uva 11806 容斥原理+二进制

很容易想到要用容斥原理，这里有一个小技巧就是用二进制数来表示集合的交。

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;

typedef long long ll;
const int MOD = 1000007;
const int N = 501;
int cn[N][N];

void init()
{
    memset( cn, 0, sizeof(cn) );
    cn[0][0] = 1;
    for ( int i = 1; i < N; i++ )
    {
        cn[i][0] = cn[i][i] = 1;
        for ( int j = 1; j < i; j++ )
        {
            cn[i][j] = ( cn[i - 1][j] + cn[i - 1][j - 1] ) % MOD;
        }
    }
}

int main ()
{
    init();
    int t;
    cin >> t;
    for ( int _case = 1; _case <= t; _case++ )
    {
        int n, m, k;
        cin >> n >> m >> k;
        int ans = cn[n * m][k];
        for ( int s = 1; s < 16; s++ )
        {
            int cnt = 0, r = n, c = m;
            for ( int i = 0; i < 4; i++ )
            {
                if ( s & ( 1 << i ) )
                {
                    cnt++;
                    if ( i & 1 )
                    {
                        r--;
                    }
                    else
                    {
                        c--;
                    }
                }
            }
            if ( cnt & 1 )
            {
                ans = ( ans - cn[r * c][k] + MOD ) % MOD;
            }
            else
            {
                ans = ( ans + cn[r * c][k] ) % MOD;
            }
        }
        cout << "Case " << _case << ": " << ans << endl;
    }
    return 0;
}