POJ 3358 Period of an Infinite Binary Expansion( 数论好题 + 欧拉定理 + 欧拉函数 )

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <algorithm>
using namespace std;
typedef long long LL;
LL fac[ 100000 ], pf;

LL gcd( LL a, LL b )
{
    LL x, y, z;
    if( a > b ) x = a, y = b;
    else        x = b, y = a;
    while( y )
    {
        z = x % y;
        x = y;
        y = z;
    }
    return x;
}

LL mul( LL a, LL b, LL c )
{
    LL res = 0;
    a %= c;
    while( b )
    {
        if( b & 1 )
        {
            res += a;
            if( res >= c ) res -= c;
        }
        a <<= 1;
        if( a >= c ) a -= c;
        b >>= 1;
    }
    return res;
}

LL fast_mod( LL a, LL b, LL c )
{
    LL res = 1;
    while( b ) 
    {
        if( b & 1 )    res = mul( res, a, c );
        a = mul( a, a, c );
        b >>= 1;
    }
    return res;
}

LL euler( LL x )    //得到欧拉函数phi 
{
    LL res = x, i;
    for( i = 2; i * i <= x; ++i )
    {
        if( x % i == 0 )
        {
            x /= i;
            res = res - res / i;
            while( x % i == 0 )
                x /= i;
        }
    }
    if( x > 1 )
        res = res - res / x;
    return res;
}

void factor( LL x )    //得到x的所有约数 
{
    pf = 0;
    for( LL i = 2; i * i <= x; ++i )
    {
        if( x % i == 0 )
        {
            fac[ pf++ ] = i;
            fac[ pf++ ] = x / i;
        }
    }
    fac[pf++] = x;
}

int main()
{
    LL cas = 1, p, q, d, start, eul, id;
    while( ~scanf( "%lld %*c %lld", &p, &q ) )
    {
        printf( "Case #%d: ", cas++ );
        if( p == 0 )
        {
            puts( "1,1" );
            continue;
        }
        d = gcd( p, q );
        p /= d;
        q /= d;
        start = 1;
        while( (q & 1) == 0 ) 
        {
            start++;
            q >>= 1;
        }
        eul = euler( q );
        factor( eul );
        sort( fac, fac + pf ); 
        
        for( id = 0; id < pf; ++id )
            if( fast_mod( 2, fac[id], q ) == 1 )    
                break;
        printf( "%lld,%lld\n", start, fac[id] );
    }
    return 0;
}