class Solution {
    //用dp[i][j]表示s1的前i个字符和s2的前j个字符能否组成s3的前i+j个字符
    public boolean isInterleave(String s1, String s2, String s3) {
        int n1 = s1.length();
        int n2 = s2.length();
        int n3 = s3.length();
        if(n1 + n2 != n3){
            return false;
        }
        boolean[][] dp = new boolean[n1 + 1][n2 + 1];
        dp[0][0] = true;
        for(int i = 0; i <= n1; i++){
            for(int j = 0; j <= n2; j++){
                //如果s1[i - 1] == s3[i + j - 1]那么dp[i][j]可以由状态dp[i - 1][j] 转移来
                //注意dp下标从1开始
                if(i - 1 >= 0 && s1.charAt(i - 1) == s3.charAt(i + j - 1)){
                    dp[i][j] |= dp[i - 1][j];
                }
                if(j - 1 >= 0 && s2.charAt(j - 1) == s3.charAt(i + j - 1)){
                    dp[i][j] |= dp[i][j - 1];
                }
            }
        }
        return dp[n1][n2];
    }
}