LeetCode87 Scramble String

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

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.

分析：

先考虑递归地解法， 对于字符串，枚举其分割位置i - 1，只有有一种分割位置满足

(isScramble(s1.substr(0, i),s2.substr(0, i))  &&  isScramble(s1.substr(i, s1.size() - i),s2.substr(i, s1.size() - i))

或者

(isScramble(s1.substr(0, i),s2.substr(s1.size() - i, i)) && isScramble(s1.substr(i, s1.size() - i), s2.substr(0,s1.size() - i)))

二者之一成立，则返回true，每个位置枚举后均不成立，则返回false

注：要有一些优化，否则超时过不了，比如s1 == s2 直接返回true， 将s1 s2排个序，之后不相等则直接返回false。

代码：

class Solution {
public:
    bool isScramble(string s1, string s2) {
        if (s1 == s2) {
            return true;
        }
        if (s1.size() != s2.size()) {
            return false;
        }
        if (s1.size() == 1 && s1[0] == s2[0]) {
            return true;
        }
        string cmps1 = s1;
        string cmps2 = s2;
        sort(cmps1.begin(), cmps1.end());
        sort(cmps2.begin(), cmps2.end());
        if (cmps1 != cmps2) {
            return false;
        }
        for (int i = 1; i < s1.size(); ++i) {
            if ( (isScramble(s1.substr(0, i),s2.substr(0, i)) 
                  && isScramble(s1.substr(i, s1.size() - i),s2.substr(i, s1.size() - i)))
             || (isScramble(s1.substr(0, i),s2.substr(s1.size() - i, i)) 
                  && isScramble(s1.substr(i, s1.size() - i), s2.substr(0,s1.size() - i))) ) {
                return true;
            }
        }
        return false;
    }
};

好像还有三维动态规划的解法，回头再学习一个...