Bzoj1997 [hnoi2010]planar

Posted by yjjr's blog on February 6, 2018

标签:2-sat,平面图

题目

题目传送门

Description

Input

Output

Sample Input

2

6 9

1 4

1 5

1 6

2 4

2 5

2 6

3 4

3 5

3 6

1 4 2 5 3 6

5 5

1 2

2 3

3 4

4 5

5 1

1 2 3 4 5

Sample Output

NO

YES HINT

Source

Day1

分析

平面图的定理:$m<=3*n-6$

可以用这个剪枝

反正用2-sat乱搞了啊qwq

code

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
#include<algorithm>
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define dep(i,a,b) for(int i=a;i>=b;i--)
#define ll long long
#define mem(x,num) memset(x,num,sizeof x)
#define reg(x) for(int i=last[x];i;i=e[i].next)
using namespace std;
inline ll read()
{
    ll f=1,x=0;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
const int maxn=1e5+6;
int u[maxn],v[maxn],c[maxn],pos[maxn],last[maxn],que[maxn],belong[maxn];
int cnt=1,n,m,low[maxn],dfn[maxn],ind,top,scc,Que;
bool inq[maxn];
struct edge{int to,next;}e[maxn<<2];

void insert(int u,int v){e[++cnt]=(edge){v,last[u]};last[u]=cnt;}

void tarjan(int x){
	low[x]=dfn[x]=++ind;
	inq[x]=1;que[++top]=x;
	reg(x)
		if(!dfn[e[i].to])tarjan(e[i].to),low[x]=min(low[x],low[e[i].to]);
		else if(inq[e[i].to])low[x]=min(low[x],dfn[e[i].to]);
	if(low[x]==dfn[x]){
		scc++;	
		int now=-1;
		while(now!=x){
			now=que[top--];inq[now]=0;
			belong[now]=scc;
		}
	}
}

bool jud()
{
	rep(i,1,m)
		if(belong[2*i]==belong[2*i-1])return 0;
	return 1;
}
int main()
{
	Que=read();
	while(Que--){
		n=read(),m=read();
		rep(i,1,m)u[i]=read(),v[i]=read();
		mem(last,0);cnt=1;scc=ind=0;
		mem(low,0);mem(dfn,0);
		rep(i,1,n)c[i]=read();
		if(m>3*n-6){puts("NO");continue;}
		rep(i,1,n)pos[c[i]]=i;
		top=0;
		rep(i,1,m){
			v[i]=pos[v[i]];u[i]=pos[u[i]];
			if(u[i]>v[i])swap(u[i],v[i]);
			if(v[i]-u[i]==1||(v[i]==n&&u[i]==1))continue;
			u[++top]=u[i],v[top]=v[i];
		}
		m=top;
		rep(i,1,m)
			rep(j,i+1,m)
				if((u[i]<u[j]&&u[j]<v[i]&&v[i]<v[j])||(u[j]<u[i]&&u[i]<v[j]&&v[j]<v[i]))
				{
					insert(2*i-1,2*j);
					insert(2*i,2*j-1);
					insert(2*j-1,2*i);
					insert(2*j,2*i-1);
				}
		top=0;
		rep(i,1,2*m)
			if(!dfn[i])tarjan(i);
		if(jud())puts("YES");
		else puts("NO");
	}
	return 0;
}
		
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