leetcode@ [87] Scramble String (Dynamic Programming)

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.

 1 class Solution {
 2 public:
 3     bool check(string s1, string s2) {
 4         if(s1.length() != s2.length()) return false;
 5         
 6         string cp1 = s1, cp2 = s2;
 7         sort(cp1.begin(), cp1.end());
 8         sort(cp2.begin(), cp2.end());
 9         for(int i=0; i<cp1.length(); ++i) {
10             if(cp1[i] != cp2[i]) return false;
11         }
12         return true;
13     }
14     bool dfs(string s1, string s2) {
15         int m = s1.length(), n = s2.length();
16         if(!check(s1, s2))  return false;
17         if(m == 1) {
18             if(s1 == s2)  return true;
19             return  false;
20         }
21         
22         string l, r, p, q;
23         for(int le = 1; le < m; ++le) {
24             l = s1.substr(0, le);
25             r = s1.substr(le, m - le);
26             p = s2.substr(0, le);
27             q = s2.substr(le, m - le);
28             if(dfs(l, p) && dfs(r, q))  return true;
29             else {
30                 p = s2.substr(m - le, le);
31                 q = s2.substr(0, m - le);
32                 if(dfs(l, p) && dfs(r, q))  return true;
33             }
34         }
35         
36         return false;
37     }
38 
39     bool isScramble(string s1, string s2) {
40         int m = s1.length(), n = s2.length();
41         
42         if(m != n)  return false;
43         
44         return dfs(s1, s2);
45     }
46 };

View Code