This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
#define N 100100
#define C cyc.abp
struct unionf{
int par[N];
unionf(){
for(int i=0;i<N;i++)
par[i]=i;
}
int abp(int a){
return (par[a]-a?par[a]=abp(par[a]):a);
}
} cyc,comp;
int par[N],sz[N],dep[N];
set<pair<int,int>>st;
vector<pair<int,int>>adj[N];
int depth=0,times=0;
void repos(int x,int p,int d){
depth++;
if(depth>1.5e5)
exit(1);
par[x]=p,dep[x]=d;
for(auto[i,j]:adj[x])
if(C(i)-p&&C(i)!=x)
repos(C(i),x,d+1);
depth--;
}
int mergepar(int a){
times++;
if(times>1.5e5){
cout<<"by";
exit(0);
}
int b=par[a];
dep[a]=dep[b];
par[a]=par[b];
if(adj[a].size()<adj[b].size())
swap(a,b);
cyc.par[b]=a;
for(auto[i,j]:adj[b])
if(C(i)-a&&C(i)-par[a]&&C(i)-b)
adj[a].push_back({i,j}),par[i]=a;
adj[b].clear();
return a;
}
int main(){
int n,m;
cin>>n>>m;
for(int i=1;i<=n;i++)
sz[i]=1;
while(m--){
int a,b;
cin>>a>>b;
if(C(a)==C(b))
continue;
if(comp.abp(a)==comp.abp(b)){
int acyc=C(a),bcyc=C(b);
while(acyc-bcyc){
if(dep[acyc]<dep[bcyc])
swap(acyc,bcyc);
acyc=mergepar(acyc),
bcyc=C(bcyc);
}
} else {
int acyc=C(a),bcyc=C(b);
int acomp=comp.abp(a),bcomp=comp.abp(b);
if(sz[acomp]<sz[bcomp]) swap(a,b),
swap(acyc,bcyc),swap(acomp,bcomp);
sz[acomp]+=sz[bcomp];
comp.par[bcomp]=acomp;
repos(bcyc,acyc,dep[acyc]+1);
adj[acyc].push_back({b,a});
adj[bcyc].push_back({a,b});
}
}
for(int i=1;i<=n;i++)if(C(i)==i)
for(auto[j,k]:adj[i]) if(C(j)-i)
st.insert({min(j,k),max(j,k)});
for(auto[i,j]:st)
cout<<i<<' '<<j<<'\n';
}
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