LeetCode 1092. Shortest Common Supersequence

本题的核心是找到LCS，然后通过dp数组，反向构建出 Common Supersequence。这和 print LCS 的思路极其相似。

LCS: Longest Common Subsequence / String 总结

https://www.geeksforgeeks.org/printing-longest-common-subsequence/

class Solution {
public:
    string shortestCommonSupersequence(string str1, string str2) {
        int m=str1.size(), n=str2.size();
        vector<vector<int>> dp(m+1, vector<int>(n+1, 0));
        for (int i=1;i<=m;++i){
            for (int j=1;j<=n;++j){
                if (str1[i-1]==str2[j-1]) dp[i][j] = dp[i-1][j-1]+1;
                else dp[i][j] = max(dp[i-1][j], dp[i][j-1]);
            }
        }

        int i=m, j=n;
        string res="";
        while (i>0 || j>0){
            if (i==0){
                res += str2[--j];
            }else if (j==0){
                res += str1[--i];
            }else if (str1[i-1] == str2[j-1]){
                res += str1[i-1];
                --i; --j;
            }else if (dp[i-1][j] > dp[i][j-1]){
                res += str1[--i];
            }else{
                res += str2[--j];
            }
        }
        reverse(res.begin(),res.end());
        return res;
    }
};

时间复杂度 O(mn)