Luogu4111 [HEOI2015]小Z的房间 （矩阵树，辗转相除高斯消元）

除法不能用于同余系，要辗转相除。注意不能加入柱子到矩阵。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#define R(a,b,c) for(register int  a = (b); a <= (c); ++ a)
#define nR(a,b,c) for(register int  a = (b); a >= (c); -- a)
#define Max(a,b) ((a) > (b) ? (a) : (b))
#define Min(a,b) ((a) < (b) ? (a) : (b))
#define Fill(a,b) memset(a, b, sizeof(a))
#define Abs(a) ((a) < 0 ? -(a) : (a))
#define Swap(a,b) a^=b^=a^=b
#define ll long long

#define ON_DEBUG

#ifdef ON_DEBUG

#define D_e_Line printf("\n\n----------\n\n")
#define D_e(x)  cout << #x << " = " << x << endl
#define Pause() system("pause")
#define FileOpen() freopen("in.txt","r",stdin);

#else

#define D_e_Line ;
#define D_e(x)  ;
#define Pause() ;
#define FileOpen() ;

#endif

struct ios{
    template<typename ATP>ios& operator >> (ATP &x){
        x = 0; int f = 1; char c;
        for(c = getchar(); c < '0' || c > '9'; c = getchar()) if(c == '-')  f = -1;
        while(c >= '0' && c <= '9') x = x * 10 + (c ^ '0'), c = getchar();
        x*= f;
        return *this;
    }
}io;
using namespace std;

const int N = 107;
const int mod = 1000000000;

int n, m;
int a[N][N];
//inline void Gauss(int n){
//  R(i,1,n){
//      int r = i;
//      R(j,i + 1,n){
//          if(Abs(a[r][i]) > Abs(a[i][i])){
//              r = i;
//          }
//      }
//      if(a[r][i] == 0){
//          printf("0");
//          return;
//      }
//      swap(a[r], a[i]);
//      R(j,i + 1,n){
//          int t = a[j][i] / a[i][i];
//          R(k,1,n){
//              a[j][k] -= t * a[i][k];
//          }
//      }
//  }
//  long long ans = 1;
//  R(i,1,n) ans = 1ll * ans * a[i][i] % mod;
//  printf("%lld", ans);
//}
inline void Gauss(int n){
    int ans = 1;
    R(i,1,n){
        R(j,i + 1,n){
            while(a[j][i]){
                int t = a[i][i] / a[j][i];
                R(k,1,n){
                    a[i][k] = (a[i][k] - 1ll * t * a[j][k] % mod + mod) % mod;
                }
                swap(a[i], a[j]);
                ans = -ans;
            }
        }
        ans = (1ll * ans * a[i][i] % mod + mod) % mod;
    }
    printf("%d", ans);
}
int mp[N][N], mpIndex;
char str[N][N];
inline void add(int x, int y){
    ++a[x][x];
    ++a[y][y];
    --a[x][y];
    --a[y][x];
}
int main(){
    io >> n >> m;
    R(i,1,n){
        scanf("%s", str[i] + 1);
    }
    R(i,1,n){
        R(j,1,m){
            if(str[i][j] == '.'){
                mp[i][j] = ++mpIndex;
            }
        }
    }
    R(i,1,n){
        R(j,1,m){
            if(str[i][j] == '.'){
                if(str[i - 1][j] == '.'){
                    add(mp[i][j], mp[i - 1][j]);
                }
                if(str[i][j - 1] == '.'){
                    add(mp[i][j], mp[i][j - 1]);
                }
            }
        }
    }
    
    Gauss(mpIndex - 1);
    
    return 0;
}