{ "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: Given two strings, find the longest common subsequence.\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 subsequence a non-contiguous block of chars?\n", " * Yes\n", "* Do we expect a string as a result?\n", " * Yes\n", "* Can we assume this fits memory?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "* str0 or str1 is None -> Exception\n", "* str0 or str1 equals 0 -> ''\n", "* General case\n", "\n", "str0 = 'ABCDEFGHIJ'\n", "str1 = 'FOOBCDBCDE'\n", "\n", "result: 'BCDE'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "We'll use bottom up dynamic programming to build a table. \n", "\n", "
\n",
    "\n",
    "The rows (i) represent str0.\n",
    "The columns (j) represent str1.\n",
    "\n",
    "                       str1\n",
    "  -------------------------------------------------\n",
    "  |   |   | A | B | C | D | E | F | G | H | I | J |\n",
    "  -------------------------------------------------\n",
    "  |   | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
    "  | F | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |\n",
    "  | O | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |\n",
    "s | O | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |\n",
    "t | B | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |\n",
    "r | C | 0 | 0 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |\n",
    "0 | D | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | B | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | C | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | D | 0 | 0 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |\n",
    "  | E | 0 | 0 | 1 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 |\n",
    "  -------------------------------------------------\n",
    "\n",
    "if str1[j] != str0[i]:\n",
    "    T[i][j] = max(\n",
    "        T[i][j - 1],\n",
    "        T[i - 1][j])\n",
    "else:\n",
    "    T[i][j] = T[i - 1][j - 1] + 1\n",
    "
\n", "\n", "Complexity:\n", "* Time: O(m * n), where m is the length of str0 and n is the length of str1\n", "* Space: O(m * n), where m is the length of str0 and n is the length of str1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "class StringCompare(object):\n", "\n", " def longest_common_subseq(self, str0, str1):\n", " if str0 is None or str1 is None:\n", " raise TypeError('str input cannot be None')\n", " # Add one to number of rows and cols for the dp table's\n", " # first row of 0's and first col of 0's\n", " num_rows = len(str0) + 1\n", " num_cols = len(str1) + 1\n", " T = [[None] * num_cols for _ in range(num_rows)]\n", " for i in range(num_rows):\n", " for j in range(num_cols):\n", " if i == 0 or j == 0:\n", " T[i][j] = 0\n", " elif str0[j - 1] != str1[i - 1]:\n", " T[i][j] = max(T[i][j - 1],\n", " T[i - 1][j])\n", " else:\n", " T[i][j] = T[i - 1][j - 1] + 1\n", " results = ''\n", " i = num_rows - 1\n", " j = num_cols - 1\n", " # Walk backwards to determine the subsequence\n", " while T[i][j]:\n", " if T[i][j] == T[i][j - 1]:\n", " j -= 1\n", " elif T[i][j] == T[i - 1][j]:\n", " i -= 1\n", " elif T[i][j] == T[i - 1][j - 1] + 1:\n", " results += str1[i - 1]\n", " i -= 1\n", " j -= 1\n", " else:\n", " raise Exception('Error constructing table')\n", " # Walking backwards results in a string in reverse order\n", " return results[::-1] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unit Test" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting test_longest_common_subseq.py\n" ] } ], "source": [ "%%writefile test_longest_common_subseq.py\n", "from nose.tools import assert_equal, assert_raises\n", "\n", "\n", "class TestLongestCommonSubseq(object):\n", "\n", " def test_longest_common_subseq(self):\n", " str_comp = StringCompare()\n", " assert_raises(TypeError, str_comp.longest_common_subseq, None, None)\n", " assert_equal(str_comp.longest_common_subseq('', ''), '')\n", " str0 = 'ABCDEFGHIJ'\n", " str1 = 'FOOBCDBCDE'\n", " expected = 'BCDE'\n", " assert_equal(str_comp.longest_common_subseq(str0, str1), expected)\n", " print('Success: test_longest_common_subseq')\n", "\n", "\n", "def main():\n", " test = TestLongestCommonSubseq()\n", " test.test_longest_common_subseq()\n", "\n", "\n", "if __name__ == '__main__':\n", " main()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Success: test_longest_common_subseq\n" ] } ], "source": [ "%run -i test_longest_common_subseq.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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }