ZOJ 3687 The Review Plan I ( 禁位排列 + 容斥原理 )

ZOJ 3687 The Review Plan I ( 禁位排列 + 容斥原理 )

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long LL;
#define CLR( a, b ) memset( a, b, sizeof(a) )
#define MOD 55566677
#define MAXN 55
LL fac[MAXN], res;
int n, m, row[MAXN], col[MAXN], g[MAXN][2], hash[MAXN][MAXN] ;

void init()
{
    fac[0] = 1;
    for( int i = 1; i < MAXN; ++i )
        fac[i] = ( fac[i-1] * i ) % MOD;
}

void dfs( int id, int num )
{
    if( id > m )
    {
        if( num & 1 )    res = ( ( res - fac[ n - num ] ) % MOD + MOD ) % MOD;
        else             res = ( res + fac[ n - num ] ) % MOD;
        return;
    }
    dfs( id + 1, num );
    if( row[g[id][0]] == 0 && col[g[id][1]] == 0 )
    {
        row[g[id][0]] = col[g[id][1]] = 1;
        dfs( id + 1, num + 1 );
        row[g[id][0]] = col[g[id][1]] = 0;
    }
}

int main()
{
    init();
    while( ~scanf( "%d %d", &n, &m ) )
    {
        CLR( row, 0 ), CLR( col, 0 ), CLR( hash, 0 );
        for( int i = 1; i <= m; ++i )
        {
            scanf( "%d %d", &g[i][0], &g[i][1] );
            if( hash[g[i][0]][g[i][1]] )
            {
                --i;
                --m;
            }
            else
                hash[g[i][0]][g[i][1]] = 1;
        }
        res = 0;
        dfs( 1, 0 );
        res = ( res % MOD + MOD ) % MOD;
        printf( "%lld\n", res );
    }
    return 0;
}

学习的暴搜

#include <cstdio>
#include <cstring>
typedef long long LL;
#define CLR( a, b ) memset( a, b, sizeof(a) )
#define MAXN 55
#define MOD 55566677
LL fac[ MAXN ], C[ MAXN][ MAXN ], r[ MAXN ], R[ MAXN ], res;
bool vis_r[ MAXN ], vis_c[ MAXN ], hash[ MAXN ][ MAXN ];
int n, m, h[ MAXN ], v[ MAXN ], one, x, y;

void init()    //递推初始化阶乘和组合数公式
{
    fac[0] = 1;
    for( int i = 1; i < MAXN; ++i )
        fac[i] = ( fac[i-1] * i ) % MOD;

    for( int i = 0; i < MAXN; ++i )
        C[i][i] = C[i][0] = 1;
    for( int i = 2; i < MAXN; ++i )
    {
        for( int j = 1; j < i; ++j )
        {
            C[i][j] = C[i - 1][j] + C[i - 1 ][j - 1];
            if( C[i][j] >= MOD )    C[i][j] -= MOD;
        }
    }
}

void dfs( int k, int id )
{
    if( k > n )
        return;
    for( int i = id; i < n; ++i )
    {
        for( int j = 0; j < n; ++j )
        {
            if( !vis_r[i] && !vis_c[j] && hash[i][j] )
            {
                r[k]++;
                if( r[k] >= MOD )    r[k] -= MOD;

                vis_r[i] = vis_c[j] = true;
                dfs( k + 1, i );
                vis_r[i] = vis_c[j] = false;
            }
        }
    }
} 

void cal()
{
    CLR( R, 0 );
    R[0] = 1;
    R[1] = m;
    for( int i = 2; i <= n; ++i )
    {
        for( int j = 0; j <= one && j <= i; ++j )
        {
            R[i] += r[i - j] * C[one][j];
            R[i] %= MOD;
        }
    }
}

LL solve()
{
    LL ans = fac[n];
    LL k = -1;
    for( int i = 1; i <= n; ++i )
    {
        ans += k * fac[n-i] * R[i];
        k *= -1;
    }
    ans = ( ans % MOD + MOD ) % MOD;
    return ans;
}

int main()
{
    init();
    while( ~scanf( "%d %d", &n, &m ) )
    {
        CLR( h, 0 ); CLR( v, 0 );
        CLR( r, 0 ); CLR( hash, false );
        CLR( vis_r, false ); CLR( vis_c, false );
        for( int i = 0; i < m; ++i )
        {
            scanf( "%d %d", &x, &y );
            x--;
            y--;
            if( hash[x][y] )
            {
                i--;
                m--;
                continue;
            }
            h[x]++;
            v[y]++;
            hash[x][y] = 1;
        }

        one = 0;
        for( int i = 0; i < n; ++i )
        {
            for( int j = 0; j < n; ++j )
            {
                if( hash[i][j] && ( h[i] <= 1 && v[j] <= 1 ) )
                {
                    hash[i][j] = false;
                    one++;
                }
            }
        }
        r[0] = 1;
        dfs( 1, 0 );
        cal();
        printf( "%lld\n", solve() );
    }
    return 0;
}

禁位排列