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
    
     #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
     
       V[MAXN];std::pair
      
        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
       
         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
        
          inline void write(T x,char ch='\0'){    if(x<0)putchar('-'),x=-x;    if(x>9)write(x/10);    putchar(x%10+'0');    if(ch!='\0')putchar(ch);}template
         
           inline bool chkmin(T &x,T y){return y
          
           
             inline bool chkmax(T &x,T y){return y>x?(x=y,true):false;}template
            
              inline T min(T x,T y){return x
             
              
                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])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?'\n':' '); return 0;}