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 ll = long long;
using namespace std;
#define pll pair <ll,ll>
#define fi first
#define se second
#define MP make_pair
#define sz(a) (ll((a).size()))
#define BIT(mask,i) (((mask) >> (i))&1)
#define MASK(i) (1LL << (i))
const ll MAXN = 2e5+100;
ll n;
vector <ll> g[MAXN];
bool del[MAXN];
ll sz[MAXN];
ll sub[MAXN];
ll in[MAXN];
ll out[MAXN];
ll max1[MAXN];
ll ans[MAXN];
ll timeDFS;
void dfs_sub(ll u,ll p){
in[u] = ++timeDFS;
sub[u] = 1;
for (auto v:g[u]){
if (v==p)continue;
dfs_sub(v,u);
sub[u] += sub[v];
}
out[u] = timeDFS;
}
void dfs_sz(ll u,ll p){
sz[u] = 1;
for (auto v:g[u]){
if (del[v] || v==p)continue;
dfs_sz(v,u);
sz[u]+=sz[v];
}
}
ll f(ll x,ll y){
if (in[x] <= in[y] && in[y] <= out[x])return n-sub[y];
else return sub[x];
}
ll find_centroid(ll u,ll p,ll root){
for (auto v:g[u]){
if (del[v] || v==p)continue;
if (sz[v]*2>sz[root]){
return find_centroid(v,u,root);
}
}
return u;
}
struct node{
ll comp,u,sz,dist;
};
vector <node> all;
void dfs(ll u,ll p,ll root1,ll root2,ll dist){
all.push_back({root1,u,f(u,p),dist});
for (auto v:g[u]){
if (del[v] || v==p)continue;
dfs(v,u,root1,root2,dist+1);
}
}
void solve_centroid(ll u){
dfs_sz(u,u);
u = find_centroid(u,u,u);
all.clear();
for (auto v:g[u]){
if (!del[v]){
max1[v] = -1;
dfs(v,u,v,u,1);
}
}
sort(all.begin(),all.end(),[](node x,node y){return x.sz > y.sz;});
ll best1 = 0,best2 = 0;
// cout<<"CENTROID "<<u<<endl;
for (auto x:all){
// cout<<x.comp<<' '<<x.u<<' '<<x.sz<<' '<<x.dist<<'\n';
if (best1 != 0 && best1 != x.comp)ans[x.sz*2] = max(ans[x.sz*2],x.dist+max1[best1]);
else if (best2 != 0)ans[x.sz*2] = max(ans[x.sz*2],x.dist+max1[best2]);
max1[x.comp] = max(max1[x.comp],x.dist);
vector <ll> tmp = {best1,best2,x.comp};
sort(tmp.begin(),tmp.end(),[](ll x,ll y){return max1[x] > max1[y];});
tmp.resize(unique(tmp.begin(),tmp.end())-tmp.begin());
best1 = tmp[0],best2 = tmp[1];
ll sus = min(x.sz,f(u,x.comp))*2;
ans[sus] = max(ans[sus], x.dist);
}
del[u] = 1;
for (auto v:g[u]){
if (!del[v])solve_centroid(v);
}
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(nullptr);
cin>>n;
for (ll i = 1;i < n;i ++){
ll u,v;
cin>>u>>v;
g[u].push_back(v);
g[v].push_back(u);
}
for (ll i = 1;i <= n;i ++)sort(g[i].begin(),g[i].end());
dfs_sub(1,1);
solve_centroid(1);
for (ll i = 1;i <= n;i ++)cout<<ans[i]+1<<'\n';
return 0;
}
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