Problem p02906 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using gpp_set = tree<T, null_type, less<T>, rb_tree_tag,
tree_order_statistics_node_update>; template<typename T, typename L> using
gpp_map = tree<T, L, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using gpp_multiset = tree<T, null_type, less_equal<T>,
rb_tree_tag, tree_order_statistics_node_update>;*/
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  cout << #v << "=" << endl;                                                   \
  REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                        \
  cout << endl;
#define mdebug(m)                                                              \
  cout << #m << "=" << endl;                                                   \
  REP(i_debug, m.size()) {                                                     \
    REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }    \
    cout << endl;                                                              \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;
// #define Add(x, y) x = (x + (y)) % mod
// #define Mult(x, y) x = (x * (y)) % mod

struct UnionFind {
  vector<int> par, sz;
  int n_cc;

  UnionFind(int N) {
    par = vector<int>(N);
    REP(i, N) par[i] = i;
    sz = vector<int>(N, 1);
    n_cc = N;
  }

  int find(int x) {
    if (par[x] == x)
      return x;
    else
      return par[x] = find(par[x]);
  }

  void unite(int x, int y) {
    x = find(x);
    y = find(y);
    if (x == y)
      return;

    if (sz[x] < sz[y])
      swap(x, y);

    par[y] = x;
    sz[x] += sz[y];
    n_cc--;
  }

  bool is_union(int x, int y) {
    x = find(x);
    y = find(y);
    return x == y;
  }

  int union_size(int x) { return sz[find(x)]; }
};

signed main() {

  int N, M, Q;
  cin >> N >> M >> Q;
  vec A(Q), B(Q), C(Q);
  UnionFind UF(N);
  REP(i, Q) {
    cin >> A[i] >> B[i] >> C[i];
    if (C[i] == 0) {
      /*
      if(UF.is_union(A[i], B[i])){
          Out("No");
          return 0;
      }else{
          UF.unite(A[i], B[i]);
      }*/
      UF.unite(A[i], B[i]);
    }
  }
  // debug(UF.n_cc);

  bool f1 = false;
  REP(i, Q) if (C[i] == 1) {
    f1 = true;
    if (UF.is_union(A[i], B[i])) {
      Out("No");
      return 0;
    }
  }

  if (f1 && UF.n_cc == 2) {
    Out("No");
  } else {
    assert(false);
    Out("Yes");
  }

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using gpp_set = tree<T, null_type, less<T>, rb_tree_tag,
tree_order_statistics_node_update>; template<typename T, typename L> using
gpp_map = tree<T, L, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using gpp_multiset = tree<T, null_type, less_equal<T>,
rb_tree_tag, tree_order_statistics_node_update>;*/
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  cout << #v << "=" << endl;                                                   \
  REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                        \
  cout << endl;
#define mdebug(m)                                                              \
  cout << #m << "=" << endl;                                                   \
  REP(i_debug, m.size()) {                                                     \
    REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }    \
    cout << endl;                                                              \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;
// #define Add(x, y) x = (x + (y)) % mod
// #define Mult(x, y) x = (x * (y)) % mod

struct UnionFind {
  vector<int> par, sz;
  int n_cc;

  UnionFind(int N) {
    par = vector<int>(N);
    REP(i, N) par[i] = i;
    sz = vector<int>(N, 1);
    n_cc = N;
  }

  int find(int x) {
    if (par[x] == x)
      return x;
    else
      return par[x] = find(par[x]);
  }

  void unite(int x, int y) {
    x = find(x);
    y = find(y);
    if (x == y)
      return;

    if (sz[x] < sz[y])
      swap(x, y);

    par[y] = x;
    sz[x] += sz[y];
    n_cc--;
  }

  bool is_union(int x, int y) {
    x = find(x);
    y = find(y);
    return x == y;
  }

  int union_size(int x) { return sz[find(x)]; }
};

signed main() {

  int N, M, Q;
  cin >> N >> M >> Q;
  vec A(Q), B(Q), C(Q);
  UnionFind UF(N);
  REP(i, Q) {
    cin >> A[i] >> B[i] >> C[i];
    if (C[i] == 0) {
      /*
      if(UF.is_union(A[i], B[i])){
          Out("No");
          return 0;
      }else{
          UF.unite(A[i], B[i]);
      }*/
      UF.unite(A[i], B[i]);
    }
  }
  // debug(UF.n_cc);

  bool f1 = false;
  REP(i, Q) if (C[i] == 1) {
    f1 = true;
    if (UF.is_union(A[i], B[i])) {
      Out("No");
      return 0;
    }
  }

  if (f1 && UF.n_cc == 2) {
    Out("No");
  } else {
    int n_tree = UF.n_cc;
    int Mmin = N - 1;
    if (f1)
      Mmin++;
    int Mmax = N - n_tree + n_tree * (n_tree - 1) / 2;
    if (Mmin <= M && M <= Mmax)
      Out("Yes");
    else
      Out("No");
  }

  return 0;
}