Organising the Organisation UVA

Organising the Organisation

UVA - 10766

生成树计数

要用到Matric-Tree定理。

#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int maxn = 52;
const long double eps = 1e-8;
long double a[maxn][maxn];
int vis[maxn][maxn];
int dcmp(long double x){
    if(fabs(x) < eps) return 0;
    return x < 0 ? -1 : 1;
}
long double solve(long double a[][maxn], int n){
    long double ans = 1;
    int cnt = 0;
    for(int i = 0; i < n; i++){
        if(dcmp(a[i][i]) == 0){
            int j;
            for(j = i + 1; j < n; j++){
                if(!dcmp(a[j][i])) break;
            }
            if(j == n){
                return 0;
            }
            for(int k = i; k < n; k++){
                swap(a[i][k], a[j][k]);
            }
            cnt++;
        }
        ans *= a[i][i];
        for(int j = i + 1; j < n; j++){
            long double ta = a[j][i] / a[i][i];
            for(int k = i; k < n; k++){
                a[j][k] -= ta * a[i][k];
            } 
        }
    }
    if(cnt & 1) ans = -ans;
    return ans;
}

int main(){
    int n, m, k;
    while(scanf("%d %d %d", &n, &m, &k) != EOF){
        memset(vis, 0, sizeof(vis));
        memset(a, 0, sizeof(a));    
        for(int i = 0; i < m; i++){
            int u, v;
            scanf("%d %d", &u, &v);
            u--;
            v--;
            vis[u][v] = vis[v][u] = 1;
        }
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(!vis[i][j] && i != j){
                    a[i][i]++;
                    a[i][j] = -1;
                }
            }
        }
        printf("%.0f
", (double)solve(a, n-1));
    }    
}