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;
vector<vector<int>> g;
vector<int> alatt;
vector<bool> volt;
int meret(int akt, int os){
alatt[akt] = 1;
for(int x : g[akt])
if(!volt[x] && x != os)
alatt[akt] += meret(x, akt);
return alatt[akt];
}
int getc(int akt, int os, int m){
for(int x : g[akt])
if(!volt[x] && x != os && alatt[x]*2 > m)
return getc(x, akt, m);
return akt;
}
void upd(set<pair<int, int>> &s, pair<int, int> p){
auto it = s.insert(p).first;
if(next(it) != s.end() && next(it)->second >= it->second){
s.erase(it);
}else{
while(it != s.begin() && prev(it)->second <= it->second)
s.erase(prev(it));
}
}
void bejar(set<pair<int, int>> &s1, set<pair<int, int>> &s2, int akt, int t, int os, int rem){
auto it = s1.lower_bound({alatt[akt], 0});
if(it != s1.end()){
//cout<<"uj: "<<2*alatt[akt]<<' '<<t<<" | "<<it->first<<' '<<it->second<<'\n';
upd(s2, {2*alatt[akt], t + it->second + 1});
}
upd(s2, {min(alatt[akt], rem)*2, t+1});
for(int x : g[akt])
if(!volt[x] && x != os)
bejar(s1, s2, x, t+1, akt, rem);
}
void berak(set<pair<int, int>> &s, int akt, int t, int os){
//cout<<"berak: "<<akt<<' '<<alatt[akt]<<'\n';
upd(s, {alatt[akt], t});
for(int x : g[akt])
if(!volt[x] && x != os)
berak(s, x, t+1, akt);
}
vector<int> ki;
void decomposition(int c){
c = getc(c, -1, meret(c, -1));
volt[c] = true;
meret(c, -1);
set<pair<int, int>> s1, s2;
for(int x : g[c]){
if(!volt[x]){
bejar(s1, s2, x, 1, c, alatt[c] - alatt[x]);
berak(s1, x, 1, c);
}
}
s1.clear();
reverse(g[c].begin(), g[c].end());
for(int x : g[c]){
if(!volt[x]){
bejar(s1, s2, x, 1, c, alatt[c] - alatt[x]);
berak(s1, x, 1, c);
}
}
//cout<<"centroid: "<<c<<'\n';
for(auto p : s2){
//cout<<p.first<<' '<<p.second<<'\n';
ki[p.first] = max(ki[p.first], p.second);
}
for(int x : g[c])
if(!volt[x])
decomposition(x);
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
int n;
cin>>n;
g.resize(n);
ki.resize(n+1);
alatt.resize(n);
volt.assign(n, false);
for(int i = 0; i < n-1; i++){
int a, b;
cin>>a>>b;
--a, --b;
g[a].push_back(b);
g[b].push_back(a);
}
decomposition(0);
/*cout<<"ki: ";
for(int i = 0; i <= n; i++) cout<<ki[i]<<' ';
cout<<'\n';*/
ki[n] = max(ki[n], 1);
for(int i = n-1; i >= 0; i--){
ki[i] = max(ki[i], ki[i+1]);
}
for(int i = 1; i <= n; i++){
cout<<(i%2 ? 1 : ki[i])<<'\n';
}
return 0;
}
/*
4
1 2
2 3
3 4
*/
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