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 all(v) v.begin(), v.end()
typedef long long ll;
const int NMAX = 1e5 + 5;
set<pair<ll, ll>> adj[NMAX];
int dg[NMAX], vis[NMAX];
ll dp[NMAX][2], S[NMAX];
vector<int> D[NMAX];
set<int> X;
multiset<ll> C[NMAX];
void dfs(int now, int k) {
vis[now] = 1;
ll& ret = dp[now][0] = S[now];
vector<ll> tmp;
for(auto& p : adj[now]) {
ll nx = p.first, w = p.second;
if(vis[nx]) continue;
dfs(nx, k);
ret += dp[nx][0] + w;
ll t = dp[nx][1] - dp[nx][0] - w;
C[now].emplace(t);
tmp.emplace_back(t);
}
auto it = C[now].begin();
for(int i = 0; i < k - 1; i++) ret += min(*it++, 0LL);
dp[now][1] = ret;
ret += min(*it, 0LL);
//cout << "Now is : " << now << '\n';
//for(ll x : C[now]) cout << x << ' ';
//cout << '\n';
for(ll t : tmp) C[now].erase(C[now].find(t));
return;
}
vector<ll> minimum_closure_costs (int N, vector<int> U, vector<int> V, vector<int> W) {
vector<ll> ans(N, 0);
for(int i = 0; i < N - 1; i++) {
adj[U[i]].emplace(V[i], W[i]);
adj[V[i]].emplace(U[i], W[i]);
dg[U[i]]++; dg[V[i]]++;
ans[0] += W[i];
}
for(int i = 0; i < N; i++) {
D[dg[i]].emplace_back(i);
X.emplace(i);
}
for(int k = 1; k < N; k++) {
// 노드 삭제하기
//cout << "NOW TURN IS : " << k << '\n';
for(int x : D[k]) {
X.erase(x);
//cout << "erase : " << x << '\n';
for(auto& p : adj[x]) {
ll nx = p.first, w = p.second;
adj[nx].erase({ x, w });
S[nx] += w; C[nx].emplace(-w);
}
}
// 각 트리에 대해서 탐색
for(int x : X) if(!vis[x]) {
dfs(x, k);
ans[k] += dp[x][0];
}
for(int x : X) vis[x] = 0;
}
return ans;
}
//
//int main(void) {
// ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//
// freopen("input.txt", "r", stdin);
// int N;
// cin >> N;
// vector<int> U(N), V(N), W(N);
// for(int i = 0; i < N - 1; i++) cin >> U[i] >> V[i] >> W[i];
// vector<ll> ans = minimum_closure_costs(N, U, V, W);
// for(int i = 0; i < N; i++) cout << ans[i] << ' ';
// return 0;
//}
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