Added notebook solving the following: Implement merge sort.

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Donne Martin 2015-05-29 06:51:37 -04:00
parent d72cd4fe2c
commit bee2530749
2 changed files with 149 additions and 0 deletions

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@ -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

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{
"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))"
]
}
],
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"language": "python",
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},
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"file_extension": ".py",
"mimetype": "text/x-python",
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"nbconvert_exporter": "python",
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