leetcode -- 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.

[解题思路]

DP

Let F(i, j) denote if s1 of length i and s2 of length j could form s3 of lenght i+j, then we have four cases:
(1) F(i, j) = F(i-1, j)                              if s1[i-1] == s3[i+j-1] && s2[j-1] != s3[i +j -1]
(2) F(i, j) = F(i, j-1)                              if s1[i-1] != s3[i+j-1]  && s2[j-1] == s3[i +j -1]
(3) F(i, j) = F(i-1, j) || F(i, j-1)             if s1[i-1] == s3[i+j-1] && s2[j-1] == s3[i +j -1]
(4) F(i, j) = false                                   if s1[i-1] != s3[i+j-1] && s2[j-1] != s3[i +j -1]

public class Solution {
    public boolean isInterleave(String s1, String s2, String s3) {
        // Start typing your Java solution below
        // DO NOT write main() function
        int len1 = s1.length(), len2 = s2.length(), len3 = s3.length();
        if(len3 != len1 + len2){
            return false;
        }
        
        boolean[][] match = new boolean[len1 + 1][len2 + 1];
        match[0][0] = true;
        
        // j == 0
        int i = 1;
        while(i <= len1 && s1.charAt(i-1) == s3.charAt(i-1)){
            match[i][0] = true;
            i++;
        }
        
        // i == 0
        int j = 1;
        while(j <= len2 && s2.charAt(j-1) == s3.charAt(j-1)){
            match[0][j] = true;
            j++;
        }
        
        for(int m = 1; m <= len1; m++){
            for(int n = 1; n <= len2; n++){
                char c = s3.charAt(m + n - 1);
                if(c == s1.charAt(m - 1)){
                    match[m][n] |= match[m-1][n];
                }
                if(c == s2.charAt(n - 1)){
                    match[m][n] |= match[m][n-1];
                }
            }
        }
        return match[len1][len2];
    }
}

 ref:http://fisherlei.blogspot.com/2012/12/leetcode-interleaving-string.html