8.交叉字符串

题目：给出三个字符串:s1、s2、s3，判断s3是否由s1和s2交叉构成。

class Solution {
public:
    /**
     * Determine whether s3 is formed by interleaving of s1 and s2.
     * @param s1, s2, s3: As description.
     * @return: true of false.
     */
    bool isInterleave(string s1, string s2, string s3) {
        // write your code here
      if (s3.length() != s1.length()+s2.length())
            return false;
        if (s1.length() == 0)
            return s2 == s3;
        if (s2.length() == 0)
            return s1 == s3;
        vector<vector<bool> > dp(s1.length()+1, vector<bool>(s2.length()+1, false));
        dp[0][0] = true;
        for (int i = 1; i <= s1.length(); i++)
            dp[i][0] = dp[i-1][0]&&(s3[i-1] == s1[i-1]);
        for (int i = 1; i <= s2.length(); i++)
            dp[0][i] = dp[0][i-1]&&(s3[i-1] == s2[i-1]);
        for (int i = 1; i <= s1.length(); i++) {
            for (int j = 1; j <= s2.length(); j++) {
                int t = i+j;
                if (s1[i-1] == s3[t-1])
                    dp[i][j] = dp[i][j]||dp[i-1][j];
                if (s2[j-1] == s3[t-1])
                    dp[i][j] = dp[i][j]||dp[i][j-1];
            }
        }
        return dp[s1.length()][s2.length()];
    }
};