poj2191 pollard-rho大数分解质因子+Miller_Rabin判断质数

/*
Time:2019.12.11
Author: Goven
type：pollard-rho大数分解质因子+Miller_Rabin判断质数
ref:
*/
#include
#include
#include
#include 
using namespace std;
typedef long long ll;
 
int cnt = 0;
ll factor[1000];

ll Mult_mod (ll a, ll b, ll mod) {//大数乘法 
    a %= mod;
    b %= mod;
    ll res = 0;
    while (b) {
        if (b & 1) res = (res + a) % mod;
        a = (a << 1) % mod;
        b >>= 1;
    }
    return res;
}

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

bool Miller_Rabin (ll n, int k) {//Miller_Rabin判断素数 
    if (n < 2) return false;
    if (n == 2) return true;
    if (n & 1 == 0) return false;//step1:粗筛
    //step2:二次探测
    ll t = 0, x = n - 1;//att1: x这里的赋值别忘了减1 
    while (x & 1 == 0) x >>= 1, t++;  
    for (int i = 0; i < k; i++) {
        ll a = rand() % (n - 1) + 1;
        if (Check(a, x, t, n))
            return false; 
    }
    return true;
}

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

ll f (ll x, ll c, ll mod) {//生成随机数：f(x) = (x * x + c) % mod 
    return (Mult_mod(x, x, mod) + c) % mod; 
}

ll Pollard_rho (ll n, ll c) {//Pollard_rho找到n的某个因子 
    ll a = rand() % n;
    ll b = a;
    ll i = 1, k = 2;
    while (1) {
        i++;
        a = f(a, c, n);
        ll d = gcd(a - b, n);
        if (d != 1 && d != n) return d;
        if (a == b) return n;//到了随机数的循环节
        if (i == k) {
            b = a;
            k += k;
        } 
    }
}
void findFac (ll n) {//求解n的素因子
    if (Miller_Rabin(n, 5)) {
        factor[cnt++] = n;
        return;
    } 
    ll p = n;
    while (p >= n) p = Pollard_rho(p, (ll)rand() % (n - 1) + 1);
    findFac(p);
    findFac(n / p); 
}

bool isPrime (int x) {
    for (int i = 2; i <= x >> 1; i++) {
        if (x % i == 0) return false;
    }
    return true;
}
int main()
{
    srand(time(NULL));
    
    int k;
    cin >> k;
    ll n;
    
    for (int i = 2; i <= k; i++) {
        if (!isPrime(i)) continue;
        n = ((ll)1 << i ) - 1;//err1:1前面要加（ll） 
        cnt = 0;
        findFac(n); 
        if (cnt == 1) continue;
        sort(factor, factor + cnt);
        printf("%lld", factor[0]);
        for (int j = 1; j < cnt; j++) {
            printf(" * %lld", factor[j]);
        }
        printf(" = %lld = ( 2 ^ %d ) - 1\n", n, i);
    }
    
    return 0;
}