Prime Test POJ - 1811(Miller_Rabin+pollard_rho)

最新推荐文章于 2020-10-06 21:03:05 发布

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本文介绍了一种基于Miller-Rabin素性测试的算法，用于判断一个大整数是否为素数，并通过Pollard's Rho算法进行质因数分解。代码实现包括了快速幂取模、扩展欧几里得算法等关键数学操作。

题目：Prime Test POJ - 1811

咱也不知道啥原理，会用就行了。
代码：

#include<stdio.h>
#include<string>
#include<algorithm>
#include <stdlib.h>
#include<iostream>
#include<time.h>
using namespace std;
#define LL long long
const int S = 8;
LL factor[100];
int tol;
LL mult_mod(LL a, LL b, LL c)
{
    a %= c;
    b %= c;
    LL ret = 0;
    LL tmp = a;
    while(b)
    {
        if(b&1)
        {
            ret += tmp;
            if(ret > c)ret -= c;
        }
        tmp <<= 1;
        if(tmp > c) tmp -= c;
        b >>= 1;
    }
    return ret;
}
LL pow_mod(LL a, LL n, LL mod)
{
    LL ret = 1;
    LL temp = a % mod;
    while(n)
    {
        if(n & 1)ret = mult_mod(ret, temp, mod);
        temp = mult_mod(temp, temp, mod);
        n >>= 1;
    }
    return ret;
}
bool check(LL a, LL n, LL x, LL t)
{
    LL ret = pow_mod(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;
    else 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++;
    }
    srand(time(NULL));
    for(int i = 0; i < S; i++ )
    {
        LL a = rand()%(n-1)+1;
        if(check(a, n, x, t))
            return false;
    }
    return true;
}
LL gcd(LL a, LL b)
{
    LL t;
    while(b)
    {
        t = a;
        a = b;
        b = t % b;
    }
    if(a >= 0)return a;
    else return -a;
}
LL pollard_rho(LL x, LL c)
{
    LL i = 1, k = 2;
    srand(time(NULL));
    LL x0 = rand() % (x - 1) + 1;
    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, int k)
{
    if(n == 1)return;
    if(Miller_Rabin(n))
    {
        factor[tol++] = n;
        return;
    }
    LL p = n;
    int c= k;
    while(p >= n)p = pollard_rho(p, c--);
    findfac(p, k);
    findfac(n/p, k);
}
int main()
{
    int T;
    cin>>T;
    while(T--)
    {
        LL n;
        scanf("%I64d", &n);
        if(Miller_Rabin(n))printf("Prime\n");
        else
        {
            tol = 0;
            findfac(n, 107);
            LL ans = factor[0];
            for(int i = 1; i < tol; i++)
            {
                ans = min(ans, factor[i]);
            }
            printf("%I64d\n", ans);
        }
    }

    return 0;
}