72. 编辑距离(DP)(LeetCode)

class Solution {
public:
    int minDistance(string word1, string word2) {
        int n = word1.size(), m = word2.size();
        word1 = " " + word1; word2 = " " + word2;
        vector<vector<int>> f(n + 1, vector<int>(m + 1));
        
        //初始化边界
        for(int i = 0; i <= n; ++i) f[i][0] = i;
        for(int i = 0; i <= m; ++i) f[0][i] = i;

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