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.

判斷是否有s1和s2組成，用二維dp，相當與在一個二維數組畫個路線圖判斷能否組成s3

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        if(s1.size()+s2.size() != s3.size()) return false;
        bool f[1000][1000];
        memset(f,0,sizeof(f));
        f[0][0] = true;
        for(int i = 1; i <= s1.length(); i++)
            f[i][0] = f[i-1][0] && s1[i-1] == s3[i-1];
        for(int j = 1; j <= s2.length(); j++)
            f[0][j] = f[0][j-1] && s2[j-1] == s3[j-1];
        for(int i = 1; i <= s1.size(); i++)
            for(int j = 1; j <= s2.size(); j++)
              f[i][j] = (f[i][j-1] && s2[j-1] == s3[i+j-1]) || (f[i-1][j] && s1[i-1] == s3[i+j-1]);
        return f[s1.size()][s2.size()];    
    }
};