minimum_edit_distance.cpp

/**
 * @file
 * @brief Implementation of [Minimum Edit
 * Distance](https://en.wikipedia.org/wiki/Edit_distance) using Dynamic
 * Programing
 *
 * @details
 *
 * Given two strings str1 & str2 and we have to calculate the minimum
 * number of operations (Insert, Remove, Replace) required to convert
 * str1 to str2.
 *
 * ### Algorithm
 *
 * We will solve this problem using Naive recursion. But as we are
 * approaching with a DP solution. So, we will take a DP array to
 * store the solution of all sub-problems so that we don't have to
 * perform recursion again and again. Now to solve the problem, We
 * can traverse all characters from either right side of the strings
 * or left side. Suppose we will do it from the right side. So, there
 * are two possibilities for every pair of characters being traversed.
 * 1. If the last characters of two strings are the same, Ignore
 * the characters and get the count for the remaining string.
 * So, we get the solution for lengths m-1 and n-1 in a DP array.
 *
 * 2. Else, (If last characters are not the same), we will consider all
 * three operations (Insert, Remove, Replace) on the last character of
 * the first string and compute the minimum cost for all three operations
 * and take the minimum of three values in the DP array.
 * For Insert: Recur for m and n-1
 * For Remove: Recur for for m-1 and n
 * For Replace: Recur for for m-1 and n-1
 *
 * @author [Nirjas Jakilim](github.com/nirzak)
 */

#include <cassert>   /// for assert
#include <cstdint>   /// for std::uint64_t
#include <iostream>  /// for IO operations
#include <vector>    /// for std::vector

/**
 * @namespace dynamic_programming
 * @brief Dynamic Programming algorithms
 */

namespace dynamic_programming {

/**
 * @namespace Minimum Edit Distance
 * @brief Implementation of [Minimum Edit
 * Distance](https://en.wikipedia.org/wiki/Edit_distance) algorithm
 */

namespace minimum_edit_distance {

/**
 * @brief Takes input of the cost of
 * three operations: Insert, Replace and Delete
 * and return the minimum cost among them.
 * @param x used to pass minimum cost of Insert operations
 * @param y used to pass minimum cost of Replace operations
 * @param z used to pass minimum cost of Delete operations
 * @returns x if `x` is the minimum value
 * @returns y if `y` is the minimum value
 * @returns z if `z` is the minimum value
 */
uint64_t min(uint64_t x, uint64_t y, uint64_t z) {
    if (x <= y && x <= z) {
        return x;  /// returns x, if x is the minimum value
    }
    if (y <= x && y <= z) {
        return y;  /// returns y, if y is the minimum value
    } else {
        return z;  /// returns z if z is the minimum value
    }
}

/**
 * @brief Calculates and stores the result
 * of all the sub-problems, so that we don't have to recur to compute
 * the minimum cost of a particular operation if it is already
 * computed and stored in the `dp` vector.
 * @param dp vector to store the computed minimum costs
 * @param str1 to pass the 1st string
 * @param str2 to pass the 2nd string
 * @param m the length of str1
 * @param n the length of str2
 * @returns dp[m][n] the minimum cost of operations
 * needed to convert str1 to str2
 */
uint64_t editDistDP(std::string str1, std::string str2, uint64_t m,
                    uint64_t n) {
    /// Create a table to store results of subproblems
    std::vector<std::vector<uint64_t>> dp(
        m + 1,
        std::vector<uint64_t>(
            n +
            1));  /// creasting 2D vector dp to store the results of subproblems

    /// Fill d[][] in bottom up manner
    for (uint64_t i = 0; i <= m; i++) {
        for (uint64_t j = 0; j <= n; j++) {
            /// If first string is empty, only option is to
            /// insert all characters of second string
            if (i == 0) {
                dp[i][j] = j;  /// Minimum operations = j
            }

            /// If second string is empty, only option is to
            /// remove all characters of second string
            else if (j == 0) {
                dp[i][j] = i;  /// Minimum operations = i
            }

            /// If last characters are same, ignore last char
            /// and recur for remaining string
            else if (str1[i - 1] == str2[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1];
            }

            /// If the last character is different, consider all
            /// possibilities and find the minimum
            else {
                dp[i][j] = 1 + min(dp[i][j - 1],       // Insert
                                   dp[i - 1][j],       // Remove
                                   dp[i - 1][j - 1]);  // Replace
            }
        }
    }

    return dp[m][n];  /// returning the minimum cost of operations needed to
                      /// convert str1 to str2
}
}  // namespace minimum_edit_distance
}  // namespace dynamic_programming

/**
 * @brief Self-test implementations
 * @returns void
 */
static void test() {
    // 1st test
    std::string str1 = "INTENTION";  // Sample input of 1st string
    std::string str2 = "EXECUTION";  // Sample input of 2nd string
    uint64_t expected_output1 = 5;   // Expected minimum cost
    uint64_t output1 = dynamic_programming::minimum_edit_distance::editDistDP(
        str1, str2, str1.length(),
        str2.length());  // calling the editDistDP function and storing the
                         // result on output1
    assert(output1 ==
           expected_output1);  // comparing the output with the expected output
    std::cout << "Minimum Number of Operations Required: " << output1
              << std::endl;

    // 2nd test
    std::string str3 = "SATURDAY";
    std::string str4 = "SUNDAY";
    uint64_t expected_output2 = 3;
    uint64_t output2 = dynamic_programming::minimum_edit_distance::editDistDP(
        str3, str4, str3.length(), str4.length());
    assert(output2 == expected_output2);
    std::cout << "Minimum Number of Operations Required: " << output2
              << std::endl;
}

/**
 * @brief main function
 * @param argc commandline argument count (ignored)
 * @param argv commandline array of arguments (ignored)
 * @returns 0 on exit
 */
int main(int argc, char *argv[]) {
    test();  // run self-test implementations
    return 0;
}