#include "roads.h"
#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>
typedef long long llong;
const int MAXN = 2000 + 10;
const llong INF = 1e18;
const int INTINF = 1e9;
int n;
std::vector <std::pair <int,int>> g[MAXN];
bool bl[MAXN][2][2];
llong dp[MAXN][2][2];
void firstDFS(int node, int par)
{
for (auto &curr : g[node])
{
if (curr.first == par)
{
std::swap(curr, g[node].back());
g[node].pop_back();
break;
}
}
for (const auto &[u, w] : g[node])
{
firstDFS(u, node);
}
}
llong f(int node, int k, bool k2)
{
// if (k == 1) std::cout << "call: " << node << ' ' << g[node].size() << ' ' << k << '\n';
if (g[node].empty())
{
return 0;
}
if (bl[node][k][k2])
{
return dp[node][k][k2];
}
bl[node][k][k2] = true;
std::vector <std::pair <llong,int>> vals;
for (const auto &[u, w] : g[node])
{
dp[node][k][k2] += w + f(u, k + k2, false);
vals.push_back({f(u, k + k2 - 1, true) - (w + f(u, k + k2, false)), u});
}
std::sort(vals.begin(), vals.end());
for (int i = 0 ; i < std::min((int)vals.size(), k) ; ++i)
{
if (vals[i].first >= 0) break;
dp[node][k][k2] += vals[i].first;
}
return dp[node][k][k2];
}
std::vector <llong> minimum_closure_costs(int N, std::vector <int> U, std::vector <int> V, std::vector <int> W)
{
n = N;
for (int i = 0 ; i < n - 1 ; ++i)
{
g[U[i] + 1].push_back({V[i] + 1, W[i]});
g[V[i] + 1].push_back({U[i] + 1, W[i]});
}
std::sort(W.begin(), W.end(), std::greater <int> ());
std::vector <llong> ans(n, 0);
llong sum = 0;
for (int i = n - 1 ; i >= 0 ; --i)
{
if (W.size() > i)
{
sum += W.back();
W.pop_back();
}
ans[i] = sum;
}
return ans;
firstDFS(1, 0);
int cnt = 0;
for (int i = 0 ; i <= 1 ; ++i)
{
ans[i] = f(1, i, false);
}
// for (int i = 1 ; i <= n ; ++i)
// {
// for (int k = 0 ; k + 1 < n ; ++k)
// {
// assert(f(i, k, false) - f(i, k + 1, false) >= f(i, k + 1, false) - f(i, k + 2, false));
// assert(f(i, k, true) - f(i, k + 1, true) >= f(i, k + 1, true) - f(i, k + 2, true));
// }
// }
return ans;
}
