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

2310

 

Sample Output

20

 

Source

BestCoder Round #51 (div.2)

 

官方题解：

这题就是求 $(n-1)!modn$

如果$n$为合数，显然答案为0.

如果$n$为素数，那么由威尔逊定理可得答案为 $n-1$

注意有个trick为 $n$ = 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 1000010using namespace std;const int INF=0x3f3f3f3f;const int N = 100005;const int MOD = 9901;LL n,ans;bool prime[N];int p[N];//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;}