Problem p02573 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>

#define F first
#define S second
#define MP make_pair
#define pb push_back
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define LCM(a, b) (a) / __gcd((a), (b)) * (b)
#define CEIL(a, b) (a) / (b) + (((a) % (b)) ? 1 : 0)
#define log_2(a) (log((a)) / log(2))
#define ln '\n'

using namespace std;
using LL = long long;
using ldouble = long double;
using P = pair<int, int>;
using LP = pair<LL, LL>;

static const int INF = INT_MAX;
static const LL LINF = LLONG_MAX;
static const int MIN = INT_MIN;
static const LL LMIN = LLONG_MIN;
static const int MOD = 1e9 + 7;
static const int SIZE = 200005;

const int dx[] = {0, -1, 1, 0};
const int dy[] = {-1, 0, 0, 1};

vector<LL> Div(LL n) {
  vector<LL> ret;
  for (LL i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      ret.pb(i);
      if (i * i != n)
        ret.pb(n / i);
    }
  }
  sort(all(ret));
  return ret;
}

int root[SIZE];
int sz[SIZE];
void init() {
  for (int i = 0; i < SIZE; ++i) {
    root[i] = i;
    sz[i] = 1;
  }
}

int Root(int x) {
  if (x == root[x])
    return x;
  int rt = Root(root[x]);
  sz[x] = sz[rt];
  return rt;
}

bool Unite(int x, int y) {
  int rx, ry;
  rx = Root(x);
  ry = Root(y);

  if (rx == ry)
    return false;
  if (rx < ry) {
    root[ry] = rx;

  } else {
    root[rx] = ry;
  }
  sz[rx] += sz[ry];
  sz[ry] = sz[rx];
  return true;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int N;
  int M;
  cin >> N >> M;
  init();

  for (int i = 0; i < M; ++i) {
    int a, b;
    cin >> a >> b;
    Unite(a, b);
  }

  int res = 0;
  for (int i = 1; i <= N; ++i) {
    Root(i);
    res = max(res, sz[i]);
  }

  cout << res << endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>

#define F first
#define S second
#define MP make_pair
#define pb push_back
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define LCM(a, b) (a) / __gcd((a), (b)) * (b)
#define CEIL(a, b) (a) / (b) + (((a) % (b)) ? 1 : 0)
#define log_2(a) (log((a)) / log(2))
#define ln '\n'

using namespace std;
using LL = long long;
using ldouble = long double;
using P = pair<int, int>;
using LP = pair<LL, LL>;

static const int INF = INT_MAX;
static const LL LINF = LLONG_MAX;
static const int MIN = INT_MIN;
static const LL LMIN = LLONG_MIN;
static const int MOD = 1e9 + 7;
static const int SIZE = 200005;

const int dx[] = {0, -1, 1, 0};
const int dy[] = {-1, 0, 0, 1};

vector<LL> Div(LL n) {
  vector<LL> ret;
  for (LL i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      ret.pb(i);
      if (i * i != n)
        ret.pb(n / i);
    }
  }
  sort(all(ret));
  return ret;
}

int root[SIZE];
int sz[SIZE];
void init() {
  for (int i = 0; i < SIZE; ++i) {
    root[i] = i;
    sz[i] = 1;
  }
}

int Root(int x) {
  if (x == root[x])
    return x;
  int rt = Root(root[x]);
  sz[x] = sz[rt];
  return rt;
}

bool Unite(int x, int y) {
  int rx, ry;
  rx = Root(x);
  ry = Root(y);

  if (rx == ry)
    return false;
  if (sz[rx] > sz[ry]) {
    root[ry] = rx;

  } else {
    root[rx] = ry;
  }
  sz[rx] += sz[ry];
  sz[ry] = sz[rx];
  return true;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  int N;
  int M;
  cin >> N >> M;
  init();

  for (int i = 0; i < M; ++i) {
    int a, b;
    cin >> a >> b;
    Unite(a, b);
  }

  int res = 0;
  for (int i = 1; i <= N; ++i) {
    Root(i);
    res = max(res, sz[i]);
  }

  cout << res << endl;
  return 0;
}