CSU-ACM2017暑假集训比赛7 A

A - Equivalent Strings

Today on a lecture about strings Gerald learned a new definition of string equivalency. Two strings a and b of equal length are called equivalent in one of the two cases:    They are equal.    If we split string a into two halves of the same size a1 and a2, and string b into two halves of the same size b1 and b2, then one of the following is correct:        a1 is equivalent to b1, and a2 is equivalent to b2        a1 is equivalent to b2, and a2 is equivalent to b1As a home task, the teacher gave two strings to his students and asked to determine if they are equivalent.Gerald has already completed this home task. Now it's your turn!

Input

The first two lines of the input contain two strings given by the teacher. Each of them has the length from 1 to 200 000 and consists of lowercase English letters. The strings have the same length.

Output

Print "YES" (without the quotes), if these two strings are equivalent, and "NO" (without the quotes) otherwise.

Example
Input

aabaabaaOutputYESInputaabbababOutputNO

Note

In the first sample you should split the first string into strings "aa" and "ba", the second one — into strings "ab" and "aa". "aa" is equivalent to "aa"; "ab" is equivalent to "ba" as "ab" = "a" + "b", "ba" = "b" + "a".In the second sample the first string can be splitted into strings "aa" and "bb", that are equivalent only to themselves. That's why string "aabb" is equivalent only to itself and to string "bbaa".

考深度优先搜索的一道题。

给出两个字符串a、b，判断他们是否“等价”。满足以下条件之一时称两个字符串“等价”：
1、两字符串相等；
2、将a均分为a1、a2两个子串，将b均分为b1、b2两个子串。存在： ①“a1与b1‘等价’，且a2与b2‘等价’” 或者 ②“a1与b2‘等价’，且a2与b1‘等价’”

可以看出，“等价”这个条件是递归地作用于子串上的。即我们在认定两个字符串“等价”前，先要判断它们各自的子串是否满足“等价”条件，故使用深度优先搜索进行判断。

需要注意一点：如果分出的两子串不相等，需要判断串的长度，若长度数值为奇数是不能继续均分的，递归过程不能继续进行，这时候可以得出子串“不等价”的结论。

#include <iostream>#include <cstdio>#include <algorithm>#include <vector>#include <cstring>#include <string>#include <queue>using namespace std;bool check(string strA, string strB) {    int len = strA.length();    if(strA == strB)        return true;    if(len & 1) // 已知不相等的两子串长度数值为奇数，不可再分，返回假。        return false;    string subA1 = strA.substr(0, len / 2);    string subB1 = strB.substr(0, len / 2);    string subA2 = strA.substr(len / 2, len / 2);    string subB2 = strB.substr(len / 2, len / 2);    if(check(subA1, subB2) && check(subA2, subB1))        return true;    if(check(subA1, subB1) && check(subA2, subB2))        return true;    return false;}int main() {#ifdef TEST    freopen("test.txt", "r", stdin);#endif // TEST    string strA, strB;    cin >> strA >> strB;    if(check(strA, strB))        cout << "YES" << endl;    else        cout << "NO" << endl;    return 0;}