#include "race.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long int
#define INF 100000000000000LL
int flagAtual=1;
vector<pair<int, ll>> melhor;
vector<pair<int, ll>> edges_dist;
vector<bool> block;
// Respota.
ll menor_K = INF;
//calcula o tamanho da subarvore
void get_SubTreeSize( vector<vector<pair<int, ll>>> &adj, vector<int> &subtreeSz, int v, int pai) {
subtreeSz[v] = 1;
for(auto& [u, val] : adj[v]) {
if(u == pai || block[u]) continue;
get_SubTreeSize(adj,subtreeSz,u,v);
subtreeSz[v] += subtreeSz[u];
}
}
//percorre todos os vertices e retorna o centroide...
int findCentroid(vector<vector<pair<int, ll>>> &adj, vector<int> &subtreeSz, int v, int pai, int size) {
bool isCentroid = true;
int maiorVerts=-1;
int next=-1;
for (int i=0; i<adj[v].size(); i++) if (adj[v][i].first != pai && !block[adj[v][i].first]) {
if (subtreeSz[adj[v][i].first] > maiorVerts) {maiorVerts = subtreeSz[adj[v][i].first]; next = adj[v][i].first; }
if (subtreeSz[adj[v][i].first] > size / 2)
isCentroid = false;
}
if (!isCentroid) {
subtreeSz[v] = size - subtreeSz[v] + 1;
return findCentroid(adj, subtreeSz, next, v, size);
}
return v;
}
void dfs1(vector<vector<pair<int, ll>>>&adj, int v, int pai, ll dist, int total, int K) {
if(dist > K) return;
edges_dist[v] = {total, dist};
ll aux = melhor[K-dist].second == flagAtual? melhor[K-dist].first : INF;
if(aux + total < menor_K)
menor_K = aux + total;
for(auto& [ch, val] : adj[v])
if(ch != pai && !block[ch])
dfs1(adj, ch, v, dist + val, total+1, K);
}
void dfs2(vector<vector<pair<int, ll>>>&adj, int v, int pai, int K) {
int edges = edges_dist[v].first;
ll dist = edges_dist[v].second;
if(dist > K) return;
if(melhor[dist].second != flagAtual || melhor[dist].first > edges) {
melhor[dist].first = edges;
melhor[dist].second = flagAtual;
}
for (auto& [ch, val] : adj[v])
if(!block[ch] && ch != pai)
dfs2(adj, ch, v, K);
}
int best_path(int N, int K, int H[][2], int L[]) {
vector<vector<pair<int, ll>>> adj(N);
vector<int> subtreeSz(N);
melhor.assign(K+1, {INF, 0});
block.assign(N, false);
edges_dist.assign(N, {0, 0});
menor_K = INF;
flagAtual = 1;
for(int i = 0; i < N-1; i++) {
adj[H[i][0]].push_back({H[i][1], L[i]});
adj[H[i][1]].push_back({H[i][0], L[i]});
}
queue<int> Q;
Q.push(0);
while (!Q.empty()) {
int node = Q.front();
get_SubTreeSize(adj, subtreeSz, node, -1);
node= findCentroid(adj, subtreeSz, node, -1, subtreeSz[node]);
block[node] = true;
melhor[0] = {0, flagAtual};
Q.pop();
for (auto& [ch, val] : adj[node])
if (!block[ch]) {
dfs1(adj, ch, node, val, 1, K);
dfs2(adj, ch, node, K);
Q.push(ch);
}
flagAtual++;
}
if(menor_K == INF) menor_K = -1;
return menor_K;
}
