Problem p03441 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
#define ALL(x) x.begin(), x.end()
#define rep(i, n) for (int i = 0; i < (n); i++)
#define debug(v)                                                               \
  cout << #v << ":";                                                           \
  for (auto x : v) {                                                           \
    cout << x << ' ';                                                          \
  }                                                                            \
  cout << endl;
#define mod 1000000007
using ll = long long;
const int INF = 1000000000;
const ll LINF = 1001002003004005006ll;
int dx[] = {1, 0, -1, 0};
int dy[] = {0, 1, 0, -1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

struct IOSetup {
  IOSetup() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(12);
  }
} iosetup;

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

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;
}

signed main() {
  int n;
  cin >> n;
  vector<vector<int>> g(n);
  rep(i, n - 1) {
    int u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }

  function<int(int, int)> dfs = [&](int pre, int now) {
    int c = 0, sum = 0, non0 = 0;
    for (auto to : g[now])
      if (pre != to) {
        int k = dfs(now, to);
        sum += k;
        if (k)
          non0++;
        c++;
      }
    int ad = c - 1 - non0;
    chmax(ad, 0);
    return sum + ad;
  };

  int ans = INF;
  vector<int> st(n);
  iota(ALL(st), 0);
  random_shuffle(ALL(st));
  rep(i, min(500, n)) { chmin(ans, 1 + dfs(-1, st[i])); }
  cout << ans << endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
#define ALL(x) x.begin(), x.end()
#define rep(i, n) for (int i = 0; i < (n); i++)
#define debug(v)                                                               \
  cout << #v << ":";                                                           \
  for (auto x : v) {                                                           \
    cout << x << ' ';                                                          \
  }                                                                            \
  cout << endl;
#define mod 1000000007
using ll = long long;
const int INF = 1000000000;
const ll LINF = 1001002003004005006ll;
int dx[] = {1, 0, -1, 0};
int dy[] = {0, 1, 0, -1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

struct IOSetup {
  IOSetup() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(12);
  }
} iosetup;

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

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;
}

signed main() {
  int n;
  cin >> n;
  vector<vector<int>> g(n);
  rep(i, n - 1) {
    int u, v;
    cin >> u >> v;
    g[u].push_back(v);
    g[v].push_back(u);
  }

  function<int(int, int)> dfs = [&](int pre, int now) {
    int c = 0, sum = 0, non0 = 0;
    for (auto to : g[now])
      if (pre != to) {
        int k = dfs(now, to);
        sum += k;
        if (k)
          non0++;
        c++;
      }
    int ad = c - 1 - non0;
    chmax(ad, 0);
    return sum + ad;
  };

  int ans = INF;
  vector<int> st;
  rep(i, n) if (g[i].size() == 1) st.push_back(i);
  mt19937 mt(time(0));
  shuffle(ALL(st), mt);
  rep(i, min(100, (int)st.size())) { chmin(ans, 1 + dfs(-1, st[i])); }
  cout << ans << endl;
  return 0;
}