poj 3641 快速幂+米勒罗宾判断大素数

来源：互联网发布：蚁群算法的应用编辑：程序博客网时间：2024/05/10 03:20

题意：

判断一个数p是否满足：

1.p不是素数；

2.pow_mod(a, p, p) == a % p。

代码：

#include <iostream>#include <cstdio>#include <cstdlib>#include <algorithm>#include <cstring>#include <cmath>#include <stack>#include <vector>#include <queue>#include <map>#include <climits>#include <cassert>#define LL long long#define lson lo, mi, rt << 1#define rson mi + 1, hi, rt << 1 | 1using namespace std;const int maxn = 1000001 + 10;const int inf = 0x3f3f3f3f;const double eps = 1e-8;const double pi = acos(-1.0);const double ee = exp(1.0);LL pow_mod(LL a, LL n, LL mod){    if (n == 0)        return 1;    LL x = pow_mod(a, n >> 1, mod);    LL res = x * x % mod;    if (n % 2)        res = res * a % mod;    return res;}bool Witness(LL a, LL n){    LL t = 0, m = n - 1;    while (!(m & 1))    {        t++;        m >>= 1;    }    LL x = pow_mod(a, m, n);    if (x == 1 || x == n - 1)        return false;    while (t--)    {        x = x * x % n;        if (x == n - 1)            return false;    }    return true;}const int Times = 11;bool Miller_Rabin(LL n){    if (n < 2)        return false;    if (n == 2)        return true;    if (!(n & 1))        return false;    for (int i = 1; i <= Times; i++)    {        LL a = rand() % (n - 1) + 1;        if (Witness(a, n))            return false;    }    return true;}int main(){#ifdef LOCAL    freopen("in.txt", "r", stdin);#endif // LOCAL    LL p, a;    while (~scanf("%lld%lld", &p, &a))    {        if (!p && !a)            break;        if (!Miller_Rabin(p) && pow_mod(a, p, p) == a % p)        {            printf("yes\n");        }        else        {            printf("no\n");        }    }    return 0;}

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