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 +}