97. Interleaving String

Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.

Example 1:

Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbcbcac"
Output: true

Example 2:

Input: s1 = "aabcc", s2 = "dbbca", s3 = "aadbbbaccc"
Output: false

 

Approach #1: DP. [C++]

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        //if (s1 == "" && s2 == "" && s3 == "") return true;
        //if (s1 == "" || s2 == "" || s3 == "") return false;
        if (s1.length() + s2.length() != s3.length()) return false;
        
        vector<vector<bool>> match(s1.length()+1, vector<bool>(s2.length()+1, false));
        match[0][0] = true;
        
        for (int idx = 0; idx < s1.length() + s2.length(); ++idx) {
            for (int s1Len = 0; s1Len <= idx+1 && s1Len <= s1.length(); ++s1Len) {
                int s2Len = idx + 1 - s1Len;
                if (s2Len > s2.length()) continue;
                if ((s1Len > 0 && match[s1Len-1][s2Len] && s3[idx] == s1[s1Len-1]) ||
                    (s2Len > 0 && match[s1Len][s2Len-1] && s3[idx] == s2[s2Len-1]))
                    match[s1Len][s2Len] = true;
            }
        }
        
        return match[s1.length()][s2.length()];
    }
};

　　

Analysis:

status: match[s1Len][s2Len] represent s1Len characters in s1 and s2Len characters in s2 wether match with s1Len+s2Len characters in s3.

init: match[0][0] = true;

func: 

result: match[s1.length()][s2.length()].