题面:
An anagram is a word or phrase formed by rearranging the letters of another word or phrase, using all the original letters exactly once, such as "post", "stop", and "spot".
You are given a string s consisting of lowercase English letters. Your task is to count how many distinct anagrams of the string s are palindromes.
A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward, such as "madam" or "racecar".
For example, "aabb" has 6 distinct anagrams, which are: "aabb", "abab", "abba", "baab", "baba", "bbaa". Two of the previous anagrams are palindromes, which are: "abba", "baab".
Input:
The first line contains an integer T, where T is the number of test cases.
The first line of each test case contains an integer n (1 ≤ n ≤ 20), where n is the length of the string s.
The second line of each test contains a string s of length n consisting of lowercase English letters.
Output:
For each test case, print a single line containing how many distinct anagrams of the string s are palindromes.
Example:
分析:
我感觉我真是弱回文串……好像除了杭电那道入门题之外我还从来没做对过一道回文串的题,看见就脑壳痛,但是没有办法,生活所迫,迟早还是要去啃的。据大佬指点是一道排列组合题,黑板上排列组合,我果然还是解不开。首先根据n的奇偶性判断能不能产生回文串,如果n为偶数,那么每种字母出现的次数都要为偶数才会出现回文串,如果n是奇数,那么有且必须有一种字母的出现次数为奇数,其余字母都出现偶数次。判断了之后用排列组合来算回文串种类,因为是回文所以从中间为轴对称,只算前半段的情况就行了,如果是总偶数个,那么不存在正中间的数,如果是总奇数个,那么中间的字母是固定的,必须是出现次数为奇数的那种字母,所以也可以直接用n/2的方式来算前半段,刚好可以把那0.5去尾。
前半段总的排列情况就是(n/2)!,其中重复的情况就是字母相同排列互换,比如两个a,aa和aa就是重复的情况,都算在(n/2)!里了,所以要除以每一种字母的(num[i]/2)!,考虑到会不会爆int,用了long long, 不过用没用上我不确定。
然而最后还是一直有点小问题,找了半天发现出在memset上……memset(num,sizeof(num),0)这个也太丢人了……我果然是memset都写不对了啊。
AC代码:
#include
#include
#include
#include
using namespace std;
int t, n;
int num[26];
bool flag;
int main(){
cin>>t;
while(t--){
cin>>n;
string str;
cin>>str;
memset(num, 0, sizeof(num));
flag = true;
for(int i = 0; i < n; i++){
num[str[i] - 'a']++;
}
if(n % 2 == 0){
for(int i = 0; i < 26; i++) {
if(num[i] % 2 != 0) {
flag = false;
break;
}
}
}
else{
int u = 0;
for(int i = 0; i < 26; i++){
if(num[i] % 2 == 1) u++;
}
if(u != 1) flag = false;
}
if(!flag){
cout<<0<