#include "stations.h"
#include <vector>
#include <iostream>
using namespace std;
void traverse(int u, int p, vector<int> &sz, vector<vector<int>> &adj) {
sz[u] = 1;
for(int v : adj[u]) if(v != p) {
traverse(v, u, sz, adj);
sz[u] += sz[v];
}
}
/*
increment timer when going down if par == 0
increment timer when going up if par == 1
*/
void bipartite_labeling(int u, int p, int par, int &timer, vector<int> &sz,
vector<int> &labels, vector<vector<int>> &adj) {
labels[u] = par ? timer+sz[u]-1 : timer;
if(par == 0) timer++;
for(int v : adj[u]) if(v != p) {
bipartite_labeling(v, u, 1-par, timer, sz, labels, adj);
}
if(par == 1) timer++;
}
vector<int> label(int n, int k, vector<int> u, vector<int> v) {
vector<int> labels(n), sz(n);
vector<vector<int>> adj(n);
for(int i = 0; i < (int)u.size(); i++) {
adj[u[i]].push_back(v[i]);
adj[v[i]].push_back(u[i]);
}
traverse(0, -1, sz, adj);
bipartite_labeling(0, -1, 0, *new int{0}, sz, labels, adj);
return labels;
}
// c is sorted in ascending order
int find_next_station(int s, int t, vector<int> c) {
if(s == 0) {
// at root
for(int x : c) if(x >= t) return x;
}
else {
// 1 neighbor goes towards root, some down the tree
if(c.size() == 1) return c[0];
// I. determine which type of vertex is s
if(c.back() < s) {
// par = 1
// minimum label is toward the root
int up = c[0];
c.erase(c.begin());
if(t >= s) return up;
int where = up;
for(int x : c) if(x <= t) where = x;
return where;
}
else {
// par = 0
// maximum label is toward the root
int up = c.back();
c.pop_back();
if(t < s) return up;
for(int x : c) if(x > t) return x;
return up;
}
}
return -1;
}
