Added Insertion Sort

Author: OmkarPathak

Sorting/3. Insertion_Sort.ipynb

@@ -0,0 +1,184 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Insertion Sort"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def insertion_sort(array):\n",
+    "    global iterations\n",
+    "    iterations = 0\n",
+    "    for i in range(1, len(array)):\n",
+    "        current_value = array[i]\n",
+    "        for j in range(i - 1, -1, -1):\n",
+    "            iterations += 1\n",
+    "            if array[j] > current_value:\n",
+    "                array[j], array[j + 1] = array[j + 1], array[j] # swap\n",
+    "            else:\n",
+    "                array[j + 1] = current_value\n",
+    "                break"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Time Complexity:\n",
+    "\n",
+    "- Best Case: O(n)\n",
+    "- Average Case: O(n * n)\n",
+    "- Worst Case:  O(n * n)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code for executing and seeing the difference in time complexities"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Best Case Performance:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n",
+      "18\n"
+     ]
+    }
+   ],
+   "source": [
+    "# elements are already sorted\n",
+    "array = [i for i in range(1, 20)]\n",
+    "\n",
+    "insertion_sort(array)\n",
+    "# 20 ALREADY sorted elements need 18 iterations approx = n\n",
+    "print(array)\n",
+    "print(iterations)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Average Case Performance:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n",
+      "89\n"
+     ]
+    }
+   ],
+   "source": [
+    "import random\n",
+    "# elements are randomly shuffled\n",
+    "array = [i for i in range(1, 20)]\n",
+    "random.shuffle(array)\n",
+    "\n",
+    "insertion_sort(array)\n",
+    "# 20 shuffled elements need 324 iterations approx = n * n\n",
+    "print(array)\n",
+    "print(iterations)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Worst Case Performance:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n",
+      "171\n"
+     ]
+    }
+   ],
+   "source": [
+    "# elements are reverse sorted\n",
+    "array = [i for i in range(1, 20)]\n",
+    "# reversing the array\n",
+    "array = array[::-1]\n",
+    "\n",
+    "insertion_sort(array)\n",
+    "# 20 REVERSE sorted elements need 324 iterations approx = n * n\n",
+    "\n",
+    "print(array)\n",
+    "print(iterations)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Applications"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "More efficient that other sorts when N is comparatively smaller, say < 30."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}