Edit Distance – LeetCode Solution [Hard]

Problem statement:

Given two strings word1 and word2 (in lowercase alphabets), return the minimum number of operations required to convert word1 to word2.

You could only perform three following operations on a word:

  • Insert a character
  • Delete a character
  • Replace a character

Example 1:

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation: 
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')

Edit Distance solution

Pseudocode (Bottom up)

1. Traverse both strings from left to right 
2. Do: 
      If current characters of two strings are equal, do nothing and traverse for remaining string ie dp[i][j] = dp[i-1][j-1]
    if current characters are not equal, consider any of the three operations:
     1- Insert: Recur for m and n-1: dp[i][j-1]
     2- Remove: Recur for m-1 and n: dp[i-1][j]
     3- Replace: Recur for m-1 and n-1: dp[i-1][j-1]
3. And take minimum of the three + 1(for the operation)

Code Implementation

//
//  main.cpp
//  Edit Distance
//
//  Created by Himanshu on 16/09/21.
//

#include <iostream>
#include <string>
using namespace std;

int solve (string s1, string s2) {
    int n = (int) s1.length(), m = (int) s2.length();
    int dp[n+1][m+1];
    
    for (int i=0; i<=n; i++) {
        for (int j=0; j<=m; j++) {
            dp[i][j] = 0;
        }
    }
    
    for (int i=0; i<=n; i++) {
        dp[i][0] = i;
    }
    
    for (int j=0; j<=m; j++) {
        dp[0][j] = j;
    }
    
    for (int i=1; i<=n; i++) {
        for (int j=1; j<=m; j++) {
            if (s1[i-1] == s2[j-1]) {
                dp[i][j] = dp[i-1][j-1];
            }
            else {
                dp[i][j] = 1 + min((min(dp[i-1][j], 
                                      dp[i][j-1])), 
                                      dp[i-1][j-1]);
            }
            
        }
    }
    
    return dp[n][m];
}

int main() {
    string s1 = "hello", s2 = "tell";
    cout<<solve(s1, s2)<<endl;
}

Here’s a working example:

https://ideone.com/uMhxri

Practice Problem

https://leetcode.com/problems/edit-distance/

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