spoj104 HIGH - Highways 矩阵树定理

Posted 2020-10-31 poorpool

欲学矩阵树定理必先自宫学习一些行列式的姿势

然后做一道例题

#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
typedef long long ll;
int T, n, m, uu, vv;
double w[15][15];
const double eps=1e-7;
void gauss(){
	n--;
	for(int i=1; i<=n; i++){
		int maxi=i;
		for(int j=i+1; j<=n; j++)
			if(w[j][i]>w[maxi][i])
				maxi = j;
		swap(w[maxi], w[i]);
		if(fabs(w[maxi][i])<eps){
			printf("0\\n");
			return ;
		}
		for(int j=i+1; j<=n; j++){
			double bil=w[j][i]/w[i][i];
			for(int k=i; k<=n; k++)
				w[j][k] -= bil * w[i][k];
		}
	}
	double ans=1;
	for(int i=1; i<=n; i++)
		ans *= w[i][i];
	printf("%.0f\\n", fabs(ans));
}
int main(){
	cin>>T;
	while(T--){
		scanf("%d %d", &n, &m);
		memset(w, 0, sizeof(w));
		while(m--){
			scanf("%d %d", &uu, &vv);
			w[uu][uu]++; w[vv][vv]++;
			w[uu][vv]--; w[vv][uu]--;
		}
		gauss();
	}
	return 0;
}