poj1811 pollard-rho大数分解质因子+Miller_Rabin判断质数

/*
Time:2019.12.10
Author: Goven
type：pollard-rho大数分解质因子+Miller_Rabin判断质数 
ref:
代码：
https://blog.csdn.net/xiaolonggezte/article/details/60965540
https://blog.csdn.net/nash142857/article/details/8274932
解释：https://www.cnblogs.com/Doggu/p/MillerRabin_PollardRho.html 
*/

//Time Limit Exceeded
#include
#include//time
#include//rand()
using namespace std;
typedef long long ll;

ll factor[100005];
int cnt = 0;

ll Mult_mod (ll a, ll b, ll mod) {//大数乘法 
    a %= mod;//att1:不要漏 
    b %= mod;
    ll res = 0;
    while (b) {
        if (b & 1) res = (res + a) % mod;//可以用减法，速度比取模快 
        a = a * 2 % mod;
        b >>= 1; 
    }
    return res;
}

ll pow_mod (ll a, ll b, ll mod) {//快速幂 
    a = a % mod;//att2：不要漏 
    ll res = 1;
    while (b) {
        if (b & 1) res = Mult_mod(res, a, mod);
        a = Mult_mod(a, a, mod);
        b >>= 1;
    }
    return res;
}

bool Check (ll a, ll n, ll x, ll t) {//二次探测判断是否为合数 
    a = pow_mod(a, x, n);
    ll last;
    for (int i = 0; i < t; i++) {
        last = a;
        a = Mult_mod(a, a, n); 
        if (a == 1 && last != 1 && last != (n - 1)) return true;    
    }
    if (a != 1) return true;
    return false;
} 

bool Miller_Rabin (ll n, int k) {//判断是否是素数 
    if (n < 2) return false;
    if (n == 2) return true;
    if ((n & 1) == 0) return false;//step1:粗筛 
    ll x = n - 1, t = 0;//step2：二次探测 
    while ((x & 1) == 0) x >>= 1, t++;
    for (int i = 0; i < k; i++) {
        ll a = rand() % (n - 1) + 1;
        if (Check(a, n, x, t)) 
            return false;
    }
    return true;
} 

ll f (ll x, ll mod, ll c) {//伪随机函数生成xi 
    return (Mult_mod(x, x, mod) + c) % mod;
}

ll gcd (ll a, ll b) {
    if (a < 0) return gcd(-a, b);
    return b ? gcd(b, a % b) : a;
}

ll Pollard_rho (ll n, ll c) {//寻找x的某个质因数
    ll a = rand() % n;
    ll b = a;
    ll i = 1, k = 2;
    while (1) {
        i++;
        a = f(a, n, c);
        ll d = gcd(a - b, n);
        if (d != 1 && d != n) return d;
        if (a == b) return n;//循环节
        if (i == k) {
            b = a;
            k += k;
        }        
    }
} 

void findFac (ll n) {//分解质因子 
    if (Miller_Rabin(n, 5)) {
        factor[cnt++] = n;
        return;
    }
    ll p = n;
    while (p >= n) p = Pollard_rho(p, (ll)rand()%(n - 1) + 1);//err1:(ll)没加 
    findFac(p);
    findFac(n / p);
}
int main()
{
    srand(time(NULL));//头文件ctime    
    int t;
    ll n;
    cin >> t;
    while(t--) {
        cin >> n;
        cnt = 0;//err2:漏了 
        findFac(n);
        if (cnt == 1) cout << "Prime" << endl;
        else {
            ll tp = factor[0];
            for (int i = 1; i < cnt; i++) {
                if (tp > factor[i]) tp = factor[i];
            }
            cout << tp << endl;
        } 
    }
    return 0;
}