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

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

巴特西

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

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