mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
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Add rotated array search challenge
This commit is contained in:
Donne Martin
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1208e1110f
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256755a962
0
sorting_searching/rotated_array_search/__init__.py
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0
sorting_searching/rotated_array_search/__init__.py
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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 an element in a sorted array that has been rotated a number of times.\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 input an array of ints?\n",
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" * Yes\n",
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"* Do we know how many times the array was rotated?\n",
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" * No\n",
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"* Was the array originally sorted in increasing or decreasing order?\n",
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" * Increasing\n",
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"* For the output, do we return the index?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\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 -> Exception\n",
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"* [] -> None\n",
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"* Not found -> None\n",
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"* General case with duplicates\n",
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"* General case without duplicates"
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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 Array(object):\n",
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"\n",
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" def search_sorted_array(self, array, val):\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_search_sorted_array.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestArray(object):\n",
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"\n",
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" def test_search_sorted_array(self):\n",
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" array = Array()\n",
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" assert_raises(TypeError, array.search_sorted_array, None)\n",
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" assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
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" assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
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" data = [10, 12, 14, 1, 3, 5, 6, 7, 8, 9]\n",
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" assert_equal(array.search_sorted_array(data, val=1), 3)\n",
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" data = [ 1, 1, 2, 1, 1, 1, 1, 1, 1, 1]\n",
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" assert_equal(array.search_sorted_array(data, val=2), 2)\n",
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" print('Success: test_search_sorted_array')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestArray()\n",
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" test.test_search_sorted_array()\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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@ -0,0 +1,268 @@
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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 an element in a sorted array that has been rotated a number of times.\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 input an array of ints?\n",
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" * Yes\n",
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"* Can the input have duplicates?\n",
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" * Yes\n",
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"* Do we know how many times the array was rotated?\n",
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" * No\n",
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"* Was the array originally sorted in increasing or decreasing order?\n",
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" * Increasing\n",
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"* For the output, do we return the index?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\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 -> Exception\n",
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"* [] -> None\n",
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"* Not found -> None\n",
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"* General case with duplicates\n",
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"* General case without duplicates"
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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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"### General case without dupes\n",
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"\n",
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"<pre>\n",
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"\n",
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"index 0 1 2 3 4 5 6 7 8 9\n",
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"input [ 1, 3, 5, 6, 7, 8, 9, 10, 12, 14]\n",
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"input rotated 1x [10, 12, 14, 1, 3, 5, 6, 7, 8, 9]\n",
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"input rotated 2x [ 5, 6, 7, 8, 9, 10, 12, 14, 1, 3]\n",
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"input rotated 3x [10, 12, 14, 1, 3, 5, 6, 7, 8, 9]\n",
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"\n",
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"find 1\n",
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"len = 10\n",
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"mid = 10 // 2 = 5\n",
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" s m e\n",
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"index 0 1 2 3 4 5 6 7 8 9\n",
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"input [10, 12, 14, 1, 3, 5, 6, 7, 8, 9]\n",
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"\n",
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"input[start] > input[mid]: Left half is rotated\n",
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"input[end] >= input[mid]: Right half is sorted\n",
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"1 is not within input[mid+1] to input[end] on the right side, go left\n",
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"\n",
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" s m e\n",
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"index 0 1 2 3 4 5 6 7 8 9\n",
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"input [10, 12, 14, 1, 3, 5, 6, 7, 8, 9]\n",
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"\n",
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"input[start] <= input[mid]: Right half is rotated\n",
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"input[end] >= input[mid]: Left half is sorted\n",
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"1 is not within input[left] to input[mid-1] on the left side, go right\n",
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"\n",
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"</pre>\n",
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"\n",
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"### General case with dupes\n",
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"\n",
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"<pre>\n",
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"\n",
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" s m e\n",
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"index 0 1 2 3 4 5 6 7 8 9\n",
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"input [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]\n",
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"\n",
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"input[start] == input[mid], input[mid] != input[end], go right\n",
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"\n",
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"input rotated 1x [ 1, 1, 2, 1, 1, 1, 1, 1, 1, 1]\n",
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"\n",
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"input[start] == input[mid] == input[end], search both sides\n",
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"\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(log n) if there are no duplicates, else O(n)\n",
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"* Space: O(m), where m is the recursion depth"
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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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"class Array(object):\n",
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"\n",
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" def search_sorted_array(self, array, val):\n",
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" if array is None or val is None:\n",
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" raise TypeError('array or val cannot be None')\n",
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" if not array:\n",
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" return None\n",
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" return self._search_sorted_array(array, val, start=0, end=len(array) - 1)\n",
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"\n",
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" def _search_sorted_array(self, array, val, start, end):\n",
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" if end < start:\n",
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" return None\n",
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" mid = (start + end) // 2\n",
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" if array[mid] == val:\n",
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" return mid\n",
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" # Left side is sorted\n",
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" if array[start] < array[mid]:\n",
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" if array[start] <= val < array[mid]:\n",
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" return self._search_sorted_array(array, val, start, mid - 1)\n",
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" else:\n",
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" return self._search_sorted_array(array, val, mid + 1, end)\n",
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" # Right side is sorted\n",
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" elif array[start] > array[mid]:\n",
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" if array[mid] < val <= array[end]:\n",
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" return self._search_sorted_array(array, val, mid + 1, end)\n",
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" else:\n",
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" return self._search_sorted_array(array, val, start, mid - 1)\n",
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" # Duplicates\n",
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" else:\n",
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" if array[mid] != array[end]:\n",
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" return self._search_sorted_array(array, val, mid + 1, end)\n",
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" else:\n",
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" result = self._search_sorted_array(array, val, start, mid - 1)\n",
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" if result != None:\n",
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" return result\n",
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" else:\n",
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" return self._search_sorted_array(array, val, mid + 1, end)"
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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_search_sorted_array.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_search_sorted_array.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestArray(object):\n",
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"\n",
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" def test_search_sorted_array(self):\n",
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" array = Array()\n",
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" assert_raises(TypeError, array.search_sorted_array, None)\n",
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" assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
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" assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
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" data = [10, 12, 14, 1, 3, 5, 6, 7, 8, 9]\n",
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" assert_equal(array.search_sorted_array(data, val=1), 3)\n",
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" data = [ 1, 1, 2, 1, 1, 1, 1, 1, 1, 1]\n",
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" assert_equal(array.search_sorted_array(data, val=2), 2)\n",
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" print('Success: test_search_sorted_array')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestArray()\n",
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" test.test_search_sorted_array()\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_search_sorted_array\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_search_sorted_array.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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@ -0,0 +1,24 @@
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from nose.tools import assert_equal, assert_raises
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class TestArray(object):
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def test_search_sorted_array(self):
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array = Array()
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assert_raises(TypeError, array.search_sorted_array, None)
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assert_equal(array.search_sorted_array([3, 1, 2], 0), None)
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assert_equal(array.search_sorted_array([3, 1, 2], 0), None)
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data = [10, 12, 14, 1, 3, 5, 6, 7, 8, 9]
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assert_equal(array.search_sorted_array(data, val=1), 3)
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data = [ 1, 1, 2, 1, 1, 1, 1, 1, 1, 1]
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assert_equal(array.search_sorted_array(data, val=2), 2)
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print('Success: test_search_sorted_array')
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def main():
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test = TestArray()
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test.test_search_sorted_array()
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if __name__ == '__main__':
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main()
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