【LeetCode】Scramble String 解题报告

【题目】

Given a string s1, we may represent it as a binary tree by partitioning it to two non-empty substrings recursively.

Below is one possible representation of s1 = "great":

    great
   /    \
  gr    eat
 / \    /  \
g   r  e   at
           / \
          a   t

To scramble the string, we may choose any non-leaf node and swap its two children.

For example, if we choose the node "gr" and swap its two children, it produces a scrambled string "rgeat".

    rgeat
   /    \
  rg    eat
 / \    /  \
r   g  e   at
           / \
          a   t

We say that "rgeat" is a scrambled string of "great".

Similarly, if we continue to swap the children of nodes "eat" and "at", it produces a scrambled string "rgtae".

    rgtae
   /    \
  rg    tae
 / \    /  \
r   g  ta  e
       / \
      t   a

We say that "rgtae" is a scrambled string of "great".

Given two strings s1 and s2 of the same length, determine if s2 is a scrambled string of s1.

【解析】

题意：判断两个字符串是否能通过二叉树的左右子树交换相等。

【递归解法】

其实也是暴力遍历，把s1，s2分别分成两部分，判断s1的两部分和s2的两部分是否分别可以交换相等。

public class Solution {
    public boolean isScramble(String s1, String s2) {
        if (s1.length() != s2.length()) return false;
        if (s1.equals(s2)) return true;
        char[] c1 = s1.toCharArray();
        char[] c2 = s2.toCharArray();
        Arrays.sort(c1);
        Arrays.sort(c2);
        if (!Arrays.equals(c1, c2)) return false;
        for (int i = 1; i < s1.length(); i++) {
            if (isScramble(s1.substring(0, i), s2.substring(0, i)) && isScramble(s1.substring(i), s2.substring(i))) return true;
            if (isScramble(s1.substring(0, i), s2.substring(s2.length() - i)) && isScramble(s1.substring(i), s2.substring(0, s2.length() - i))) return true;
        }
        return false;
    }
}

参考：https://leetcode.com/discuss/3632/any-better-solution

【动态规划解法】

这道题用二维数组来存储中间结果已经不行了，需要一个三维数组 dp[i][j][len]，表示从s1的第i个字符开始长度为len的子串，和从s2的第j个字符开始长度为len的子串，是否互为scramble。

初始化为dp[i][j][1] = s1.charAt(i) == s2.charAt(j)，即长度为1的子串是否互为scramble。

三维数组就要三层循环，最终结果为dp[0][0][s1.length()]，即从s1的第0个字符开始长度为s1.length()的子串，即s1本身和s2本身是否互为scramble。

要判断dp[i][j][len]的值，就要把s1从i开始长度为len的串分别从k=1, 2 ... len-1处切开，判断切成的两半和s2同样切成的两半是否互为scramble，只要有一种切法满足条件，那么dp[i][j][len]就为true，否则为false。

public class Solution {
    public boolean isScramble(String s1, String s2) {
        if (s1.length() != s2.length()) return false;
        if (s1.equals(s2)) return true;
        
        boolean[][][] dp = new boolean[s1.length()][s2.length()][s1.length() + 1];
        for (int i = 0; i < s1.length(); i++) {
            for (int j = 0; j < s2.length(); j++) {
                dp[i][j][1] = s1.charAt(i) == s2.charAt(j);
            }
        }
        
        for (int len = 2; len <= s1.length(); len++) {
            for (int i = 0; i < s1.length() - len + 1; i++) {
                for (int j = 0; j < s2.length() - len + 1; j++) {
                    for (int k = 1; k < len; k++) {
                        dp[i][j][len] |= dp[i][j][k] && dp[i + k][j + k][len - k] || dp[i][j + len - k][k] && dp[i + k][j][len - k];
                    }
                }
            }
        }
        
        return dp[0][0][s1.length()];
    }
}

参考：http://blog.youkuaiyun.com/linhuanmars/article/details/24506703