doc/OpenAnalysis/03 - Searching.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Searching Analysis\n",
    "\n",
    "Consider a finite collection of element. Finding whether element exsists in collection is known as Searching. Following are some of the comparision based Searching Algorithms.\n",
    "\n",
    "- Linear Search\n",
    "- Binary Search\n",
    "\n",
    "Before looking at the analysis part, we shall examine the Language in built methods to searching\n",
    "\n",
    "## The `in` operator and `list.index()`\n",
    "\n",
    "We have already seen the `in` operator in several contexts. Let's see the working of `in` operator again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = list(range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "6 in x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "100 in x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.index(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "100 is not in list",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-0f87238c301b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: 100 is not in list"
     ]
    }
   ],
   "source": [
    "x.index(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standard `import` statement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from openanalysis.searching import SearchingAlgorithm,SearchAnalyzer\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_formats={\"svg\", \"pdf\"}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`SearchingAlgorithm` is the base class providing the standards to implement searching algorithms, `SearchAnalyzer` analyses the algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `SearchingAlgorithm` class\n",
    "\n",
    "Any searching 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 Searching Algorithm\n",
    "- `count` - Holds the number of basic operations performed\n",
    "\n",
    "### Member Functions\n",
    "\n",
    "- `__init__(self, name):` - Initializes algorithm with a `name`\n",
    "- `search(self, array, key):` _ The base searching function. Sets `count` to 0. `array` is 1D `numpy` array,`key` is the key of element to be found out\n",
    "\n",
    "## An example .... Binary Search\n",
    "\n",
    "Now we shall implement the class `BinarySearch`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class BinarySearch(SearchingAlgorithm):                    # Inheriting\n",
    "    def __init__(self):\n",
    "        SearchingAlgorithm.__init__(self, \"Binary Search\") # Initailizing with name\n",
    "\n",
    "    def search(self, arr, key):\n",
    "        SearchingAlgorithm.search(self, arr, key)          # call base class search\n",
    "        low, high = 0, arr.size - 1\n",
    "        while low <= high:\n",
    "            mid = int((low + high) / 2)\n",
    "            self.count += 1                                # Increment for each basic operation performed\n",
    "            if arr[mid] == key:\n",
    "                return True\n",
    "            elif arr[mid] < key:\n",
    "                low = mid + 1\n",
    "            else:\n",
    "                high = mid - 1\n",
    "        return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `SearchAnalyzer` class\n",
    "\n",
    "This class provides the visualization and analysis methods. Let's see its methods in detail\n",
    "\n",
    "- `__init__(self, searcher):` Initializes visualizer with a Searching Algorithm. \n",
    "    - `searcher` is a class, which is derived from `SearchingAlgorithm`\n",
    "    \n",
    "    \n",
    "- `analyze(self, maxpts=1000):`\n",
    "    - Plots the running time of searching algorithm by searching in 3 cases\n",
    "    - Key is the first element, Key is the last element, Key at random index\n",
    "    - Analysis is done  by inputting sorted 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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff57329b978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bin_visualizer = SearchAnalyzer(BinarySearch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Please wait while analyzing Binary Search Algorithm\n"
     ]
    },
    {
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6eIR4iD0Jw3JdxYXRDT/etsw0vI4y3I31Zcb4qLFATtAHGCITV6NJ9e2KM1Tp4dVirqOi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\nGxsiQmM/6U46wQ4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    "bin_visualizer.analyze(progress=False)"
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   "source": [
    "Note $\\mathcal{O}(\\log{}n)$ performance in all cases"
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   "source": [
    "## `compare(algs)`\n",
    "\n",
    "`algs` is a list of classes derived from `SearchingAlgorithm`. It performs tests and plots the bar graph comapring the number of basic operations performed by each algorithm.\n"
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   "source": [
    "## Example File\n",
    "\n",
    "You can see more examples at [Github](https://github.com/OpenWeavers/openanalysis/blob/master/analysistest/searching.py)"
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