mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
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Add magic index challenge
This commit is contained in:
Donne Martin
parent
e5ccefb389
commit
54cee3457a
0
recursion_dynamic/magic_index/__init__.py
Normal file
0
recursion_dynamic/magic_index/__init__.py
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196
recursion_dynamic/magic_index/magic_index_challenge.ipynb
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196
recursion_dynamic/magic_index/magic_index_challenge.ipynb
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@ -0,0 +1,196 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Challenge Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Find the magic index in an array, where array[i] = i.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Is the array sorted?\n",
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" * Yes\n",
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"* Are the elements in the array distinct?\n",
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" * No\n",
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"* Does a magic index always exist?\n",
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" * No\n",
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"* If there is no magic index, do we just return -1?\n",
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" * Yes\n",
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"* Are negative values allowed in the array?\n",
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" * Yes\n",
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"* If there are multiple magic values, what do we return?\n",
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" * Return the left-most one\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* None input -> -1\n",
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"* Empty array -> -1\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 2 6 6 6 6 10\n",
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" i 0 1 2 3 4 5 6 7\n",
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"</pre>\n",
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"\n",
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"Result: 2\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 1 6 6 6 6 10\n",
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" i 0 1 2 3 4 5 6 7\n",
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"</pre>\n",
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"\n",
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"Result: 6\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 1 6 6 6 7 10\n",
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" i 0 1 2 3 4 5 6 7\n",
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"</pre>\n",
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"\n",
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"Result: -1"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"Refer to the [Solution Notebook](). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class MagicIndex(object):\n",
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"\n",
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" def find_magic_index(self, array):\n",
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" # TODO: Implement me\n",
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" pass"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# %load test_find_magic_index.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestFindMagicIndex(object):\n",
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"\n",
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" def test_find_magic_index(self):\n",
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" magic_index = MagicIndex()\n",
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" assert_equal(magic_index.find_magic_index(None), -1)\n",
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" assert_equal(magic_index.find_magic_index([]), -1)\n",
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" array = [-4, -2, 2, 6, 6, 6, 6, 10]\n",
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" assert_equal(magic_index.find_magic_index(array), 2)\n",
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" array = [-4, -2, 1, 6, 6, 6, 6, 10]\n",
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" assert_equal(magic_index.find_magic_index(array), 6)\n",
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" array = [-4, -2, 1, 6, 6, 6, 7, 10]\n",
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" assert_equal(magic_index.find_magic_index(array), -1)\n",
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" print('Success: test_find_magic')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestFindMagicIndex()\n",
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" test.test_find_magic_index()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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256
recursion_dynamic/magic_index/magic_index_solution.ipynb
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256
recursion_dynamic/magic_index/magic_index_solution.ipynb
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@ -0,0 +1,256 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Find the magic index in an array, where array[i] = i.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Is the array sorted?\n",
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" * Yes\n",
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"* Are the elements in the array distinct?\n",
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" * No\n",
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"* Does a magic index always exist?\n",
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" * No\n",
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"* If there is no magic index, do we just return -1?\n",
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" * Yes\n",
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"* Are negative values allowed in the array?\n",
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" * Yes\n",
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"* If there are multiple magic values, what do we return?\n",
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" * Return the left-most one\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* None input -> -1\n",
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"* Empty array -> -1\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 2 6 6 6 6 10\n",
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" i 0 1 2 3 4 5 6 7\n",
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"</pre>\n",
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"\n",
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"Result: 2\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 1 6 6 6 6 10\n",
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" i 0 1 2 3 4 5 6 7\n",
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"</pre>\n",
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"\n",
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"Result: 6\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 1 6 6 6 7 10\n",
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" i 0 1 2 3 4 5 6 7\n",
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"</pre>\n",
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"\n",
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"Result: -1"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"We'll use a binary search to split the search space in half on each iteration. To obtain more efficiency, we can do a little better than a naive left and half split.\n",
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"\n",
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"In the example below, we see that i == 5 cannot be the magic index, otherwise a[5] would have to equal 5 (note a[4] == 6).\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 2 6 6 6 6 10\n",
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" i 0 1 1 3 4 5 6 7\n",
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" mid\n",
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"</pre>\n",
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"\n",
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"Similarly, in the example below we can further trim the left search space.\n",
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"\n",
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"<pre>\n",
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"a[i] -4 -2 2 2 2 6 6 10\n",
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" i 0 1 2 3 4 5 6 7\n",
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" mid\n",
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"</pre>\n",
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"\n",
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"\n",
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"* Calculate mid\n",
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"* If mid == array[mid], return mid\n",
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"* Recurse on the left side of the array\n",
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" * start: 0\n",
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" * end: min(mid-1, array[mid]\n",
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"* Recurse on the right side of the array\n",
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" * start: max(mid+1, array[mid]\n",
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" * end: end\n",
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"\n",
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"Complexity:\n",
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"* Time: O(log(n))\n",
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"* Space: O(log(n))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from __future__ import division\n",
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"\n",
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"\n",
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"class MagicIndex(object):\n",
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"\n",
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" def find_magic_index(self, array):\n",
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" if array is None or not array:\n",
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" return -1\n",
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" return self._find_magic_index(array, 0, len(array) - 1)\n",
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"\n",
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" def _find_magic_index(self, array, start, end):\n",
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" if end < start or start < 0 or end >= len(array):\n",
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" return -1\n",
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" mid = (start + end) // 2\n",
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" if mid == array[mid]:\n",
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" return mid\n",
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" left_end = min(mid - 1, array[mid])\n",
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" left_result = self._find_magic_index(array, start, end=left_end)\n",
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" if left_result != -1:\n",
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" return left_result\n",
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" right_start = max(mid + 1, array[mid])\n",
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" right_result = self._find_magic_index(array, start=right_start, end=end)\n",
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" if right_result != -1:\n",
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" return right_result\n",
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" return -1"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_find_magic_index.py\n"
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]
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}
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],
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"source": [
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"%%writefile test_find_magic_index.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestFindMagicIndex(object):\n",
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"\n",
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" def test_find_magic_index(self):\n",
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" magic_index = MagicIndex()\n",
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" assert_equal(magic_index.find_magic_index(None), -1)\n",
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" assert_equal(magic_index.find_magic_index([]), -1)\n",
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" array = [-4, -2, 2, 6, 6, 6, 6, 10]\n",
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" assert_equal(magic_index.find_magic_index(array), 2)\n",
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" array = [-4, -2, 1, 6, 6, 6, 6, 10]\n",
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" assert_equal(magic_index.find_magic_index(array), 6)\n",
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" array = [-4, -2, 1, 6, 6, 6, 7, 10]\n",
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" assert_equal(magic_index.find_magic_index(array), -1)\n",
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" print('Success: test_find_magic')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestFindMagicIndex()\n",
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" test.test_find_magic_index()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Success: test_find_magic\n"
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]
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}
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],
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"source": [
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"%run -i test_find_magic_index.py"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.4.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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25
recursion_dynamic/magic_index/test_find_magic_index.py
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25
recursion_dynamic/magic_index/test_find_magic_index.py
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from nose.tools import assert_equal
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class TestFindMagicIndex(object):
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def test_find_magic_index(self):
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magic_index = MagicIndex()
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assert_equal(magic_index.find_magic_index(None), -1)
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assert_equal(magic_index.find_magic_index([]), -1)
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array = [-4, -2, 2, 6, 6, 6, 6, 10]
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assert_equal(magic_index.find_magic_index(array), 2)
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array = [-4, -2, 1, 6, 6, 6, 6, 10]
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assert_equal(magic_index.find_magic_index(array), 6)
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array = [-4, -2, 1, 6, 6, 6, 7, 10]
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assert_equal(magic_index.find_magic_index(array), -1)
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print('Success: test_find_magic')
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def main():
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test = TestFindMagicIndex()
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test.test_find_magic_index()
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if __name__ == '__main__':
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main()
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