Interleaving string

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        if(s3.size() != s1.size() + s2.size())
            return false;
        //create indicator
        vector<vector<bool> > match(s1.size() + 1, vector<bool>(s2.size() + 1, false));
        //initialization the first row and the first column
        match[0][0] = true;
        for( int l1 = 1; l1 <= s1.size(); ++ l1 ) {
            char c1 = s1[l1 - 1];
            char c3 = s3[l1 - 1];
            if (c1 == c3) {
                match[l1][0] = true;
            } else 
                break;
        }
        for( int l2 = 1; l2 <= s2.size(); ++ l2 ) {
            char c2 = s2[l2 - 1];
            char c3 = s3[l2 - 1];
            if (c2 == c3) {
                match[0][l2] = true;
            } else 
                break;
        }
        //work through the rest of matrix using the formula
        for( int l1 = 1; l1 <= s1.size(); ++ l1 ) {
            char c1 = s1[l1 - 1];
            for( int l2 = 1 ; l2 <= s2.size() ; ++ l2 ) {
                char c2 = s2[l2 - 1];
                int l3 = l1 + l2;
                char c3 = s3[l3 - 1];
                if (c1 == c3) {
                    match[l1][l2] = match[l1 - 1][l2] || match[l1][l2];
                }
                if (c2 == c3) {
                    match[l1][l2] = match[l1][l2 - 1] || match[l1][l2];
                }
            }
        }
        //the last element is the result
        return match[s1.size()][s2.size()];
    }
};