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>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
edi
*/
const int MOD = 1e9 + 7;
const int N = 2e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
struct suffmx {
// https://usaco.guide/adv/springboards?lang=cpp
map<ll, ll> mp;
void insert(pll p) {
auto [x, y] = p;
auto it = mp.lower_bound(x);
if (it != mp.end() and it->second >= y) {
return;
}
mp[x] = y;
it = mp.find(x);
if (it != mp.begin()) {
it--;
vector<ll> toerase;
for (; y >= it->second; --it) {
toerase.pb(it->first);
if (it == mp.begin()) break;
}
trav(i, toerase) {
mp.erase(i);
}
}
}
ll query(ll x) {
auto it = mp.lower_bound(x);
if (it == mp.end()) return -inf2;
return it->second;
}
};
vector<ll> adj[N];
vector<ll> subsiz(N), depth(N);
vector<ll> nodes;
void dfs1(ll u, ll p){
subsiz[u] = 1;
nodes.pb(u);
trav(v,adj[u]){
if(v == p) conts;
depth[v] = depth[u]+1;
dfs1(v,u);
subsiz[u] += subsiz[v];
}
}
ll dfs2(ll u, ll p){
trav(v,adj[u]){
if(v == p) conts;
if(subsiz[v] > subsiz[1]/2){
return dfs2(v,u);
}
}
return u;
}
void solve(int test_case)
{
ll n; cin >> n;
rep1(i,n-1){
ll u,v; cin >> u >> v;
adj[u].pb(v), adj[v].pb(u);
}
dfs1(1,-1);
ll r = dfs2(1,-1);
vector<ll> ans(n+5);
auto go = [&](){
suffmx smx;
smx.insert({n,0});
trav(v,adj[r]){
nodes.clear();
depth[v] = 1;
dfs1(v,r);
trav(w,nodes){
ll x = subsiz[w];
ll mxd = smx.query(x);
amax(ans[x],depth[w]+mxd);
}
trav(w,nodes){
smx.insert({subsiz[w],depth[w]});
}
}
};
go();
reverse(all(adj[r]));
go();
rev(i,n,1) amax(ans[i],ans[i+1]);
rep1(i,n){
if(i&1) cout << 1 << endl;
else cout << ans[i/2]+1 << endl;
}
}
int main()
{
fastio;
int t = 1;
// cin >> t;
rep1(i, t) {
solve(i);
}
return 0;
}
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