72. Edit Distance

class Solution {
public:
    int minDistance(string word1, string word2)
    {
        int m = word1.size(), n = word2.size();
        vector<vector<int>> dp(m + 1, vector<int>(n + 1));

        for (int i = 0; i <= m; ++i) dp[i][0] = i;
        for (int j = 0; j <= n; ++j) dp[0][j] = j;

        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                if (word1[i - 1] == word2[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1];
                } else {
                    dp[i][j] = 1 + min({dp[i - 1][j - 1], dp[i - 1][j], dp[i][j - 1]});
                }
            }
        }
        return dp[m][n];
    }
};

• T: $O(M \cdot N)$
• S: $O(M \cdot N)$