BZOJ 4031([HEOI2015]小Z的房间-矩阵树定理+辗转相除)

矩阵树定理，注意gauss消元辗转相除的写法

#include<bits/stdc++.h> 
using namespace std;
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#define
                        For(j,m-1) cout<<a[i][j]<<' ';\
                        cout<<a[i][m]<<endl; \
                        } 
#pragma
#define
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
#define
ll a[MAXN][MAXN];
ll det(int n) {
    bool f=0;
    For(i,n) {
        int k=i;
        Fork(j,i,n) if (abs(a[j][i])>abs(a[k][i])) {k=j;break;}
        For(j,n) swap(a[i][j],a[k][j]);
        if (i^k) f^=1;
        Fork(j,i+1,n) {
            while(a[j][i]) {
                ll t=a[j][i]/a[i][i];
                For(k,n) {
                    a[j][k]+=F-t*a[i][k]%F;
                    a[j][k]%=F;
                }
                if (!a[j][i]) break;
                f^=1;
                For(k,n) swap(a[j][k],a[i][k]); 
            }
        }
    }
    ll r=1;
    For(i,n) r=r*a[i][i]%F;
    if (f) r=F-r;
    return r%F;
}
int id[MAXN][MAXN],cnt=0;
int main()
{
//  freopen("bzoj4031.in","r",stdin);
//  freopen(".out","w",stdout);

    int n=read(),m=read();
    char s[MAXN][MAXN];
    int cnt=0;
    For(i,n) {
        scanf("%s",s[i]+1);
        For(j,m) if (s[i][j]=='.') id[i][j]=++cnt;
    }
    For(i,n) For(j,m) if (s[i][j]=='.'){
        if (i>1) {
            int x=i,y=j,nx=i-1,ny=j;
            if (s[nx][ny]=='.') {
                int u=id[x][y],v=id[nx][ny];
                a[u][v]--; a[v][u]--;
                a[u][u]++; a[v][v]++;
            }
        }
        if (j>1) {
            int x=i,y=j,nx=i,ny=j-1;
            if (s[nx][ny]=='.') {
                int u=id[x][y],v=id[nx][ny];
                a[u][v]--; a[v][u]--;
                a[u][u]++; a[v][v]++;
            }

        }

    }
    printf("%lld\n",det(cnt-1));
    return 0;
}