97.Interleaving String

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        int m = s1.size();
        int n = s2.size();
        if(m+n != s3.size())
            return false;
        vector<vector<bool> > path(m+1, vector<bool>(n+1, false));
        for(int i = 0; i < m+1; i ++)
        {
            for(int j = 0; j < n+1; j ++)
            {
                if(i == 0 && j == 0)
                // start
                    path[i][j] = true;
                else if(i == 0)
                    path[i][j] = path[i][j-1] & (s2[j-1]==s3[j-1]);
                else if(j == 0)
                    path[i][j] = path[i-1][j] & (s1[i-1]==s3[i-1]);
                else
                    path[i][j] = (path[i][j-1] & (s2[j-1]==s3[i+j-1])) || (path[i-1][j] & (s1[i-1]==s3[i+j-1]));
            }
        }
        return path[m][n];
    }
};