leetcode Interleaving String

InterleavingString.cpp

class Solution {
public:
    bool dfs(const string &s1, int i, const string &s2, int j, const string&s3, int k, vector<vector<int> > &dp) {   
        if(i == s1.size() && j == s2.size() && k == s3.size()) {
            return true;
        } 
        
        if(i == s1.size()) {
            return s2.substr(j) == s3.substr(k);
        }
        if(j == s2.size()) {
            return s1.substr(i) == s3.substr(k);
        }
        
        if(dp[i][j] == 1) {
            return false;
        }
        
        if(s1[i] == s3[k]) {
            if(dfs(s1, i+1, s2, j, s3, k+1, dp)) {
                return true;
            }
        }
        if(s2[j] == s3[k]) {
            if(dfs(s1, i, s2, j+1, s3, k+1, dp)) {
                return true;
            }
        }
        
        dp[i][j] = 1;
        return false;        
    }
    
    bool isInterleave(string s1, string s2, string s3) {
        vector<vector<int> > dp(s1.size());
        for(int i = 0; i < s1.size(); i++) {
            dp[i].assign(s2.size(), 0);
        }
        
        if(s1.size() + s2.size() != s3.size()) {
            return false;
        }
        
        return dfs(s1, 0, s2, 0, s3, 0, dp);    
    }
};