POJ 3641 Pseudoprime numbers (miller-rabin 素数判定)

时间:2022-02-06 12:34:42

模板题,直接用

/********************* Template ************************/
#include <set>
#include <map>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <cstdio>
#include <string>
#include <vector>
#include <cassert>
#include <cstdlib>
#include <cassert>
#include <cstring>
#include <sstream>
#include <fstream>
#include <numeric>
#include <iomanip>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std;
#define EPS 1e-8
#define DINF 1e15
#define MAXN 100050
#define MOD 1000000007
#define INF 0x7fffffff
#define LINF 1LL<<60
#define PI 3.14159265358979323846
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define BUG cout<<"BUG! "<<endl
#define ABS(a) ((a)>0?(a):(-a))
#define LINE cout<<"------------------ "<<endl
#define FIN freopen("in.txt","r",stdin)
#define FOUT freopen("in.txt","w",stdout)
#define mem(a,b) memset(a,b,sizeof(a))
#define FOR(i,a,b) for(int i = a ; i < b ; i++)
#define read(a) scanf("%d",&a)
#define read2(a,b) scanf("%d%d",&a,&b)
#define read3(a,b,c) scanf("%d%d%d",&a,&b,&c)
#define write(a) printf("%d\n",a)
#define write2(a,b) printf("%d %d\n",a,b)
#define write3(a,b,c) printf("%d %d %d\n",a,b,c)
#pragma comment (linker,"/STACK:102400000,102400000")
template<class T> inline T L(T a) {return (a << );}
template<class T> inline T R(T a) {return (a << | );}
template<class T> inline T lowbit(T a) {return (a & -a);}
template<class T> inline T Mid(T a,T b) {return ((a + b) >> );}
template<class T> inline T gcd(T a,T b) {return b ? gcd(b,a%b) : a;}
template<class T> inline T lcm(T a,T b) {return a / gcd(a,b) * b;}
template<class T> inline T Min(T a,T b) {return a < b ? a : b;}
template<class T> inline T Max(T a,T b) {return a > b ? a : b;}
template<class T> inline T Min(T a,T b,T c) {return min(min(a,b),c);}
template<class T> inline T Max(T a,T b,T c) {return max(max(a,b),c);}
template<class T> inline T Min(T a,T b,T c,T d) {return min(min(a,b),min(c,d));}
template<class T> inline T Max(T a,T b,T c,T d) {return max(max(a,b),max(c,d));}
template<class T> inline T mod(T x,T y) {y = ABS(y); return x >= ? x % y : x % y + y;}
template<class T> inline T mul_mod(T a,T b,T n) {
T ret = ,tmp = a % n;
while(b){
if((b&) && (ret+=tmp)>=n) ret -= n;
if((b>>=) && (tmp<<=)>=n) tmp -= n;
}return ret;
}
template<class T> inline T pow_mod(T a,T b,T n){
T ret = ; a = a % n;
while(b){
if (b&) ret = mul_mod(ret,a,n);
if (b>>=) a = mul_mod(a,a,n);
}return ret;
}
template<class T> inline T exGCD(T a, T b, T &x, T &y){
if(!b) return x = ,y = ,a;
T res = exGCD(b,a%b,x,y),tmp = x;
x = y,y = tmp - (a / b) * y;
return res;
}
template<class T> inline T reverse_bits(T x){
x = (x >> & 0x55555555) | ((x << ) & 0xaaaaaaaa); x = ((x >> ) & 0x33333333) | ((x << ) & 0xcccccccc);
x = (x >> & 0x0f0f0f0f) | ((x << ) & 0xf0f0f0f0); x = ((x >> ) & 0x00ff00ff) | ((x << ) & 0xff00ff00);
x = (x >> & 0x0000ffff) | ((x <<) & 0xffff0000); return x;
} typedef long long LL; typedef unsigned long long ULL;
//typedef __int64 LL; typedef unsigned __int64 ULL;
/********************* By F *********************/
inline bool witness(LL a,LL x){
LL m = x-,s = ;
while(!(m&)) m>>=,s++;
LL res = pow_mod(a,m,x);
if(res == || res == x-) return ;
while(s--){
res = mul_mod(res,res,x);
if(res == x-) return ;
}return ;
}
inline bool miller(LL x,int time){
if(x == || x == || x == || x == ) return ;
if(x == || !(x&) || x% == || x% == || x% == ) return ;
while(time--){
LL r = rand()%(x-) + ;
if(gcd(r,x) != || !witness(r%x,x)) {return ;}
}return ;
}
int main(){
//FIN;
LL p,a;
while(~scanf("%lld%lld",&p,&a)){
if(p == && a == ) break;
if(miller(p,)){
printf("no\n");
}else{
LL t = pow_mod(a,p,p);
if(t == a) printf("yes\n");
else printf("no\n");
}
}
return ;
}