CPH page 148

#include <bits/stdc++.h>

using namespace std;

const int NMAX = 2e5 + 1;

vector < int > G[NMAX], d(NMAX), ans(NMAX);

void dfs1(int nod, int parent) {
    for(int it : G[nod]) {
        if(it == parent)
            continue;
        dfs1(it, nod);
        d[nod] = max(d[nod], d[it] + 1);
    }
}

void dfs2(int nod, int parent, int parent_dist) {
    ans[nod] = max(d[nod], parent_dist);
    multiset < pair < int , int > > S;
    S.insert(make_pair(parent_dist, 0));
    for(int it : G[nod]) {
        if(it == parent)
            continue;
        S.insert(make_pair(d[it] + 1, it));
        if(S.size() == 3)
            S.erase(S.begin());
    }
    for(int it : G[nod]) {
        if(it == parent)
            continue;
        pair < int , int > p = *S.rbegin();
        if(p.second != it)
            dfs2(it, nod, p.first + 1);
        else {
            p = *(--S.rbegin());
            dfs2(it, nod, p.first + 1);
        }
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int N;
    cin >> N;
    for(int i = 1; i < N; ++i) {
        int x, y;
        cin >> x >> y;
        G[x].emplace_back(y);
        G[y].emplace_back(x);
    }
    dfs1(1, 0);
    dfs2(1, 0, 0);
    for(int i = 1; i <= N; ++i)
        cout << ans[i] << ' ';
}