洛谷P3209 [HNOI2010]PLANAR

首先用一波神奇的操作，平面图边数m<=3*n-6，直接把m降到n，

然后对于冲突的边一条环内，一条环外，可以用并查集或者2Sat做，

当然并查集是无向的，2Sat是有向的，显然用并查集比较好 复杂度大概是O(T*n*n)

 #include<cstdio>
 #include<cstdlib>
 #include<algorithm>
 #include<cstring>
 #define pb push_back
 #define pii pair<int,int>
 #define ft first
 #define sc second
 #define MAXN 200000+10
 using namespace std;
 int n,m;
 int b[MAXN],d[MAXN],f[MAXN];
 pii E[MAXN];
 int find(int x){return (f[x]==x?x:f[x]=find(f[x]));}
 void init_find(){
     for(int i=;i<=(m<<);i++)f[i]=i;
 }
 void lik(int x,int y){
     x=find(x),y=find(y);
     if(x!=y)f[x]=y;
 }
 int solve(){
     scanf("%d%d",&n,&m);
     init_find();
     for(int i=;i<=m;i++)scanf("%d%d",&E[i].ft,&E[i].sc);
     int t;
     for(int i=;i<=n;i++)scanf("%d",&t),d[t]=i;
     if(m>*n-)return ;
     memset(b,,sizeof(b));
     for(int i=;i<=m;i++){
         E[i].ft=d[E[i].ft],E[i].sc=d[E[i].sc];
         if(E[i].ft>E[i].sc){swap(E[i].ft,E[i].sc);}
         if(E[i].sc-E[i].ft==||E[i].sc-E[i].ft==n-)b[i]=;
     }
     pii x,y;
     for(int i=;i<=m;i++){
         if(b[i])continue;
         for(int j=i+;j<=m;j++){
             if(b[j])continue;
             x=E[i],y=E[j];
             if(x.ft==y.ft||x.ft==y.sc)continue;
             if(x.sc==y.ft||x.sc==y.sc)continue;
             if(x.ft==x.sc||y.ft==y.sc)continue;
             if(x.ft>y.ft)swap(x,y);
             if(y.ft<x.sc&&x.sc<y.sc){
                 if(find(i)==find(j))return ;
                 lik(i,j+m),lik(j,i+m);
             }
         }
     }
     return ;
 }
 int main()
 {
 //    freopen("data.in","r",stdin);
     int T;
     scanf("%d",&T);
     while(T--){
         if(solve())printf("YES\n");
         else printf("NO\n");
     }
     return ;
 }

并查集

 #include<cstdio>
 #include<cstdlib>
 #include<algorithm>
 #include<cstring>
 #define pb push_back
 #define pii pair<int,int>
 #define ft first
 #define sc second
 #define MAXN 200000+10
 using namespace std;
 struct TSat{
     int n;
     int fst[MAXN],nxt[MAXN],to[MAXN];
     int cnt;
     void add(int x,int y){
         nxt[++cnt]=fst[x],fst[x]=cnt,to[cnt]=y;
     }
     void ins(int x,int y){
         add(x,y+n);
         add(x+n,y);
     }
     int dfn[MAXN],low[MAXN];
     int cmp[MAXN],sta[MAXN],vis[MAXN],top;
     int time_dex,tmp;
     void init(int n){
         this->n=n;
         time_dex=tmp=cnt=top=;
         memset(dfn,,sizeof(dfn));
         memset(low,,sizeof(low));
         memset(vis,,sizeof(vis));
         memset(fst,,sizeof(fst));
         memset(nxt,,sizeof(nxt));
         memset(to,,sizeof(to));
         memset(cmp,,sizeof(cmp));
     }
     void Tarjan(int x){
         dfn[x]=low[x]=++time_dex;
         sta[++top]=x;
         vis[x]=;
         for(int e=fst[x];e;e=nxt[e]){
             int &y=to[e];
             if(!dfn[y]){
                 Tarjan(y);
                 low[x]=min(low[x],low[y]);
             }
             else if(vis[y]){
                 low[x]=min(low[x],dfn[y]);
             }
         }
         if(low[x]==dfn[x]){
             tmp++;
             while(sta[top+]!=x){
                 cmp[sta[top]]=tmp;
                 vis[sta[top]]=;
                 top--;
             }
         }
     }
     bool check(){
         for(int i=;i<=(n<<);i++){
             if(!dfn[i])Tarjan(i);
         }
         for(int i=;i<=n;i++){
             if(cmp[i]==cmp[i+n])
                 return ;
         }
         return ;
     }
 }TS;
 int n,m;
 int b[MAXN],d[MAXN];
 pii E[MAXN];
 int solve(){
     scanf("%d%d",&n,&m);
     for(int i=;i<=m;i++)scanf("%d%d",&E[i].ft,&E[i].sc);
     int t;
     for(int i=;i<=n;i++)scanf("%d",&t),d[t]=i;
     if(m>*n-)return ;
     TS.init(m);
     memset(b,,sizeof(b));
     for(int i=;i<=m;i++){
         E[i].ft=d[E[i].ft],E[i].sc=d[E[i].sc];
         if(E[i].ft>E[i].sc){swap(E[i].ft,E[i].sc);}
         if(E[i].sc-E[i].ft==||E[i].sc-E[i].ft==n-)b[i]=;
     }
     pii x,y;
     for(int i=;i<=m;i++){
         if(b[i])continue;
         for(int j=i+;j<=m;j++){
             if(b[j])continue;
             x=E[i],y=E[j];
             if(x.ft==y.ft||x.ft==y.sc)continue;
             if(x.sc==y.ft||x.sc==y.sc)continue;
             if(x.ft==x.sc||y.ft==y.sc)continue;
             if(x.ft>y.ft)swap(x,y);
             if(y.ft<x.sc&&x.sc<y.sc){
                 TS.ins(i,j);
                 TS.ins(j,i);
             }
         }
     }
     return TS.check();
 }
 int main()
 {
 //    freopen("data.in","r",stdin);
     int T;
     scanf("%d",&T);
     while(T--){
         if(solve())printf("YES\n");
         else printf("NO\n");
     }
     return ;
 }

2Sat