Interleaving String

Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.

For example,
Given:
s1 = "aabcc",
s2 = "dbbca",

When s3 = "aadbbcbcac", return true.
When s3 = "aadbbbaccc", return false.

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        int n1 = s1.length(), n2 = s2.length(), n3 = s3.length();
        if (n1+n2 != n3) return false;

        vector<vector<bool>> V(n1+1, vector<bool>(n2+1, false));

        V[n1][n2] = (s3[n1+n2]=='\0');

        // fill bottom
        for (int j=n2-1; j>=0; j--) V[n1][j]  = (s2[j]==s3[n1+j] && V[n1][j+1]);

        // fill right
        for (int i=n1-1; i>=0; i--) V[i][n2] = (s1[i]==s3[n2+i] && V[i+1][n2]);

        // fill DP table from bottom right
        for (int j=n2-1; j>=0; j--){
            for (int i=n1-1; i>=0; i--){
                V[i][j] = (s1[i]==s3[i+j] && V[i+1][j]) | (s2[j]==s3[i+j] && V[i][j+1]);
            }
        }
        return V[0][0];
    }
};