Problem p02698 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
const long long INF = 1LL << 60;
const long long MOD = 1000000007;
const double PI = acos(-1.0);
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n - 1); i >= 0; --i)
#define perm(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define ALL(obj) (obj).begin(), (obj).end()
#define RALL(obj) (obj).rbegin(), (obj).rend()
#define pb push_back
#define to_s to_string
#define len(v) (ll) v.size()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define print(x) cout << (x) << '\\n'
#define drop(x) cout << (x) << '\\n', exit(0)
#define debug(x) cout << #x << ": " << (x) << '\\n'
using namespace std;
using ll = long long;
typedef pair<ll, ll> P;
typedef vector<ll> vec;
typedef vector<vector<ll>> vec2;
typedef vector<vector<vector<ll>>> vec3;
template <class S, class T> inline bool chmax(S &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class S, class T> inline bool chmin(S &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
inline ll msb(ll v) { return 1 << (31 - __builtin_clzll(v)); }
inline ll devc(ll x, ll y) { return (x + y - 1) / y; }
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a * (b / gcd(a, b)); }

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T1, typename T2, typename T3>
ostream &operator<<(ostream &os, const tuple<T1, T2, T3> &t) {
  os << get<0>(t) << " " << get<1>(t) << " " << get<2>(t);
  return os;
}

template <typename T1, typename T2, typename T3>
istream &operator>>(istream &is, tuple<T1, T2, T3> &t) {
  is >> get<0>(t) >> get<1>(t) >> get<2>(t);
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); ++i) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v)
    is >> in;
  return is;
}

/*---------------------------------    Tools
 * ------------------------------------------*/
template <typename T> vector<T> cumsum(const vector<T> &X) {
  vector<T> res(X.size() + 1, 0);
  for (int i = 0; i < X.size(); ++i)
    res[i + 1] += res[i] + X[i];
  return res;
}

template <typename S, typename T, typename F>
pair<T, T> bisearch(S left, T right, F f) {
  while (abs(right - left) > 1) {
    T mid = (right + left) / 2;
    if (f(mid))
      right = mid;
    else
      left = mid;
  }
  return {left, right};
}

template <typename S, typename T, typename F>
double trisearch(S left, T right, F f, int maxLoop = 90) {
  double low = left, high = right;
  while (maxLoop--) {
    double mid_left = high / 3 + low * 2 / 3;
    double mid_right = high * 2 / 3 + low / 3;
    if (f(mid_left) >= f(mid_right))
      low = mid_left;
    else
      high = mid_right;
  }
  return (low + high) * 0.5;
}

/*---------------------------------    Graph
 * ------------------------------------------*/

struct Edge {
  ll from, to, weight;
  Edge() : from(0), to(0), weight(0) {}
  Edge(ll f, ll t, ll w) : from(f), to(t), weight(w) {}
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;

void add_edge(Graph &g, ll a, ll b, ll w = 1) {
  g[a].emplace_back(a, b, w);
  g[b].emplace_back(b, a, w);
}

void add_arrow(Graph &g, ll a, ll b, ll w = 1) { g[a].emplace_back(a, b, w); }

template <typename T> vector<T> dijkstra(Graph &g, T s, bool restore = false) {
  vector<T> dist(g.size(), INF);
  priority_queue<pair<T, T>, vector<pair<T, T>>, greater<pair<T, T>>> que;
  dist[s] = 0;
  que.emplace(dist[s], s);

  vector<T> prev(g.size(), -1);

  while (!que.empty()) {
    T cost, idx;
    tie(cost, idx) = que.top();
    que.pop();
    if (dist[idx] < cost)
      continue;
    for (auto &e : g[idx]) {
      auto next_cost = cost + e.weight;
      if (dist[e.to] <= next_cost)
        continue;
      dist[e.to] = next_cost;

      if (restore)
        prev[e.to] = e.from;
      que.emplace(dist[e.to], e.to);
    }
  }
  if (restore)
    return prev;
  return dist;
}

vector<ll> shortest_path(Graph &g, ll start, ll goal) {
  vector<ll> prev = dijkstra(g, start, true);
  vector<ll> path;
  for (int cur = goal; cur != -1; cur = prev[cur])
    path.push_back(cur);
  reverse(path.begin(), path.end());
  return path;
}

/*------------------------------- Main Code Here
 * -----------------------------------------*/

int main() {
  ll N;
  cin >> N;
  vec A(N);
  cin >> A;

  Graph G(N);
  rep(i, N - 1) {
    ll a, b;
    cin >> a >> b;
    --a, --b;
    add_edge(G, a, b);
  }

  vec visited(N, 0);
  ll now = 0;
  visited[0] = 1;
  multiset<ll> s = {A[0]};

  vec ans(N, 0);
  ans[0] = 1;

  auto dfs = [&](auto &&self) -> void {
    for (auto e : G[now])
      if (!visited[e.to]) {
        now = e.to;
        visited[e.to] = 1;
        ans[now] = len(s);
        if (A[now] > *--s.end()) {
          s.insert(A[now]);
          ++ans[now];

          self(self);

          s.erase(s.lower_bound(A[now]));
        } else {
          auto itr = s.lower_bound(A[now]);
          ll val = *itr;
          s.erase(itr);
          s.insert(A[now]);

          self(self);

          s.erase(s.lower_bound(A[now]));
          s.insert(val);
        }

        now = e.from;
      }
  };

  dfs(dfs);

  print(ans);

  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
const long long INF = 1LL << 60;
const long long MOD = 1000000007;
const double PI = acos(-1.0);
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n - 1); i >= 0; --i)
#define perm(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define ALL(obj) (obj).begin(), (obj).end()
#define RALL(obj) (obj).rbegin(), (obj).rend()
#define pb push_back
#define to_s to_string
#define len(v) (ll) v.size()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define print(x) cout << (x) << '\\n'
#define drop(x) cout << (x) << '\\n', exit(0)
#define debug(x) cout << #x << ": " << (x) << '\\n'
using namespace std;
using ll = long long;
typedef pair<ll, ll> P;
typedef vector<ll> vec;
typedef vector<vector<ll>> vec2;
typedef vector<vector<vector<ll>>> vec3;
template <class S, class T> inline bool chmax(S &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class S, class T> inline bool chmin(S &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
inline ll msb(ll v) { return 1 << (31 - __builtin_clzll(v)); }
inline ll devc(ll x, ll y) { return (x + y - 1) / y; }
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a * (b / gcd(a, b)); }

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T1, typename T2, typename T3>
ostream &operator<<(ostream &os, const tuple<T1, T2, T3> &t) {
  os << get<0>(t) << " " << get<1>(t) << " " << get<2>(t);
  return os;
}

template <typename T1, typename T2, typename T3>
istream &operator>>(istream &is, tuple<T1, T2, T3> &t) {
  is >> get<0>(t) >> get<1>(t) >> get<2>(t);
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); ++i) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v)
    is >> in;
  return is;
}

/*---------------------------------    Tools
 * ------------------------------------------*/
template <typename T> vector<T> cumsum(const vector<T> &X) {
  vector<T> res(X.size() + 1, 0);
  for (int i = 0; i < X.size(); ++i)
    res[i + 1] += res[i] + X[i];
  return res;
}

template <typename S, typename T, typename F>
pair<T, T> bisearch(S left, T right, F f) {
  while (abs(right - left) > 1) {
    T mid = (right + left) / 2;
    if (f(mid))
      right = mid;
    else
      left = mid;
  }
  return {left, right};
}

template <typename S, typename T, typename F>
double trisearch(S left, T right, F f, int maxLoop = 90) {
  double low = left, high = right;
  while (maxLoop--) {
    double mid_left = high / 3 + low * 2 / 3;
    double mid_right = high * 2 / 3 + low / 3;
    if (f(mid_left) >= f(mid_right))
      low = mid_left;
    else
      high = mid_right;
  }
  return (low + high) * 0.5;
}

/*---------------------------------    Graph
 * ------------------------------------------*/

struct Edge {
  ll from, to, weight;
  Edge() : from(0), to(0), weight(0) {}
  Edge(ll f, ll t, ll w) : from(f), to(t), weight(w) {}
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;

void add_edge(Graph &g, ll a, ll b, ll w = 1) {
  g[a].emplace_back(a, b, w);
  g[b].emplace_back(b, a, w);
}

void add_arrow(Graph &g, ll a, ll b, ll w = 1) { g[a].emplace_back(a, b, w); }

template <typename T> vector<T> dijkstra(Graph &g, T s, bool restore = false) {
  vector<T> dist(g.size(), INF);
  priority_queue<pair<T, T>, vector<pair<T, T>>, greater<pair<T, T>>> que;
  dist[s] = 0;
  que.emplace(dist[s], s);

  vector<T> prev(g.size(), -1);

  while (!que.empty()) {
    T cost, idx;
    tie(cost, idx) = que.top();
    que.pop();
    if (dist[idx] < cost)
      continue;
    for (auto &e : g[idx]) {
      auto next_cost = cost + e.weight;
      if (dist[e.to] <= next_cost)
        continue;
      dist[e.to] = next_cost;

      if (restore)
        prev[e.to] = e.from;
      que.emplace(dist[e.to], e.to);
    }
  }
  if (restore)
    return prev;
  return dist;
}

vector<ll> shortest_path(Graph &g, ll start, ll goal) {
  vector<ll> prev = dijkstra(g, start, true);
  vector<ll> path;
  for (int cur = goal; cur != -1; cur = prev[cur])
    path.push_back(cur);
  reverse(path.begin(), path.end());
  return path;
}

/*------------------------------- Main Code Here
 * -----------------------------------------*/

int main() {
  ll N;
  cin >> N;
  vec A(N);
  cin >> A;

  Graph G(N);
  rep(i, N - 1) {
    ll a, b;
    cin >> a >> b;
    --a, --b;
    add_edge(G, a, b);
  }

  vec visited(N, 0);
  ll now = 0;
  visited[0] = 1;
  multiset<ll> s = {A[0]};

  vec ans(N, 0);
  ans[0] = 1;

  auto dfs = [&](auto &&self) -> void {
    for (auto e : G[now])
      if (!visited[e.to]) {
        now = e.to;
        visited[e.to] = 1;

        multiset<ll> tp = s;
        if (A[now] > *--s.end())
          s.insert(A[now]);
        else {
          auto itr = s.lower_bound(A[now]);
          s.erase(itr);
          s.insert(A[now]);
        }

        ans[now] = len(s);
        self(self);

        s = tp;
        now = e.from;
      }
  };

  dfs(dfs);

  print(ans);

  return 0;
}