#include "roads.h"
#include <stdlib.h>
#include <vector>
using namespace std;
typedef vector<int> vi;
typedef vector<long long> vl;
long long max(long long a, long long b) { return a > b ? a : b; }
const int N = 100000;
unsigned int X = 12345;
int rand_() {
return (X *= 3) >> 1;
}
long long *zz;
void sort(int *ii, int l, int r) {
while (l < r) {
int i = l, j = l, k = r, i_ = ii[l + rand_() % (r - l)], tmp;
while (j < k)
if (zz[ii[j]] == zz[i_])
j++;
else if (zz[ii[j]] < zz[i_]) {
tmp = ii[i], ii[i] = ii[j], ii[j] = tmp;
i++, j++;
} else {
k--;
tmp = ii[j], ii[j] = ii[k], ii[k] = tmp;
}
sort(ii, l, i);
l = k;
}
}
int uu[N - 1], vv[N - 1]; long long ww[N - 1]; int idx[N - 1][2];
int *eh[N], eo[N], *eh_[N], eo_[N];
void append(int **eh, int *eo, int i, int h) {
int o = eo[i]++;
if (o >= 2 && (o & o - 1) == 0)
eh[i] = (int *) realloc(eh[i], o * 2 * sizeof *eh[i]);
eh[i][o] = h;
}
long long *st[N]; int *kk_[N], nn_[N];
void build(int u, int n) {
int n_;
n_ = 1;
while (n_ < n)
n_ <<= 1;
nn_[u] = n_;
st[u] = (long long *) calloc(n_ * 2, sizeof *st[u]), kk_[u] = (int *) calloc(n_ * 2, sizeof *kk_[u]);
}
void pul(int u, int i) {
int l = i << 1, r = l | 1;
st[u][i] = st[u][l] + st[u][r], kk_[u][i] = kk_[u][l] + kk_[u][r];
}
void update(int u, int i, int x, int k) {
int n_ = nn_[u];
i += n_;
st[u][i] += x, kk_[u][i] += k;
while (i > 1)
pul(u, i >>= 1);
}
long long query(int u, int k) {
int n_ = nn_[u], i;
long long sum;
i = 1, sum = 0;
while (i < n_)
if (k < kk_[u][i << 1 | 0])
i = i << 1 | 0;
else
sum += st[u][i << 1 | 0], k -= kk_[u][i << 1 | 0], i = i << 1 | 1;
if (k >= kk_[u][i])
sum += st[u][i], k -= kk_[u][i];
return sum;
}
long long aa[N], dp[N], dq[N]; int ii_[N], k_;
char visited[N], marked[N];
void dfs(int p, int i) {
int o, n_, i_, k;
long long x;
visited[i] = 1;
x = 0;
for (o = eo_[i]; o--; ) {
int h = eh_[i][o], j = i ^ uu[h] ^ vv[h];
if (j != p) {
dfs(i, j);
x += dp[j];
}
}
n_ = 0;
for (o = eo_[i]; o--; ) {
int h = eh_[i][o], j = i ^ uu[h] ^ vv[h];
if (j != p)
aa[n_++] = dq[j] + ww[h] - dp[j];
}
for (i_ = 0; i_ < n_; i_++)
ii_[i_] = i_;
zz = aa, sort(ii_, 0, n_);
dp[i] = 0, dq[i] = 0;
for (k = 0; k <= k_ && k <= n_; k++) {
dp[i] = max(dp[i], x + query(i, k_ - k));
if (k < k_)
dq[i] = max(dq[i], x + query(i, k_ - 1 - k));
if (k < n_)
x += aa[ii_[n_ - 1 - k]];
}
}
int ii[N], cnt[N];
vl minimum_closure_costs(int n, vi uu_, vi vv_, vi ww_) {
vl ans(n);
int g, g_, h, i, j, k, o;
long long sum;
for (h = 0; h < n - 1; h++)
uu[h] = uu_[h], vv[h] = vv_[h], ww[h] = ww_[h];
for (i = 0; i < n; i++)
eh[i] = (int *) malloc(2 * sizeof *eh[i]);
for (h = 0; h < n - 1; h++)
append(eh, eo, uu[h], h), append(eh, eo, vv[h], h);
for (i = 0; i < n; i++)
cnt[eo[i]]++;
for (k = 1; k < n; k++)
cnt[k] += cnt[k - 1];
for (i = 0; i < n; i++)
ii[cnt[eo[i] - 1]++] = i;
for (h = 0; h < n - 1; h++)
ans[0] += ww[h];
for (i = 0; i < n; i++) {
zz = ww, sort(eh[i], 0, eo[i]);
for (o = 0; o < eo[i]; o++) {
h = eh[i][o];
idx[h][uu[h] == i ? 0 : 1] = eo[i] - 1 - o;
}
build(i, eo[i]);
}
for (i = 0; i < n; i++)
eh_[i] = (int *) malloc(2 * sizeof *eh_[i]);
sum = ans[0];
for (k_ = n - 1, g = n - 1; k_ > 0; k_--) {
while (g >= 0 && eo[ii[g]] > k_) {
i = ii[g--];
marked[i] = 1;
for (o = eo[i]; o--; ) {
h = eh[i][o], j = i ^ uu[h] ^ vv[h];
if (!marked[j])
update(i, idx[h][uu[h] == i ? 0 : 1], ww[h], 1), sum -= ww[h];
else {
update(j, idx[h][uu[h] == j ? 0 : 1], -ww[h], -1);
append(eh_, eo_, i, h), append(eh_, eo_, j, h);
}
}
}
for (g_ = g + 1; g_ < n; g_++)
visited[ii[g_]] = 0;
ans[k_] = ans[0] - sum;
for (g_ = g + 1; g_ < n; g_++) {
i = ii[g_];
if (!visited[i]) {
dfs(-1, i);
ans[k_] -= dp[i];
}
}
}
return ans;
}
