Equivalent Strings————分治与归并

太过爱你忘了你带给我的痛 2022-05-17 00:51 131阅读 0赞

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 b1  
As 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.

**Examples**  
Input  
aaba  
abaa  
**Output**  
YES  
Input  
aabb  
abab  
**Output**  
NO  
**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”.

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利用分治的思想，递归的将两个字符串不断地分，然后比较是否相等

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#include<bits/stdc++.h>
    using namespace std;
    const int MAXN=200000+50;
    char a[MAXN],b[MAXN];
    
    bool DFS(char *p1,char *p2,int len)//递归真强大 
    {
        if(!strncmp(p1,p2,len))
            return true;
        if(len%2)//字符串为长度为奇数时 
            return false;
        int n=len/2;
        if( DFS(p1,p2+n,n) && DFS(p1+n,p2,n))//a 的前一半与 b 的后一半相比 b 的前一半与a的后一般相比 相等 
            return true;
        if( DFS(p1,p2,n) && DFS(p1+n,p2+n,n))//a的前一半与b的前一半相等，a的后一半与b的后一半相等 
            return true;
        return false;
    }
    int main()
    {
        scanf("%s %s",a,b);
        if(DFS(a,b,strlen(a)))
            printf("YES\n");
        else
            printf("NO\n");
        return 0;
    }