发现 (m) 只有两种取值，于是可做了
树的直接贪心
图的枚举环上的边去掉，然后做树的贪心，搜的时候剪一下枝吧
写得有点乱
#include<bits/stdc++.h>
#define ui unsigned int
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
#define ft first
#define sd second
#define pb(a) push_back(a)
#define mp(a,b) std::make_pair(a,b)
#define REP(a,b,c) for(register int a=(b),a##end=(c);a<=a##end;++a)
#define DEP(a,b,c) for(register int a=(b),a##end=(c);a>=a##end;--a)
const int MAXN=5000+10;
int n,m,e=1,key,beg[MAXN],nex[MAXN<<1],to[MAXN<<1],was[MAXN<<1],cnt,dfn[MAXN],ans[MAXN],vis[MAXN],arv[MAXN];
std::vector<int> V[MAXN];
std::pair<int,int> ext,from[MAXN];
struct Unique{
int fa[MAXN];
inline void init(int x)
{
REP(i,1,x)fa[i]=i;
}
inline int found(int x)
{
if(fa[x]!=x)fa[x]=found(fa[x]);
return fa[x];
}
inline int link(int x,int y,int val)
{
int u=found(x),v=found(y),res=0;
if(u!=v)fa[u]=v,res=val;
return res;
}
};
Unique U;
template<typename T> inline void read(T &x)
{
T data=0,w=1;
char ch=0;
while(ch!='-'&&(ch<'0'||ch>'9'))ch=getchar();
if(ch=='-')w=-1,ch=getchar();
while(ch>='0'&&ch<='9')data=((T)data<<3)+((T)data<<1)+(ch^'0'),ch=getchar();
x=data*w;
}
template<typename T> inline void write(T x,char ch=' ')
{
if(x<0)putchar('-'),x=-x;
if(x>9)write(x/10);
putchar(x%10+'0');
if(ch!=' ')putchar(ch);
}
template<typename T> inline bool chkmin(T &x,T y){return y<x?(x=y,true):false;}
template<typename T> inline bool chkmax(T &x,T y){return y>x?(x=y,true):false;}
template<typename T> inline T min(T x,T y){return x<y?x:y;}
template<typename T> inline T max(T x,T y){return x>y?x:y;}
inline void insert(int x,int y,int z)
{
to[++e]=y;
nex[e]=beg[x];
beg[x]=e;
was[e]=z;
}
inline void sortdfs(int x,int f)
{
if(arv[x])return ;arv[x]=1;
for(register int i=beg[x];i;i=nex[i])V[x].pb(to[i]),sortdfs(to[i],x);
std::sort(V[x].begin(),V[x].end());
}
inline void initdfs(int x,int f)
{
for(register int i=beg[x];i;i=nex[i])
if(to[i]==f||!was[i])continue;
else initdfs(to[i],x),from[to[i]]=mp(x,i);
}
inline bool dfs(int x,int f,int &fl)
{
dfn[++cnt]=x;
if(dfn[cnt]<ans[cnt])chkmin(fl,0);
if(fl&&dfn[cnt]>ans[cnt])return false;
int lack=-1;
for(register int i=beg[x];i;i=nex[i])
if(to[i]==f)continue;
else if(!was[i])lack=to[i];
REP(i,0,V[x].size()-1)
if(V[x][i]==lack||V[x][i]==f)continue;
else if(!dfs(V[x][i],x,fl))return false;
return true;
}
inline int LCA(int u,int v)
{
while(u)vis[u]=1,u=from[u].ft;
while(v)
if(vis[v])return v;
else v=from[v].ft;
}
inline void solve(int x)
{
int fl;
while(x!=key)
{
was[from[x].sd]=was[from[x].sd^1]=0;
cnt=0;if(dfs(1,0,fl=1))memcpy(ans,dfn,sizeof(ans));
was[from[x].sd]=was[from[x].sd^1]=1;
x=from[x].ft;
}
}
int main()
{
freopen("travel.in","r",stdin);
freopen("travel.out","w",stdout);
read(n);read(m);
U.init(n);int fl;
REP(i,1,n)ans[i]=n+1;
REP(i,1,m)
{
int u,v;read(u);read(v);
if(U.link(u,v,1))insert(u,v,1),insert(v,u,1);
else ext=mp(u,v);
}
if(m==n-1)sortdfs(1,0),dfs(1,0,fl=1),memcpy(ans,dfn,sizeof(ans));
else
{
initdfs(1,0);
insert(ext.ft,ext.sd,0);
insert(ext.sd,ext.ft,0);
sortdfs(1,0);
dfs(1,0,fl=1),memcpy(ans,dfn,sizeof(ans));
was[e]=was[e-1]=1;
key=LCA(ext.ft,ext.sd);
solve(ext.ft),solve(ext.sd);
}
REP(i,1,n)write(ans[i],i==iend?'
':' ');
return 0;
}