POJ1811(SummerTrainingDay04-G miller-rabin判断素性 && pollard-rho分解质因数)

Prime Test

Time Limit: 6000MS		Memory Limit: 65536K
Total Submissions: 35528		Accepted: 9479
Case Time Limit: 4000MS

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

 

 //2017-08-16
 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <algorithm>
 #define ll long long

 using namespace std;

 const int TIMES = ;

 ll random0(ll n){
     return ((double)rand() / RAND_MAX*n + 0.5);
 }

 //快速乘a*b%mod
 ll quick_mul(ll a, ll b, ll mod){
     ll ans = ;
     while(b){
         if(b&){
             b--;
             ans = (ans+a)%mod;
         }
         b >>= ;
         a = (a+a) % mod;
     }
     return ans;
 }

 //快速幂a^b%mod
 ll quick_pow(ll a, ll n, ll mod){
     ll ans = ;
     while(n){
         if(n&)ans = quick_mul(ans, a, mod);
         a = quick_mul(a, a, mod);
         n >>= ;
     }
     return ans;
 }

 bool witness(ll a, ll n){
     ll tmp = n-;
     int i = ;
     while(tmp %  == ){
         tmp >>= ;
         i++;
     }
     ll x = quick_pow(a, tmp, n);
     if(x ==  || x == n-)return true;
     while(i--){
         x = quick_mul(x, x, n);
         if(x == n-)return true;
     }
     return false;
 }

 bool miller_rabin(ll n){
     if(n == )return true;
     if(n <  || n %  == )return false;
     for(int i  = ; i <= TIMES; i++){
         ll a = random0(n-)+;
         if(!witness(a, n))
               return false;
     }
     return true;
 }

 //factor存放分解出来的素因数
 ll factor[];
 int tot;

 ll gcd(ll a, ll b){
     if(a == )return ;
     if(a < )return gcd(-a, b);
     while(b){
         ll tmp = a % b;
         a = b;
         b = tmp;
     }
     return a;
 }

 ll pollard_rho(ll x, ll c){
     ll i = , k = ;
     ll x0 = rand()%x, x1 = x0;
     while(){
         i++;
         x0 = (quick_mul(x0, x0, x)+c)%x;
         ll d = gcd(x1-x0, x);
         if(d !=  && d != x)return d;
         if(x1 == x0)return x;
         if(i == k){
             x1 = x0;
             k += k;
         }
     }
 }

 //对n分解质因数
 void decomposition_factor(ll n){
     if(miller_rabin(n)){
         factor[tot++] = n;
         return;
     }
     ll p = n;
     while(p >= n){
         p = pollard_rho(p, rand()%(n-)+);
     }
     decomposition_factor(p);
     decomposition_factor(n/p);
 }

 int main()
 {
     int T;
     scanf("%d", &T);
     while(T--){
         ll n;
         scanf("%lld", &n);
         if(miller_rabin(n))
               printf("Prime\n");
         else{
             tot = ;
             decomposition_factor(n);
             ll ans = factor[];
             for(int i = ; i < tot; i++)
                   if(factor[i] < ans)ans  = factor[i];
             printf("%lld\n", ans);
         }
     }

     return ;
 }