87. Scramble String

Given a strings1, we may represent it as a binary tree by partitioning it to two non-empty substrings recursively.

Below is one possible representation ofs1="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.

Discussion

区间dp:

dp[start][end] = dp[start][mid] && dp[mid+1][end]

(s1, s1start, mid, s2, s2start, mid) || (s1, s1start, s1end, s2end - mid, s2end)