P4455 [CQOI2018]社交网络(矩阵树定理)

题目

P4455 [CQOI2018]社交网络

\(CQOI\)的题都这么裸的吗？？

做法

有向图，指向叶子方向 \(D^{out}(G)-A(G)\)

至于证明嘛，反正也就四个定理，先挖个坑，省选后再来补

My complete code

#include<cstdio>
#include<iostream>
#include<cstring>
#include<string>
#include<algorithm>
#include<ctime>
using namespace std;
typedef int LL;
const int p=10007;
const int maxn=300;
inline LL Read(){
	LL x(0),f(1); char c=getchar();
	while(c<'0'||c>'9'){
		if(c=='-') f=-1; c=getchar();
	}
	while(c>='0'&&c<='9')
	    x=(x<<3)+(x<<1)+c-'0',c=getchar();
	return x*f;
}
LL n,m;
LL D[maxn][maxn];
inline LL Pow(LL base,LL b){
	LL ret(1);
	while(b){
		if(b&1)
		    ret=ret*base%p;
		base=base*base%p,
		b>>=1;
	}return ret;
}
inline LL Solve(){
	LL N(n),tr(0),ans(1);
	for(LL i=2;i<=N;++i){
		LL mx(i);
		for(LL j=i+1;j<=N;++j)
		    if(D[mx][i]<D[j][i])
		        mx=j;
		if(D[mx][i]==0)
		    return 0;
		if(mx!=i){
			swap(D[mx],D[i]),
			tr^=1;
		}
		for(LL j=i+1;j<=N;++j){
			LL tmp=D[j][i]*Pow(D[i][i],p-2)%p;
			for(LL k=1;k<=N;++k)
			    D[j][k]=(D[j][k]-tmp*D[i][k]%p+p)%p;
		}
		ans=ans*D[i][i]%p;
	}
	if(tr)
	    ans=p-ans;
	return ans;
}
int main(){
	n=Read(),m=Read();
	while(m--){
		LL v(Read()),u(Read());
		++D[v][v],D[u][v]=(D[u][v]+p-1)%p;
	}
	printf("%d\n",Solve());
	return 0;
}/*
*/