#include "roads.h"
#include <algorithm>
#include <functional>
#include <utility>
#include <vector>
using namespace std;
vector<long long> st1(int N, vector<int> U, vector<int> V, vector<int> W)
{
vector<long long> answer(N);
sort(W.rbegin(), W.rend());
for (int i = N - 1; i >= 1; --i)
answer[i - 1] = answer[i] + W[i - 1];
return answer;
}
vector<long long> st2(int N, vector<int> U, vector<int> V, vector<int> W)
{
long long take = W[0], skip = 0, total = W[0];
for (int i = 1; i < N - 1; i++)
{
long long new_take = min(take, skip) + W[i];
long long new_skip = take;
long long new_total = total + W[i];
take = new_take, skip = new_skip, total = new_total;
}
vector<long long> answer(N);
answer[0] = total;
answer[1] = min(take, skip);
return answer;
}
vector<long long> st3(int N, vector<int> U, vector<int> V, vector<int> W)
{
vector<vector<pair<int, int>>> adj(N);
vector<long long> answer(N);
for (int i = 0; i < N - 1; i++)
{
adj[U[i]].emplace_back(V[i], W[i]);
adj[V[i]].emplace_back(U[i], W[i]);
answer[0] += W[i];
}
function<pair<long long, long long>(int, int, int)> dfs = [&](int a, int p, int k)
{
long long base = 0;
vector<long long> save_cost;
for (auto [x, w] : adj[a])
if (x != p)
{
auto [lt, le] = dfs(x, a, k);
long long pick = lt, no_pick = le + w;
base += no_pick;
save_cost.push_back(min(0LL, pick - no_pick));
}
sort(save_cost.begin(), save_cost.end());
long long lt = base, le = base;
for (int i = 0; i < (int)save_cost.size(); i++)
{
if (i < k - 1)
lt += save_cost[i];
if (i <= k - 1)
le += save_cost[i];
}
return make_pair(lt, le);
};
for (int i = 1; i < N; i++)
answer[i] = dfs(0, -1, i).second;
return answer;
}
auto st4 = st3;
vector<long long> st5(int N, vector<int> U, vector<int> V, vector<int> W)
{
vector<vector<int>> adj(N);
vector<long long> answer(N);
for (int i = 0; i < N - 1; i++)
{
adj[U[i]].push_back(V[i]);
adj[V[i]].push_back(U[i]);
answer[0] += W[i];
}
vector<vector<int>> targets(N);
for (int i = 0; i < N; i++)
{
sort(adj[i].begin(), adj[i].end(), [&](int a, int b)
{ return adj[a].size() > adj[b].size(); });
for (int j = 0; j < (int)adj[i].size(); j++)
targets[j].push_back(i);
}
vector<bool> vis(N);
for (int k = 1; k < N; k++)
{
function<pair<long long, long long>(int, int)> dfs = [&](int a, int p)
{
vis[a] = true;
long long base = 0;
vector<long long> save_cost;
int leaf_count = (int)adj[a].size() - (p != -1);
for (int x : adj[a])
{
if ((int)adj[x].size() < k)
break;
if (x == p)
continue;
leaf_count--;
auto [lt, le] = dfs(x, a);
long long pick = lt, no_pick = le + 1;
base += no_pick;
save_cost.push_back(min(0LL, pick - no_pick));
}
base += leaf_count;
sort(save_cost.begin(), save_cost.end());
long long lt = base, le = base;
for (int i = 0; i < (int)save_cost.size(); i++)
{
if (i < k - 1)
lt += save_cost[i];
if (i < k)
le += save_cost[i];
}
lt += min(0, (int)save_cost.size() - min((int)save_cost.size() + leaf_count, k - 1));
le += min(0, (int)save_cost.size() - min((int)save_cost.size() + leaf_count, k));
return make_pair(lt, le);
};
for (int u : targets[k - 1])
vis[u] = false;
for (int u : targets[k - 1])
if (!vis[u])
answer[k] += dfs(u, -1).second;
}
return answer;
}
vector<long long> minimum_closure_costs(int N, vector<int> U, vector<int> V, vector<int> W)
{
auto c1 = [&]()
{
for (int i = 0; i < N - 1; i++)
if (U[i] != 0)
return false;
return true;
};
auto c2 = [&]()
{
for (int i = 0; i < N - 1; i++)
if (U[i] != i || V[i] != i + 1)
return false;
return true;
};
auto c3 = [&]()
{
return N <= 200;
};
auto c4 = [&]()
{
return N <= 2000;
};
auto c5 = [&]()
{
for (int i = 0; i < N - 1; i++)
if (W[i] != 1)
return false;
return true;
};
if (c1())
return st1(N, U, V, W);
if (c2())
return st2(N, U, V, W);
if (c3())
return st3(N, U, V, W);
if (c4())
return st4(N, U, V, W);
if (c5())
return st5(N, U, V, W);
return vector<long long>(N);
}
