#include "roads.h"
#include <bits/stdc++.h>
using namespace std;
vector <long long> minimum_closure_costs(int N, vector <int> U, vector <int> V, vector <int> W)
{
int n = N;
vector <vector <array <int, 3>>> adj(n);
for (int i = 0; i < n - 1; i++)
{
int u = U[i], v = V[i], w = W[i];
adj[u].push_back({v, w, 0});
adj[v].push_back({u, w, 0});
}
struct FenwickTree
{
//1 - indexed
int n;
vector <int> f;
vector <long long> g;
FenwickTree () : n(0), f(), g() {};
FenwickTree (int n) : n(n), f(n + 1), g(n + 1) {};
void insert(int x, long long d)
{
for (; x <= n; x += x & -x)
{
f[x]++;
g[x] += d;
}
}
int size()
{
int x = n, sum = 0;
for (; x; x &= x - 1)
{
sum += f[x];
}
return sum;
}
long long prefix_kth(int k)
{
int idx = 0;
long long sum = 0;
for (int mask = 1 << 20; mask; mask >>= 1)
{
if (idx + mask <= n && f[idx + mask] <= k)
{
idx += mask;
k -= f[idx];
sum += g[idx];
}
}
return sum;
}
};
vector <FenwickTree> f(n);
for (int i = 0; i < n; i++)
{
sort(adj[i].begin(), adj[i].end(), [](const array <int, 3> &x, const array <int, 3> &y)
{
return x[1] < y[1];
});
f[i] = FenwickTree(adj[i].size());
for (int j = 0; j < (int)adj[i].size(); j++)
{
adj[i][j][2] = j + 1;
}
}
vector <int> sorted_deg(n);
iota(sorted_deg.begin(), sorted_deg.end(), 0);
sort(sorted_deg.begin(), sorted_deg.end(), [&](int x, int y)
{
return adj[x].size() < adj[y].size();
});
vector <int> erased(n);
set <int> not_erased;
vector <int> flag(n);
for (int i = 0; i < n; i++)
{
not_erased.insert(i);
}
int id = 0;
vector <array <long long, 2>> dp(n);
vector <long long> ans(n);
const long long inf = 1e15;
ans[0] = accumulate(W.begin(), W.end(), 0LL);
vector <int> deg(n);
for (int i = 0; i < n; i++)
{
deg[i] = (int)adj[i].size();
}
for (int k = 1; k < n; k++)
{
vector <int> pending;
while (id < n && (int)deg[sorted_deg[id]] <= k)
{
int u = sorted_deg[id];
//remove u
for (auto &e: adj[u])
{
pending.push_back(e[0]);
}
erased[u] = 1;
not_erased.erase(u);
adj[u].clear();
id++;
}
sort(pending.begin(), pending.end());
pending.resize(unique(pending.begin(), pending.end()) - pending.begin());
for (auto &u: pending)
{
vector <array <int, 3>> new_adj;
for (auto &e: adj[u])
{
int v = e[0];
if (erased[v])
{
f[u].insert(e[2], e[1]);
}
else
{
new_adj.push_back(e);
}
}
adj[u].swap(new_adj);
}
function <void (int)> dfs([&](int u)
{
flag[u] = 1;
dp[u][0] = dp[u][1] = inf;
long long sum[2] = {};
vector <long long> vec;
for (auto &e: adj[u])
{
int v = e[0], w = e[1];
if (!flag[v])
{
dfs(v);
sum[0] += dp[v][0];
sum[1] += dp[v][0];
vec.push_back(dp[v][1] + w - dp[v][0]);
}
}
sort(vec.begin(), vec.end());
partial_sum(vec.begin(), vec.end(), vec.begin());
int need = (int)deg[u] - k, cnt = f[u].size();
if (cnt >= need)
{
dp[u][0] = min(dp[u][0], f[u].prefix_kth(need) + sum[0]);
}
if (cnt >= need - 1)
{
dp[u][1] = min(dp[u][1], f[u].prefix_kth(need - 1) + sum[1]);
}
for (int i = 0; i < (int)vec.size(); i++)
{
if (cnt + i + 1 >= need && i + 1 <= need)
{
dp[u][0] = min(dp[u][0], sum[0] + vec[i] + f[u].prefix_kth(need - i - 1));
}
if (cnt + i + 1 >= need - 1 && i + 1 <= need - 1)
{
dp[u][1] = min(dp[u][1], sum[1] + vec[i] + f[u].prefix_kth(need - 1 - i - 1));
}
}
});
for (auto &u: not_erased)
{
if (!flag[u])
{
dfs(u);
ans[k] += dp[u][0];
}
}
for (auto &u: not_erased)
{
flag[u] = 0;
}
}
return ans;
}
