题目传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=4031
仍然是裸的矩阵树
#include<iostream>
#include<iostream>
#include<cstdio>
#define LL long long
using namespace std;
const LL MAXN = 100;
const LL MOD = 1000000000;
LL G[MAXN][MAXN],n,m,num[MAXN][MAXN],cnt;
char pat[MAXN];
inline int Gauss(){
for (LL j=1;j<=n;j++) for (LL i=1;i<=n;i++)
G[i][j] = (G[i][j]%MOD + MOD) % MOD;
LL ret = 1;
for (LL j=1;j<=n;j++) {
for (LL k=j+1;k<=n;k++) while (G[j][k]) {
LL t = G[j][j] / G[j][k];
for (LL i=1;i<=n;i++) G[i][j] = ((G[i][j] - G[i][k]*t) % MOD + MOD) % MOD;
for (LL i=1;i<=n;i++) swap(G[i][j], G[i][k]); ret *= -1; ret = (ret%MOD + MOD) % MOD;
}
ret = (G[j][j]*ret%MOD + MOD) % MOD;
} return ret;
}
inline void AddEdge(LL u, LL v){
G[u][u]++; G[v][v]++;
G[u][v]--; G[v][u]--;
}
int main(){
scanf("%d%d",&m,&n);
for (LL j=1;j<=m;j++) {
scanf("%s",pat+1);
for (LL i=1;i<=n;i++) if (pat[i] == '.') {
num[i][j] = ++cnt;
if (num[i-1][j]) AddEdge(num[i][j],num[i-1][j]);
if (num[i][j-1]) AddEdge(num[i][j],num[i][j-1]);
}
} n = cnt-1; printf("%d\n",Gauss());
return 0;
}
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