hdu5651 xiaoxin juju needs help (多重集的全排列+逆元)

Posted 2020-07-03 Shentr

xiaoxin juju needs help

 

题意：给你一个字符串，求打乱字符后，有多少种回文串。                      （题于文末）

 

知识点：

    n个元素，其中a1，a2，····，an互不相同，进行全排列，可得n!个不同的排列。

    若其中某一元素ai重复了ni次，全排列出来必有重复元素，其中真正不同的排列数应为 ，即其重复度为ni!

    同理a1重复了n1次，a2重复了n2次，····，ak重复了nk次，n1+n2+····+nk=n。

    对于这样的n个元素进行全排列，可得不同排列的个数实际上是

   

题解：

字符串长度为len,若每个元素的重复次数ni为奇数的个数count>1,则无法形成回文串。

当能构成回文串时，我们只需考虑这个回文串左半部分的情况，所以这个问题也就变成了求一半字符串的有重复的全排列。

因为涉及到除法取模的问题，所以用到逆元。

逆元可以用扩展欧几里得，或费马小定理。/*6.逆元*/

 

 

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
typedef long long LL;
const LL MOD=1e9+7;
int cnt[260];
char ch[1005];

LL jiecheng(int n)
{
    if(n==0)
        return 1;
    LL ans=1;
    for(int i=1;i<=n;i++)
        ans=ans*i%MOD;
    return ans;
}

LL x,y;
LL gcd(LL a,LL b)
{
    LL t,d;
    if(b==0)
    {
         x=1,y=0;
         return a;
    }
     d=gcd(b,a%b);
     t=x, x=y, y=t-(a/b)*y;
     return d;
 }

int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        memset(cnt,0,sizeof(cnt));
        scanf("%s",ch);
        int len=strlen(ch);
        for(int i=0;i<len;i++)
        {
            cnt[ch[i]-\' \']++;
        }
        int count=0;
        for(int i=0;i<260;i++)
        {
            if(cnt[i]&1)
                count++;
            cnt[i]/=2;
        }
        if(count>1)
        {
            cout<<0<<endl;
            continue;
        }
        LL ans=jiecheng(len/2)%MOD;
        for(int i=0;i<260;i++)
        {
            if(cnt[i]>0)
            {
                gcd(jiecheng(cnt[i]),MOD);
                if(x<0)
                    x+=MOD;
                ans=ans*x%MOD;
            }
        }
        cout<<ans<<endl;
    }
}

 

 

 

xiaoxin juju needs help

Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status

Description

As we all known, xiaoxin is a brilliant coder. He knew **palindromic** strings when he was only a six grade student at elementry school.
This summer he was working at Tencent as an intern. One day his leader came to ask xiaoxin for help. His leader gave him a string and he wanted xiaoxin to generate palindromic strings for him. Once xiaoxin generates a different palindromic string, his leader will give him a watermelon candy. The problem is how many candies xiaoxin\'s leader needs to buy?

Input

This problem has multi test cases. First line contains a single integer $T(T\\leq 20)$ which represents the number of test cases.
For each test case, there is a single line containing a string $S(1 \\leq length(S) \\leq 1,000)$.

Output

For each test case, print an integer which is the number of watermelon candies xiaoxin\'s leader needs to buy after mod $1,000,000,007$.

Sample Input

3 aa aabb a

Sample Output

1 2 1