[bzoj1997][Hnoi2010]Planar 2-sat

1997: [Hnoi2010]Planar

Time Limit: 10 Sec  Memory Limit: 64 MB
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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

平面图m<=3n-6，我也不知道为什么

然后2-sat建模

ai->bj

aj->bi

判ai，aj是否在同一强连通分量

#include<iostream>#include<cstring>#include<cstdio>using namespace std;const int N = 2005;int T,n,m,id,top,cnt,scnt,tail;int dfn[N],low[N],inq[N],q[N],u[N*5],v[N*5],pos[N],last[N],belong[N];struct Edge{int to,next;}e[N*500];void insert( int u, int v ){e[++cnt].to = v; e[cnt].next = last[u]; last[u] = cnt;e[++cnt].to = u; e[cnt].next = last[v]; last[v] = cnt;}void tarjan( int x ){int now = 0;dfn[x] = low[x] = ++id;q[++top] = x; inq[x] = 1;for( int i = last[x]; i; i = e[i].next )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] ){scnt++;while( now != x ){now = q[top--]; inq[now] = 0;belong[now] = scnt;}}}void init(){memset(last,0,sizeof(last));memset(dfn,0,sizeof(dfn));memset(low,0,sizeof(low));memset(inq,0,sizeof(inq));cnt = id = scnt = top = tail = 0;}bool check(){for( int i = 1; i <= tail; i++ ) if( belong[i*2] == belong[i*2-1] ) return false;return true;}int main(){scanf("%d", &T);while( T-- ){scanf("%d%d", &n, &m);init();for( int i = 1; i <= m; i++ ) scanf("%d%d", &u[i], &v[i]);for( int i = 1,x; i <= n; i++ ) scanf("%d", &x), pos[x] = i;if( m > n*3-6 ){ puts("NO"); continue; }for( int i = 1; i <= m; i++ ){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[++tail] = u[i]; v[tail] = v[i];}for( int i = 1; i <= tail; i++ )for( int j = i+1; j <= tail; j++ )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(i*2-1,2*j); insert(2*i,2*j-1);}for( int i = 1; i <= 2*tail; i++ ) if( !dfn[i] ) tarjan(i);if( check() ) puts("YES");else puts("NO");}return 0;}