[杂题] Codeforces 794D Round #414 D. Labelling Cities

可以证明有相同邻接节点集合的点染色必相同 否则必不相同 缩点
然后一个点度不超过2且连通 然后就是一条链或环 环肯定不可能
然后就好了

#include<cstdio>#include<cstdlib>#include<algorithm>#include<map>#include<set>#include<vector>#define pb push_backusing namespace std;typedef pair<int,int> abcd;typedef unsigned long long ull;inline char nc(){  static char buf[100000],*p1=buf,*p2=buf;  return p1==p2&&(p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++;}inline void read(int &x){  char c=nc(),b=1;  for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;  for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;}const int N=300005;map<ull,int> idx;int tot;set<abcd> Set;vector<int> G[N];int n,m;int u[N],v[N];ull a[N],b[N];int deg[N];int c[N];inline void dfs(int u,int x){  c[u]=x;  for (int v:G[u])    if (!c[v])      dfs(v,x+1);}int main(){  freopen("t.in","r",stdin);  freopen("t.out","w",stdout);  read(n); read(m);  for (int i=1;i<=n;i++) a[i]=b[i]=(ull)rand()*rand()*rand()*rand();  for (int i=1;i<=m;i++){    read(u[i]); read(v[i]);    a[u[i]]^=b[v[i]]; a[v[i]]^=b[u[i]];  }  for (int i=1;i<=n;i++)    if (!idx.count(a[i]))      idx[a[i]]=++tot;  int ed=0;  for (int i=1;i<=m;i++){    int x=idx[a[u[i]]],y=idx[a[v[i]]];    if (x>y) swap(x,y);    if (x!=y && !Set.count(abcd(x,y))){      Set.insert(abcd(x,y)),ed++;      deg[x]++; deg[y]++;      G[x].pb(y); G[y].pb(x);    }  }  for (int i=1;i<=tot;i++) if (deg[i]>=3) return printf("NO\n"),0;  if (ed==tot) return printf("NO\n",0);  for (int i=1;i<=tot;i++)    if (deg[i]<=1 && !c[i])      dfs(i,1);  printf("YES\n");  for (int i=1;i<=n;i++)    printf("%d ",c[idx[a[i]]]);  return 0;}