leetcode Scramble String 解题思路

https://leetcode.com/problems/scramble-string/

首先递归，或说是递推是最容易想到的：

F(s1(i,j), s2(i,j)) = F(s1(i,k),s2(i,k)) && F(s1(j-k,j),s2((j-k,j))

|| F(s1(i,k),s2(j-k,j)) && F(s1(j-k,j),s2(i,k)) i<k<j;

图解：

F(s1, s2) = F(s11,s21) && F(s12,s22)

|| F(s11,s22) && F(s12,s21) i<k<j;

简单的用递归编程会超时，因为有太多重复的计算，因此，我们希望能够减少重复，即每个状态只计算一次，通常，这样的状态会用一个矩阵来记录状态。对于这个问题，一个简单的矩阵不够用，需要多个矩阵。

先看一些简单的，是或不是scramble string的状态：

总结出规律：对角有一组满足，都是true，就是scramble string。

再看一个3个字母的演化情况：

当维度再一步扩大的时候，还要综合考虑前面数个表的组合判断，这里我偷懒不画，原理其实是一样的。

代码地址：

https://github.com/LKF10051/LeetCode/blob/master/LeetCode/scramble_string.cpp

时间： 2024-10-05 18:54:10

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