HDU 5651 xiaoxin juju needs help(BestCoder Round #77 (div.1)1001)

传送门

xiaoxin juju needs help

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 861    Accepted Submission(s): 243

Problem 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≤20)  which represents the number of test cases.
For each test case, there is a single line containing a string  S(1≤length(S)≤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
   
   
   
   

 

Source

BestCoder Round #77 (div.2)

 

题目大意：

xiaoxin巨从小就喜欢字符串，六年级的时候他就知道了什么是回文串。这时，xiaoxin巨说到：如果一个字符串 $S$ 是回文串，那么该字符串从前往后看和从后往前看是一样一样的。

六年级的暑假，xiaoxin很快就做完了暑假作业，然后到腾讯做起了实习生。这日，leader给了xiaoxin一个字符串，请xiaoxin帮忙写一个函数来生成所有可能的回文串，可以任意改变字符串的顺序但是不可以扔掉某个字符。并且leader告诉xiaoxin，每生成一个不一样的回文串就可以得到一颗西瓜糖。

请你帮忙计算xiaoxin的leader最多需要买多少颗西瓜糖呢？

解题思路：

回文字符串的个数可以根据一个公式来推导一下：

条件：

1.len = strlen(str),len>>=1;

2.num[i]：表示的是字符串每个字符 -  'a' 的个数，然后将其除以2；

结果： ret  =  (len!)/(num[0]! * num[1]! * ... * num[25]!)  MOD 1e9+7;

根据这个公式我们只需要求一下阶乘的逆元就行了，因为是取模的运算，所以我们一边乘一边取模，不会超long long,最后不要忘记的是，如果是负数要转化为正数在进行取模，最后就是乘起来就行了。。。

 

My Code:

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
typedef long long LL;
const int MOD = 1e9+7;
const int MAXN = 1e3+5;
char str[MAXN];
int num[28];
LL a[28];
void Ex_gcd(LL a, LL b, LL &x, LL &y)
{
    if(b == 0)
    {
        x = 1;
        y = 0;
        return;
    }
    LL x1, y1;
    Ex_gcd(b, a%b, x1, y1);
    x = y1;
    y = x1-(a/b)*y1;
}
int main()
{
    int T;
    cin>>T;
    while(T--)
    {
        cin>>str;
        int len = strlen(str);
        memset(num, 0, sizeof(num));
        for(int i=0; i<len; i++)
            num[str[i]-'a']++;
        int sum = 0;
        for(int i=0; i<26; i++)
            if(num[i]%2)
                sum++;
        if(sum >= 2)
            puts("0");
        else
        {
            LL ret = 1;
            len>>=1;
            for(int i=0; i<26; i++)
            {
                LL x, y;
                num[i]>>=1;
                a[i] = 1;
                for(int j=1; j<=num[i]; j++)
                    a[i] = a[i]*j%MOD;
                Ex_gcd(a[i], MOD, x, y);
                x = (x%MOD+MOD)%MOD;
                a[i] = x;
            }
            for(int i=1; i<=len; i++)
                ret = ret*i%MOD;
            for(int i=0; i<26; i++)
                ret = ret*a[i]%MOD;
            printf("%lld\n",ret%MOD);
        }   
    }
    return 0;
}