LeetCode Interleaving String DP

方法：DP

dp[i][j]表示s1的前i项和s2的前j项是否可以组成s3的前i+j项；
因此构建递推式为：

dp[i + 1][j + 1] = 
dp[i][j + 1] && (s1[i] == s3[i + j + 1])
||
dp[i + 1][j] && (s2[j] == s3[i + j + 1])

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        int m = s1.length();
        int n = s2.length();
        if(m + n != s3.length()) {
            return false;
        }
        bool dp[m + 1][n + 1];
        //initial
        dp[0][0] = true;
        for(int i = 0; i < m; ++i) {
            dp[i + 1][0] = dp[i][0] && (s1[i] == s3[i]);
        }
        for(int j = 0; j < n; ++j) {
            dp[0][j + 1] = dp[0][j] && (s2[j] == s3[j]);
        }

        for(int i = 0; i < m; ++i) {
            for(int j = 0; j < n; ++j) {
                dp[i + 1][j + 1] = (dp[i][j + 1] && (s1[i] == s3[i + j + 1])) || (dp[i + 1][j] && (s2[j] == s3[i + j + 1]));
            }
        }
        return dp[m][n];
    }
};