【POJ1811】【miller_rabin + pollard rho + 快速乘】Prime Test

Description

Given a big integer number, you are required to find out whether it's a prime number.

Input

The first line contains the number of test cases T (1 <= T <= 20 ), then the following T lines each contains an integer number N (2 <= N < 2⁵⁴).

Output

For each test case, if N is a prime number, output a line containing the word "Prime", otherwise, output a line containing the smallest prime factor of N.

Sample Input

2
5
10

Sample Output

Prime
2

Source

POJ Monthly

【分析】

模板题

 /*
 宋代谢逸
 《踏莎行·柳絮风轻》
 柳絮风轻，梨花雨细。春阴院落帘垂地。碧溪影里小桥横，青帘市上孤烟起。
 镜约关情，琴心破睡。轻寒漠漠侵鸳被。酒醒霞散脸边红，梦回山蹙眉间翠。
 */
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <cmath>
 #include <queue>
 #include <vector>
 #include <iostream>
 #include <string>
 #include <ctime>
 #define LOCAL
 const int MAXN =  + ;
 using namespace std;
 typedef long long ll;
 ll n, Ans;

 //快速乘
 long long multi(long long a, long long b, long long c){
     if (b == ) return ;
     if (b == ) return a % c;
     long long tmp = multi(a, b / , c);
     if (b %  == ) return (tmp + tmp) % c;
     else return (((tmp + tmp) % c) + a) % c;
 }
 ll pow(ll a, ll b, ll p){
     if (b == ) return a % p;
     ll tmp = pow(a, b / , p);
     if (b %  == ) return (multi(tmp, tmp, p));
     else return multi(multi(tmp, tmp, p), (a % p), p);
 }
 //二次探测
 bool Sec_Check(ll a, ll p, ll c){
     ll tmp = pow(a, p, c);
     if (tmp !=  && tmp != (c - )) return ;//不通过
     if (tmp == (c - ) || (p %  != )) return ;
     return Sec_Check(a, p / , c);
 }
 bool miller_rabin(ll n){
     ll cnt = ;
     while (cnt--){
         ll a = (rand()%(n - )) + ;
         if (!Sec_Check(a, n - , n)) return ;
     }
     return ;
 }
 //int f(int ) {return }
 long long gcd(long long a, long long b){return b == ? a : gcd(b, a % b);}
 long long BIGRAND() {return rand() * RAND_MAX + rand();}
 long long pollard_rho(long long n, long long c){
     long long x, y, d;
     long long i = , k = ;
      x = ((double)rand()/RAND_MAX*(n - )+0.5) + ;
     y = x;
     while(){
         i++;
           //注意顺序
         x = (multi(x, x, n) % n + c) % n;
         d = gcd(y - x + n, n);
         if( < d && d < n) return d;
         if(y == x) return n;
         if(i == k){
             y = x;
             k <<= ;
         }
     }
 }
 //
 void find(long long n, long long c){
     if (n == ) return;
     if (miller_rabin(n)) {
         if (Ans == -) Ans = n;
         else Ans = min(Ans, n);
         return ;
     }
     long long p = n;
     while (p >= n) p = pollard_rho(n, c--);
     find(p, c);
     find(n / p, c);
     //return find(p, c) + find(n / p, c);
 }

 int main(){
     int T;
     srand(time());

     scanf("%d", &T);
     while (T--){
         scanf("%lld", &n);
         if (n !=  && miller_rabin(n)) printf("Prime\n");
         else {
             Ans = -;
             find(n, );
             printf("%lld\n", Ans);
         }
     }
     return ;
 }