{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://bit.ly/code-notes)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Determine if a string is a permutation of another string\n", "\n", "* [Clarifying Questions](#Clarifying-Questions)\n", "* [Test Cases](#Test-Cases)\n", "* [Algorithm: Compare Sorted Strings](#Algorithm:-Compare-Sorted-Strings)\n", "* [Code: Compare Sorted Strings](#Code:-Compare-Sorted-Strings)\n", "* [Algorithm: Hashmap Lookup](#Algorithm:-Hash-Map-Lookup)\n", "* [Code: Hashmap Lookup](#Code:-Hash-Map-Lookup)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Clarifying Questions\n", "\n", "* Is the string ASCII (extended)? Or Unicode?\n", " * ASCII extended, which is 256 characters\n", "* Is whitespace important?\n", " * Yes\n", "* Is this case sensitive? 'Nib', 'bin' is not a match?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "* One or more empty strings -> False\n", "* 'Nib', 'bin' -> False\n", "* 'act', 'cat' -> True\n", "* 'a ct', 'ca t' -> True" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from nose.tools import assert_equal\n", "\n", "class Test(object):\n", " def test_permutation(self, func):\n", " assert_equal(func('', 'foo'), False)\n", " assert_equal(func('Nib', 'bin'), False)\n", " assert_equal(func('act', 'cat'), True)\n", " assert_equal(func('a ct', 'ca t'), True)\n", "\n", "def run_tests(func):\n", " test = Test()\n", " test.test_permutation(func)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm: Compare Sorted Strings\n", "\n", "Anagrams contain the same strings but in different orders. This approach could be slow for large strings due to sorting.\n", "\n", "* Sort both strings\n", "* If both sorted strings are equal\n", " * return True\n", "* Else\n", " * return False\n", "\n", "Complexity:\n", "* Time: O(n log n) from the sort, in general\n", "* Space: Additional O(l + m) is created by the sorting algorithm, where l is the length of one string and m is the length of the other" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code: Compare Sorted Strings" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def permutations(str1, str2):\n", " return sorted(str1) == sorted(str2)\n", "\n", "run_tests(permutations)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm: Hash Map Lookup\n", "\n", "We'll keep a hash map (dict) to keep track of characters we encounter. \n", "\n", "Steps:\n", "* Scan each character\n", "* For each character in each string:\n", " * If the character does not exist in a hash map, add the character to a hash map\n", " * Else, increment the character's count\n", "* If the hash maps for each string are equal\n", " * Return True\n", "* Else\n", " * Return False\n", "\n", "Notes:\n", "* Since the characters are in ASCII, we could potentially use an array of size 128 (or 256 for extended ASCII)\n", "* Instead of using two hash maps, you could use one hash map and increment character values based on the first string and decrement based on the second string\n", "* You can short circuit if the lengths of each string are not equal, len() in Python is generally O(1)\n", "\n", "Complexity:\n", "* Time: O(n)\n", "* Space: Additional O(m), where m is the number of unique characters in the hash map" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code: Hash Map Lookup" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from collections import defaultdict\n", "\n", "def unique_counts(string):\n", " dict_chars = defaultdict(int)\n", " for char in string:\n", " dict_chars[char] += 1\n", " return dict_chars\n", "\n", "def permutations_alt(str1, str2):\n", " if len(str1) != len(str2):\n", " return False\n", " unique_counts1 = unique_counts(str1)\n", " unique_counts2 = unique_counts(str2)\n", " return unique_counts1 == unique_counts2\n", "\n", "run_tests(permutations_alt)" ] } ], "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": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }