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题目链接:https://leetcode.com/problems/scramble-string/
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.
思路:可以用递归来做,也可以用动态规划来做。递归的思路是两个字符串各找一个分割点,例如s1 和 s2使得要么:
1. s1分割点左边的字符串和s2分割点左边的字符串相等或者可以通过交换相等,并且s1右边的子串和s2右子串同样符合此规律
2. s1的左子串和s2的右子串相等或者可以交换使得相等,并且s1的右子串和s2的左子串符合同样的规律
如果不剪枝,会超时,可以通过判断两个字符串的字母是否个数一样来剪枝。
代码如下:
class Solution {public: bool isScramble(string s1, string s2) { if(s1 == s2) return true; if(s1.size() != s2.size() || s1.size() ==1) return false; int len = s1.size(), num = len; vector hash(26, 0); for(auto val: s1) hash[val-'a']++; for(auto val: s2) if(hash[val-'a']) hash[val-'a']--, num--; if(num != 0) return false; for(int i = 1; i < len; i++) { if(isScramble(s1.substr(0, i), s2.substr(0, i)) && isScramble(s1.substr(i), s2.substr(i))) return true; if(isScramble(s1.substr(0, i), s2.substr(len-i)) && isScramble(s1.substr(i), s2.substr(0, len-i))) return true; } return false; }};参考:http://fisherlei.blogspot.com/2013/01/leetcode-scramble-string.html
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