LeetCode *72. 编辑距离（动态规划）

if (s1[i] == s2[j]):
    i, j同时向前移动
else:
    三种状态选一：删除、增加、替换

class Solution {
private:
    string s1, s2;

public:
    int dp(int i, int j) {
        if (i == -1) return j + 1;
        if (j == -1) return i + 1;
        if (s1[i] == s2[j]) return dp(i - 1, j - 1);
        else return min(min(dp(i, j - 1) + 1, dp(i - 1, j) + 1), dp(i - 1, j - 1) + 1);
    }

    int minDistance(string word1, string word2) {
        s1 = word1;
        s2 = word2;
        return dp(word1.size() - 1, word2.size() - 1);
    }
};

class Solution {
public:
    int minDistance(string word1, string word2) {
        vector<vector<int>> dp(word1.size() + 1, vector<int>(word2.size() + 1));
        for (int i = 1; i <= word1.size(); i++) {
            dp[i][0] = i;
        }
        for (int j = 1; j <= word2.size(); j++) {
            dp[0][j] = j;
        }
        for (int i = 1; i <= word1.size(); i++) {
            for (int j = 1; j <= word2.size(); j++) {
                if (word1[i - 1] == word2[j - 1]) dp[i][j] = dp[i - 1][j - 1];
                else dp[i][j] = min(min(dp[i - 1][j] + 1, dp[i][j - 1] + 1), dp[i - 1][j - 1] + 1);
            }
        }
        return dp[dp.size() - 1][dp[0].size() - 1];
    }
};