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

样例
比如 s1 = "aabcc" s2 = "dbbca"

• 当 s3 = "aadbbcbcac"，返回 true.
• 当 s3 = "aadbbbaccc"， 返回 false.

分析

动态规划问题
dp[i][j]：表示前i个和前j 个是否构成
显然当第s3的i+j个字符，就两种可能，一个等于s1,一个等于s2。

代码

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