name`\n",
    "- `sort(self, array, visualization):` - The base sorting function. Sets `count` to 0. `array` is 1D `numpy` array, `visualization` is a `bool` indicating whether `array` has to be `vstack`ed into `hist_arr`\n",
    "\n",
    "## An example .... Bubble Sort\n",
    "\n",
    "Now we shall implement the class `BubbleSort`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class BubbleSort(SortingAlgorithm):                        # Derived from SortingAlgorithm\n",
    "    def __init__(self):\n",
    "        SortingAlgorithm.__init__(self, \"Bubble Sort\")     # Initializing with name\n",
    "\n",
    "    def sort(self, array, visualization=False):            # MUST have this signature\n",
    "        SortingAlgorithm.sort(self, array, visualization)  # sets self.count to 0\n",
    "        for i in range(0, array.size):                     # Not len(array)\n",
    "            exch = False\n",
    "            for j in range(0, array.size - i - 1):\n",
    "                self.count += 1                            # Increment self.count after each basic operation\n",
    "                if array[j] > array[j + 1]:\n",
    "                    array[j], array[j + 1] = array[j + 1], array[j]\n",
    "                    exch = True\n",
    "                if visualization:\n",
    "                    self.hist_array = np.vstack([self.hist_array, array]) # Save the current state to hist_array\n",
    "            if not exch:\n",
    "                break\n",
    "        if visualization:\n",
    "            self.hist_array = np.vstack([self.hist_array, array])  # Save the final state to hist_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `SortAnalyzer` class\n",
    "\n",
    "This class provides the visualization and analysis methods. Let's see its methods in detail\n",
    "\n",
    "- `__init__(self, sorter):` Initializes visualizer with a Sorting Algorithm. \n",
    "    - `sorter` is a class, which is derived from `SortingAlgorithm`\n",
    "    \n",
    "    \n",
    "- `visualize(self, num=100, save=False):` Visualizes the given algorithm with a randomly shuffled array.\n",
    "    - `num` size of randomly shuffled array\n",
    "    - `save` is `True` means animation is saved in `output/`\n",
    "    \n",
    "    \n",
    "- `analyze(self, maxpts=1000):`\n",
    "    - Plots the running time of sorting algorithm by sorting for 3 cases\n",
    "    - Already Sorted array, reverse sorted array and Shuffled array\n",
    "    - Analysis is done  by inputting randomly shuffled integer arrays with size staring\n",
    "      from 100, and varying upto `maxpts` in the steps of 100, and counting the number of\n",
    "      basic operations\n",
    "    - `maxpts` - Upper bound on size of elements chosen for analysing efficiency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bubble_visualizer = SortVisualizer(BubbleSort)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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C+ZkqwgNKmsxsoiD+yOkhpzIQpq7pSie3URV36slcs7m8nUkyW/dFis0UzuvCmfV3mDKr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\nZW5ndGggOTAgPj4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    "bubble_visualizer.efficiency()"
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    "As you can see in the above plot, `BubbleSort` takes $\\mathcal{O}(n)$ time on best case and $\\mathcal{O}(n^2)$ time on both avarage and worst cases\n",
    "\n",
    "\n",
    "You can call the `visualize` function as shown below and see the 'mp4' file saved at `output/` folder\n",
    "\n",
    "```python\n",
    "    bubble_visualizer.visualize(save=True)\n",
    "```   \n",
    "\n",
    "\n",
    "## `compare(algs)`\n",
    "\n",
    "`algs` is a list of classes derived from `SortingAlgorithm`. It performs tests and plots the bar graph comparing the number of basic operations performed by each algorithm.\n"
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   "source": [
    "## Why use a `class` if sorting could be done using a function\n",
    "\n",
    "We have just seen how `BubbleSort` is implemented. Every sorting algorithm is not as simple as `BubbleSort`. `QuickSort` and `MergeSort` needs several auxiliary methods to work with. If they are scattered throughout the code, they decrease the readability. So it is better to pack everything in a class.\n",
    "\n",
    "## Example File\n",
    "\n",
    "You can see more examples at [Github](https://github.com/OpenWeavers/openanalysis/blob/master/analysistest/sorting.py)"
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