poj 2191 Mersenne Composite Numbers

首先利用miller_rabin测试是否为素数；

再利用pallord进行质因子分解；

View Code

#include<iostream>

#include<cstdio>

#include<cstdlib>

#include<cmath>

#include<algorithm>

#define LL  unsigned long long

using namespace std;

LL p[10] = { 2,3,5,7,11,13,17,19,23,29 };

int cnt = 0; LL num[100];

LL Multi( LL a , LL b, LL n )

{

   LL sum = 0;

   while( b )

   {

        if( ( b&1 ) ) sum = ( sum + a )%n;

        a <<= 1;

        b >>= 1;

        if( a >= n ) a %=n;        

   }    

   return sum;

}

LL Quick_mod( LL a, LL b, LL n )

{

   LL sum = 1;

   while( b )

   {

         if( ( b&1 ) ) sum = Multi( sum , a , n );

         a = Multi( a , a ,n );

         b >>= 1;        

   }    

   return sum;

}

bool Miller_rabin( LL n )

{

    LL m = n -1,d,L;

    int k = 0;

    if( n ==2 ) return true;

    if( n < 2 || !( n & 1 ) ) return false;

    while( !( m &1 ) )

    {

        k ++ ; m >>=1;

    }    

    for( int i = 0 ; i < 9 ; i ++ )

    {

        if( p[i] >= n ) return true;

        d = Quick_mod( p[i] , m , n );

        if( d==1 ) continue;

        for( int j = 0 ; j < k ; j ++ )

        {

            L = Multi( d , d ,n );

            if( L == 1 && d != 1 && d !=( n -1 ) )

                return false;

            d = L;

        }

        if( d != 1 ) return false;

    }

    return true;

}

LL Gcd( LL a ,LL b )

{

   return b == 0 ? a : Gcd( b, a%b );    

}

LL Pallord( LL n )

{

   LL x,y,c = 0,d,i=1,k=2;

   x = y = rand()%( n -1 )     + 1;

   while( c ==0 || c == 2 )

   {

        c = abs(rand())%( n -1 ) + 1;        

   }

   do

   {

        i ++;

        d = Gcd( y + n - x ,n );

        if( d > 1 && d < n )

            return d;

        if( i == k )

        {

           y = x ; k <<= 1;

        }

        x = (Multi( x , x , n ) + c)%n;

   }while( x != y );

   return n;

}

void Pallord_Min( LL n )

{

    LL a,b,p;

    if( n == 1 ) return ;

    if( Miller_rabin( n ) )

    {

        num[cnt++] = n;    

//        printf( "safas%I64u\n",n );

        return ;

    }    

    p = Pallord( n );

    Pallord_Min( p );

    Pallord_Min( n / p );

//    return a < b ? a:b;

}

int main( )

{

    LL k = 2;

    int m;

    while( scanf( "%d",&m )==1 )

    {

        k = 2;

        for( int i = 2 ; i <= m ; i ++ )

        {

               k *= 2;

               if( Miller_rabin( (LL)i ) && Miller_rabin( k - 1 ) == false)

               {

               cnt = 0;

              Pallord_Min( k -1 );

               sort( num , num + cnt );

               for( int j = 0; j < cnt-1; j ++ )

                    printf( "%I64u * ",num[j] );

              printf( "%I64u = %I64u = ( 2 ^ %d ) - 1\n",num[cnt-1],k-1,i );

            }

        }

    }

//    system( "pause" );

    return 0;    

}