Edit Distance

Given two strings s and t. Return the minimum number of operations required to convert s to t.
The possible operations are permitted:

1. Insert a character at any position of the string.
2. Remove any character from the string.
3. Replace any character from the string with any other character.

• Time : O(nm)
• Space : O(nm)

c++

class Solution {
public:
    int editDistance(string s, string t) {
        int n = s.length(), m = t.length();

        vector<vector<int>> dp(n + 1, vector<int>(m + 1));
        for(int i = 0; i < n; i++) dp[0][i] = i;
        for(int j = 0; j < m; j++) dp[j][0] = j;
        for(int i = 1; i <= n; i++) {
            for(int j = 1; j <= m; j++) {
                if(s[i-1] == t[j-1]) dp[i][j] = dp[i-1][j-1];
                else dp[i][j] = 1 + min({ dp[i-1][j],
                    dp[i-1][j-1],
                    dp[i][j-1]
                });
            }
        }

        return dp[n][m];
    }
};