87. Scramble String *HARD* 动态规划

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.

class Solution {
public:
    bool isScramble(string s1, string s2) {
        int l = s1.length(), i, j, k, t;
        if(0 == l)
            return true;
        vector<vector<vector<bool>>> dp(l, vector<vector<bool>>(l, vector<bool>(l+1, 0)));
        //dp[i][j][k] means s1 starts from index i, s2 starts from index j, if the length k substring is the same
        for(i = 0; i < l; i++)
        {
            for(j = 0; j < l; j++)
            {
                dp[i][j][1] = (s1[i] == s2[j]);
            }
        }
        for(k = 2; k <= l; k++)
        {
            for(i = 0; i < l && i+k <= l; i++)
            {
                for(j = 0; j < l && j+k <= l; j++)
                {
                    for(t = 1; t < k; t++)
                    {
                        dp[i][j][k] = dp[i][j][t] && dp[i+t][j+t][k-t] || dp[i][j+k-t][t] && dp[i+t][j][k-t];
                        if(dp[i][j][k])
                            break;
                    }
                }
            }
        }
        return dp[0][0][l];
    }
};