Uva 10325 The Lottery ( 容斥原理 )

 

Uva 10325 The Lottery ( 容斥原理 )

 

详见：ZOJ 2836 Number Puzzle

 

#include <cstdio>

#include <cstring>

typedef long long LL;

LL x[20],n, m;



LL gcd( LL a, LL b )

{

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

}

LL lcm( LL a, LL b )

{

    return a / gcd( a, b ) * b;

}



void solve()

{

    LL ans = 0;

    for( int i = 1; i < ( 1 << m ); ++i )

    {

        LL mult = 1;

        LL bits = 0;

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

        {

            if( i & ( 1 << j ) )

            {

                mult = lcm( mult, x[j] );

                if( mult > n ) break;

                bits++;

            }

        }

        if( mult > n ) continue;

        if( bits & 1 )    ans += n / mult;

        else            ans -= n / mult;

    }

    printf( "%lld\n", n - ans );

}



int main()

{

    while( ~scanf( "%lld %lld", &n, &m ) )

    {

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

            scanf( "%lld", &x[i] );

        solve();

    }

    return 0;

}

代码君