bzoj4031: [HEOI2015]小Z的房间

直接构图

无向图生成树计数。运用矩阵树定理

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long LL;
const LL mod=1e9;
LL MOD(LL x){return ((x%mod)+mod)%mod;}

int z;LL kf[110][110];
int id[20][20];
LL gethls()
{
    LL ans=1,tp=1;
    for(int i=2;i<=z;i++)
    {
        for(int j=i+1;j<=z;j++)
        {
            int x=i,y=j;
            while(kf[y][i]!=0)
            {
                LL t=kf[x][i]/kf[y][i];
                for(int k=i;k<=z;k++)
                    kf[x][k]=MOD(kf[x][k]-kf[y][k]*t);
                swap(x,y);
            }
            if(x!=i)
            {
                for(int k=2;k<=z;k++)
                    swap(kf[x][k],kf[y][k]);
                tp=0-tp;
            }
        }
        ans=MOD(ans*kf[i][i]);
    }
    ans=MOD(ans*tp);
    return ans;
}
char ss[20];
int main()
{
    freopen("data.in","r",stdin);
    freopen("1.out","w",stdout);
    int n,m;
    scanf("%d%d",&n,&m);
    memset(id,-1,sizeof(id));
    memset(kf,0,sizeof(kf));
    for(int i=1;i<=n;i++)
    {
        scanf("%s",ss+1);
        for(int j=1;j<=m;j++)
        {
            if(ss[j]=='.')
            {
                id[i][j]=++z;
                if(id[i][j-1]!=-1)
                {
                    int x=id[i][j-1],y=z;
                    kf[x][y]--;kf[y][x]--;
                    kf[x][x]++;kf[y][y]++;
                }
                if(id[i-1][j]!=-1)
                {
                    int x=id[i-1][j],y=z;
                    kf[x][y]--;kf[y][x]--;
                    kf[x][x]++;kf[y][y]++;
                }
            }
        }
    }
    for(int i=1;i<=z;i++)
        for(int j=1;j<=z;j++)MOD(kf[i][j]);
    printf("%lld\n",gethls());
    return 0;
}