POJ 3641 Pseudoprime numbers 偽素數測試

題意：判斷一個數是否是基於a的偽素數。只有當p是合數且a^p = a ( mod p ) 時，才輸出yes。

題解：Miller_Rabin素數測試。

#include<cstdio>#include<ctime>#include<cstdlib>using namespace std;#define lint __int64lint modular_exponent ( lint a, lint b, lint n ){    lint ret = 1;    for ( ; b; b >>= 1, a = a*a%n )        if ( b & 1 )            ret = ret * a % n;    return ret;}int miller_rabin ( int n, int time = 20 ){    if ( n==1 || (n!=2&&!(n%2)) || (n!=3&&!(n%3)) || (n!=5&&!(n%5)) || (n!=7&&!(n%7)) )        return 0;    while ( time-- )    {        lint m = modular_exponent ( rand()%(n-1) + 1, n-1, n );        if ( m != 1 ) return 0;    }    return 1;}int main(){    lint p, a;    while ( 1 )    {        scanf("%I64d%I64d",&p,&a);        if ( a == 0 && p == 0 ) break;        if ( modular_exponent(a,p,p) == a && !miller_rabin(p) )            printf("yes\n");        else printf("no\n");    }    return 0;}