[POJ 1811 Prime Test] Miller_Rabin + Pollard_rho 大数质数判

[POJ 1811 Prime Test] Miller_Rabin + Pollard_rho 大数质数判断/质因子分解模板

题目链接：[POJ 1811 Prime Test]
题意描述：判断N是否为质数，如果是，求最小的质因子( 2≤N<254 )。
解题思路：Miller_Rabin + Pollard_rho 模板走起。

#include <ctime>
#include <queue>
#include <cmath>
#include <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

#define FIN freopen("input.txt","r",stdin)

typedef long long LL;

const LL MOD = 1e9 + 7;
const LL INF = 0x3f3f3f3f3f3f3f3fLL;
const int MAXN = 100;
const int S = 20;

LL T,N;
LL tol;
LL fact[MAXN];

LL mult_mod(LL a,LL b,LL c) {
    a %= c;
    b %= c;
    LL ret = 0;
    while(b) {
        if(b & 1) {
            ret += a;
            ret %= c;
        }
        a <<= 1;
        if(a >= c)a %= c;
        b >>= 1;
    }
    return ret;
}
LL quick_pow(LL x,LL n,LL mod) {
    if(n == 1)return x % mod;
    x %= mod;
    LL tmp = x;
    LL ret = 1;
    while(n) {
        if(n & 1) ret = mult_mod(ret,tmp,mod);
        tmp = mult_mod(tmp,mod);
        n >>= 1;
    }
    return ret;
}
bool check(LL a,LL x,LL t) {
    LL ret = quick_pow(a,x,n);
    LL last = ret;
    for(int i = 1; i <= t; i++) {
        ret = mult_mod(ret,ret,n);
        if(ret == 1 && last != 1 && last != n - 1) return true;
        last = ret;
    }
    if(ret != 1) return true;
    return false;
}
bool Miller_Rabin(LL n) {
    if(n < 2)return false;
    if(n == 2)return true;
    if((n & 1) == 0) return false;
    LL x = n - 1;
    LL t = 0;
    while((x & 1) == 0) {
        x >>= 1;
        t++;
    }
    for(int i = 0; i < S; i++) {
        LL a = rand() % (n - 1) + 1;
        if(check(a,n,t))
            return false;
    }
    return true;
}
LL gcd(LL a,LL b) {
    if(a == 0)return 1;
    if(a < 0) return gcd(-a,b);
    while(b) {
        LL t = a % b;
        a = b;
        b = t;
    }
    return a;
}
LL Pollard_rho(LL x,LL c) {
    LL i = 1,k = 2;
    LL x0 = rand() % x;
    LL y = x0;
    while(1) {
        i++;
        x0 = (mult_mod(x0,x0,x) + c) % x;
        LL d = gcd(y - x0,x);
        if(d != 1 && d != x) return d;
        if(y == x0) return x;
        if(i == k) {
            y = x0;
            k += k;
        }
    }
}
void findfac(LL n) {
    if(Miller_Rabin(n)) {
        fact[tol++] = n;
        return;
    }
    LL p = n;
    while(p >= n) p = Pollard_rho(p,rand() % (n - 1) + 1);
    findfac(p);
    findfac(n / p);
}

int main() {
#ifndef ONLINE_JUDGE
    FIN;
#endif // ONLINE_JUDGE
    LL ans;
    scanf("%lld",&T);
    while(T --) {
        scanf("%lld",&N);
        /// 要特判N==1的情况
        if(N == 1 || Miller_Rabin(N)) {
            printf("Primen");
            continue;
        }
        tol = 0;
        findfac(N);
        ans = fact[0];
        for (int i = 1; i < tol; i++) ans = min(ans,fact[i]);
        printf("%lldn",ans);
    }
    return 0;
}

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