POJ 1811 Prime Test（Miller-Rabin & Pollard-rho素数测试）

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.

 

题目大意：给一个数n，问是不是素数，若是输出Prime，若不是输出其最小的非1因子。

思路：http://www.2cto.com/kf/201310/249381.html

模板盗自：http://vfleaking.blog.163.com/blog/static/1748076342013231104455989/

 

代码（375MS）：

 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 #include <iterator>
 #include <vector>
 using namespace std;

 typedef long long LL;

 LL modplus(LL a, LL b, LL mod) {
    LL res = a + b;
    return res < mod ? res : res - mod;
 }

 LL modminus(LL a, LL b, LL mod) {
    LL res = a - b;
    return res >=  ? res : res + mod;
 }

 LL mult(LL x, LL p, LL mod) {
     LL res = ;
     while(p) {
         if(p & ) res = modplus(res, x, mod);
         x = modplus(x, x, mod);
         p >>= ;
     }
     return res;
 }

 LL power(LL x, LL p, LL mod) {
     LL res = ;
     while(p) {
         if(p & ) res = mult(res, x, mod);
         x = mult(x, x, mod);
         p >>= ;
     }
     return res;
 }

 bool witness(LL n, LL p) {
    int t = __builtin_ctz(n - );
    LL x = power(p % n, (n - ) >> t, n), last;
    while(t--) {
        last = x, x = mult(x, x, n);
        if(x ==  && last !=  && last != n - ) return false;
    }
    return x == ;
 }

 const int prime_n = ;
 int prime[prime_n] = {, , , , };

 bool isPrime(LL n) {
    if(n == ) return false;
    if(find(prime, prime + prime_n, n) != prime + prime_n) return true;
    if(n %  == ) return false;
    for(int i = ; i < prime_n; i++)
        if(!witness(n, prime[i])) return false;
    return true;
 }

 LL getDivisor(LL n) {
    int c = ;
    while (true) {
        int i = , k = ;
        LL x1 = , x2 = ;
        while(true) {
            x1 = modplus(mult(x1, x1, n), c, n);
            LL d = __gcd(modminus(x1, x2, n), n);
            if(d !=  && d != n) return d;
            if(x1 == x2) break;
            i++;
            if(i == k) x2 = x1, k <<= ;
        }
        c++;
    }
 }

 void getFactor(LL n, vector<LL> &ans) {
     if(isPrime(n)) return ans.push_back(n);
     LL d = getDivisor(n);
     getFactor(d, ans);
     getFactor(n / d, ans);
 }

 int main() {
     int T; LL n;
     scanf("%d", &T);
     while(scanf("%I64d", &n) != EOF) {
         if(isPrime(n)) puts("Prime");
         else {
             vector<LL> ans;
             getFactor(n, ans);
             printf("%I64d\n", *min_element(ans.begin(), ans.end()));
         }
     }
 }