{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "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)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Solution Notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Find the length of the longest substring with at most k distinct characters.\n", "\n", "* [Constraints](#Constraints)\n", "* [Test Cases](#Test-Cases)\n", "* [Algorithm](#Algorithm)\n", "* [Code](#Code)\n", "* [Unit Test](#Unit-Test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constraints\n", "\n", "* Can we assume the inputs are valid?\n", " * No\n", "* Can we assume the strings are ASCII?\n", " * Yes\n", "* Is this case sensitive?\n", " * Yes\n", "* Is a substring a contiguous block of chars?\n", " * Yes\n", "* Do we expect an int as a result?\n", " * Yes\n", "* Can we assume this fits memory?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "* None -> TypeError\n", "* '', k = 3 -> 0\n", "* 'abcabcdefgghiij', k=3 -> 6\n", "* 'abcabcdefgghighij', k=3 -> 7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "We'll use a `chars_to_index_map` dictionary: char (key) to index (val) map to maintain a sliding window.\n", "\n", "The index (val) will keep track of the character index in the input string.\n", "\n", "For each character in the string:\n", "\n", "* Add the char (key) and index (value) to the map\n", "* If the length of our map is greater than k, then we'll need to eliminate one item\n", " * Scan the map to find the lowest index and remove it\n", " * The new lowest index will therefore be incremented by 1\n", "* The max length will be the current index minus the lower index + 1\n", "\n", "Complexity:\n", "* Time: O(n * k), where n is the number of chars, k is the length of the map due to the min() call\n", "* Space: O(n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "class Solution(object):\n", "\n", " def longest_substr(self, string, k):\n", " if string is None:\n", " raise TypeError('string cannot be None')\n", " if k is None:\n", " raise TypeError('k cannot be None')\n", " low_index = 0\n", " max_length = 0\n", " chars_to_index_map = {}\n", " for index, char in enumerate(string):\n", " chars_to_index_map[char] = index\n", " if len(chars_to_index_map) > k:\n", " low_index = min(chars_to_index_map.values())\n", " del chars_to_index_map[string[low_index]]\n", " low_index += 1\n", " max_length = max(max_length, index - low_index + 1)\n", " return max_length" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unit Test" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting test_longest_substr.py\n" ] } ], "source": [ "%%writefile test_longest_substr.py\n", "import unittest\n", "\n", "\n", "class TestSolution(unittest.TestCase):\n", "\n", " def test_longest_substr(self):\n", " solution = Solution()\n", " self.assertRaises(TypeError, solution.longest_substr, None)\n", " self.assertEqual(solution.longest_substr('', k=3), 0)\n", " self.assertEqual(solution.longest_substr('abcabcdefgghiij', k=3), 6)\n", " self.assertEqual(solution.longest_substr('abcabcdefgghighij', k=3), 7)\n", " print('Success: test_longest_substr')\n", "\n", "\n", "def main():\n", " test = TestSolution()\n", " test.test_longest_substr()\n", "\n", "\n", "if __name__ == '__main__':\n", " main()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Success: test_longest_substr\n" ] } ], "source": [ "%run -i test_longest_substr.py" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 1 }