IOI '20 - Stations

#include "stations.h"
#include <bits/stdc++.h>

using namespace std;

vector<vector<int>> g;
vector<int> tin, tout, depth;
int t;
void dfs(int node, int parent = -1) {
    if (parent == -1) depth[node] = 0;
    else depth[node] = depth[parent] + 1;

    tin[node] = ++t;
    for (int child : g[node]) {
        if (child != parent) dfs(child, node);
    }
    tout[node] = ++t;
}

void compress(vector<int> &v) {
    vector<int> u = v;
    sort(u.begin(), u.end());
    // all values already unique
    for (int &x : v) {
        x = lower_bound(u.begin(), u.end(), x) - u.begin();
    }
}

vector<int> label(int n, int k, vector<int> u, vector<int> v) {
    g.clear(), tin.clear(), tout.clear(), depth.clear();
    g.resize(n);
    for (int i = 0; i < u.size(); ++i) {
        g[u[i]].push_back(v[i]);
        g[v[i]].push_back(u[i]);
    }
    t = -1;
    tin.resize(n), tout.resize(n);
    depth.resize(n);
    dfs(0);

    vector<int> labels(n);
    for (int i = 0; i < n; i++) {
        if (depth[i] & 1) labels[i] = tout[i];
        else labels[i] = tin[i];
    }
    compress(labels);
    return labels;
}

int find_next_station(int s, int t, vector<int> c) {
    int m = c.size();
    if (m == 1) return c[0];
    sort(c.begin(), c.end());
    if (s < c.front()) { // s has tin, rest have tout
        // c.back() is parent of s
        if (s <= t && t <= c[m-2]) {
            // t is in subtree of s
            // which child
            for (int x : c) {
                if (t <= x) return x;
            }
        } else {
            // t is not in subtree of s
            return c.back();
        }
    } else { // s has tout, rest have tin
        // c.front() is parent of s
        if (c[1] <= t && t <= s) {
            // t is in subtree of s
            // which child
            for (int i = m-1; i >= 0; --i) {
                if (t >= c[i]) return c[i];
            }
        } else {
            // t is not in subtree of s
            return c.front();
        }
    }
}