HDU 5391-Zball in Tina Town(威尔逊定理)

Zball in Tina Town
Time Limit: 3000/1500 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 276 Accepted Submission(s): 168

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)

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

分析：
在初等数论中，威尔逊定理给出了判定一个自然数是否为素数的充分必要条件。即：当且仅当p为素数时：( p -1 )! ≡ -1 ( mod p )，但是由于阶乘是呈爆炸增长的，其结论对于实际操作意义不大。
hdu5391用到了这一数论定理。
题意：求 （n-1）%n，
合数为0，因为1 ~ n-1中必定有积为n（除了4）
质数为n-1，威尔逊定理( p -1 )! ≡ -1 ( mod p )

#include 
#include 

using namespace std;

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        int N;
        scanf("%d",&N);
        int ok = 0;
        if(N == 4)
        {
             puts("2");
             continue;
        }
        else if(N == 1)
            printf("0\n");
        else if(N % 2 == 0)
        {
             puts("0");
             continue;
        }
        else
        {
            int m = sqrt(N);
            for(int i = 3;i <= m;i += 2)
            {
                if(N % i == 0)
                {
                    ok = 1;
                    break;
                }
            }
            if(ok)
                puts("0");
            else
                printf("%d\n",N - 1);
        }
    }
    return 0;
}