HDU 5391 Zball in Tina Town【威尔逊定理】

<题目链接>

                              Zball in Tina Town

Problem Description

Tina Town is a friendly place. People there care about each other.
Tina has a ball called zball. Zball is magic. It grows larger every day. On the first day, it becomes 1 time as large as its original size. On the second day,it will become 2times as large as the size on the first day. On the n-th day,it will become n times as large as the size on the (n-1)-th day. Tina want to know its size on the (n-1)-th day mod n.

 

Input

The first line of input contains an integer T, representing the number of cases.
The following T lines, each line contains an integer n, according to the description.
T≤105,2≤n≤109

 

Output

For each test case, output an integer representing the answer.

 

Sample Input

2

3

10

 

Sample Output

2

0

 

解题分析：
此题一看到 (n-1)! 就要立刻想到威尔逊定理，当n为素数时，毫无疑问 (n-1)! %n=n-1 ,但是如果n不是素数，而是合数，应该怎么办呢？我们可以简单的试几个数，如果n为合数，我们发现

(n-1)!中总能够找出一些因子，使它们想乘为n,但是要注意4是个例外，由于4比较靠前，所以(4-1)!不一定能够凑出4，除了这种情况，其他的合数毫无疑问答案都为0。

 

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;


int juge(int x)
{
    for(int i=2;i*i<=x;i++)
    {
        if(x%i==0)return false;
    }
    return true;
}

int main()
{
    
    int t;cin>>t;
    while(t--)
    {
        int n;
        scanf("%d",&n);
        if(n==4)
        {
            printf("2
");
        } 
        else
        {
            if(juge(n))
            {
                printf("%d
",n-1);
            }
            else
            printf("0
");
        }        
    }
    return 0;
}

 

 

2018-07-31