From bee2530749ebd5a2680d9ddc52a6eb3602b5a36c Mon Sep 17 00:00:00 2001
From: Donne Martin <donne.martin@gmail.com>
Date: Fri, 29 May 2015 06:51:37 -0400
Subject: [PATCH] Added notebook solving the following: Implement merge sort.

---
 README.md                          |   1 +
 sorting-searching/merge-sort.ipynb | 148 +++++++++++++++++++++++++++++
 2 files changed, 149 insertions(+)
 create mode 100644 sorting-searching/merge-sort.ipynb

diff --git a/README.md b/README.md
index 90ac595..667f0f6 100644
--- a/README.md
+++ b/README.md
@@ -48,6 +48,7 @@ Most solutions are in Python.
 * [Implement selection sort](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/sorting-searching/selection-sort.ipynb#)
 * [Implement insertion sort](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/sorting-searching/insertion-sort.ipynb#)
 * [Implement quick sort](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/sorting-searching/quick-sort.ipynb#)
+* [Implement merge sort](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/sorting-searching/merge-sort.ipynb#)
 
 ## Hacker Rank
 
diff --git a/sorting-searching/merge-sort.ipynb b/sorting-searching/merge-sort.ipynb
new file mode 100644
index 0000000..b87d6e2
--- /dev/null
+++ b/sorting-searching/merge-sort.ipynb
@@ -0,0 +1,148 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Implement merge sort.\n",
+    "\n",
+    "* [Clarifying Questions](#Clarifying-Questions)\n",
+    "* [Test Cases](#Test-Cases)\n",
+    "* [Algorithm](#Algorithm)\n",
+    "* [Code](#Code)\n",
+    "* [Pythonic-Code](#Pythonic-Code)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Clarifying Questions\n",
+    "\n",
+    "* Is a naiive merge sort ok?\n",
+    "    * Yes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Cases\n",
+    "\n",
+    "* Empty input\n",
+    "* One element\n",
+    "* Two or more elements\n",
+    "* Left and right subarrays of different lengths"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm\n",
+    "\n",
+    "Wikipedia's animation:\n",
+    "![alt text](http://upload.wikimedia.org/wikipedia/commons/c/cc/Merge-sort-example-300px.gif)\n",
+    "\n",
+    "* Recursively split array into left and right halves\n",
+    "* Merge split arrays\n",
+    "    * Using two pointers, one for each half starting at index 0\n",
+    "        * Add the smaller element to the result array\n",
+    "        * Inrement pointer where smaller element exists\n",
+    "    * Copy remaining elements to the result array\n",
+    "    * Return result array\n",
+    "\n",
+    "Complexity:\n",
+    "* Time: O(n log(n))\n",
+    "* Space: O(n), stable"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def merge(left, right):\n",
+    "    l = 0\n",
+    "    r = 0\n",
+    "    result = []\n",
+    "    while l < len(left) and r < len(right):\n",
+    "        if left[l] < right[r]:\n",
+    "            result.append(left[l])\n",
+    "            l += 1\n",
+    "        else:\n",
+    "            result.append(right[r])\n",
+    "            r += 1\n",
+    "    while l < len(left):\n",
+    "        result.append(left[l])\n",
+    "        l += 1\n",
+    "    while r < len(right):\n",
+    "        result.append(right[r])\n",
+    "        r += 1\n",
+    "    return result\n",
+    "\n",
+    "def merge_sort(data):\n",
+    "    if len(data) < 2:\n",
+    "        return data\n",
+    "    mid = len(data) / 2\n",
+    "    left = data[0:mid]\n",
+    "    right = data[mid:len(data)]\n",
+    "    left = merge_sort(left)\n",
+    "    right = merge_sort(right)\n",
+    "    return merge(left, right)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "print('Empty input')\n",
+    "data = []\n",
+    "merge_sort(data)\n",
+    "print(data)\n",
+    "print('One element')\n",
+    "data = [5]\n",
+    "merge_sort(data)\n",
+    "print(data)\n",
+    "print('Two or more elements')\n",
+    "data = [5, 1, 7, 2, 6, -3, 5, 7, -1]\n",
+    "print(merge_sort(data))"
+   ]
+  }
+ ],
+ "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": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}