P4455 [CQOI2018]社交网络(矩阵树定理)

时间：2022-02-03 17:30:48

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;

}/*

*/

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