Zball in Tina Town（数论规律题+特判+较大数判是否为素数的正确姿势）

Link：http://acm.hdu.edu.cn/showproblem.php?pid=5391

Zball in Tina Town

Time Limit: 3000/1500 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)

Total Submission(s): 138 Accepted Submission(s): 98



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 2 times
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 modulo 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

Source

BestCoder Round #51 (div.2)



官方题解：

这题就是求 (n-1)!modn(n−1)! mod n

如果nn为合数，显然答案为0.

如果nn为素数，那么由威尔逊定理可得答案为 n-1n−1

注意有个trick为 nn =
4

注意：输入的n比较大，要先打素数表再判是否为素数才不会TLE！！！

AC code：

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<queue>
#include<math.h>
#include<vector>
#include<map>
#include<set>
#include<cmath>
#include<string>
#include<algorithm>
#include<iostream>
#define LL long long 
#define MAXN 1000010
using namespace std;
const int INF=0x3f3f3f3f;
const int N = 100005;
const int MOD = 9901;
LL n,ans;
bool prime
;
int p
;//保存素数 
int cnt;
void isprime()//素数筛选 
{
    cnt = 0;
    memset(prime,true,sizeof(prime));
    for(int i=2; i<N; i++)
    {
        if(prime[i])
        {
            p[cnt++] = i;
            for(int j=i+i; j<N; j+=i)
                prime[j] = false;
        }
    }
}
bool Judge(LL A)//判断是否为素数，是素数则返回true 
{
    for(int i=0; p[i]*p[i] <= A; i++)
    {
        if(A % p[i] == 0)
        {
            return false;
        }
    }
    return true;
}
int main()
{
    //freopen("D:\in.txt","r",stdin);
    int t;
    isprime();
    scanf("%d",&t);
    while(t--)
    {
        scanf("%I64d",&n);
        if(n==4)//特判 
		{
			printf("2\n");
		 } 
        else if(!Judge(n))
        {
            printf("0\n");
        }
        else
        {
            printf("%I64d\n",n-1);
        }
    }
    return 0;
}