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;
}