97. 交错字符串. dp

给定三个字符串 s1, s2, s3, 验证 s3 是否是由 s1 和 s2 交错组成的。

示例 1：

输入：s1 = "aabcc", s2 = "dbbca", s3 = "aadbbcbcac"
输出：true
示例 2：

输入：s1 = "aabcc", s2 = "dbbca", s3 = "aadbbbaccc"
输出：false

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/interleaving-string
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        int n = s1.size();
        int m = s2.size();
        int t = s3.size();

        //dp[i][j] : s1的前i个与s2的前j个字符能否构成s3的前i+j
        vector <vector<int>> dp = vector (n + 1, vector<int> (m + 1, false));

        if (n + m != t) return false;

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

        return dp[n][m];
    }
};