Problem p03995 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#include <unistd.h>

using namespace std;

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \
  cerr << #v << ":";                                                           \
  for (int i = 0; i < v.size(); i++)                                           \
    cerr << " " << v[i];                                                       \
  cerr << endl
#define DEBUG_MAT(v)                                                           \
  cerr << #v << endl;                                                          \
  for (int i = 0; i < v.size(); i++) {                                         \
    for (int j = 0; j < v[i].size(); j++) {                                    \
      cerr << v[i][j] << " ";                                                  \
    }                                                                          \
    cerr << endl;                                                              \
  }

typedef long long ll;

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first - t.first, s.second - t.second);
}
template <class S, class T> ostream &operator<<(ostream &os, pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i <= (n); i++)
#define rrep(i, n) for (int i = (n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const ll MOD = 1000000007;
// const ll MOD = 998244353;
const double pi = 3.14159265358979323846;
#define Sp(p) cout << setprecision(15) << fixed << p << endl;
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dx2[8] = {1, 1, 0, -1, -1, -1, 0, 1}, dy2[8] = {0, 1, 1, 1, 0, -1, -1, -1};
#define fio()                                                                  \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);
// #define mp make_pair
// #define endl '\n'

class WeightedUF {
public:
  vi par, ran, num;
  vl diff_weight; // 親ノード(根ノードではない)との値の差分

  WeightedUF(int n) {
    par.resize(n);
    ran.resize(n);
    num.resize(n);
    diff_weight.resize(n);
    for (int i = 0; i < n; i++) {
      par[i] = i;
      ran[i] = 0;
      num[i] = 1;
      diff_weight[i] = 0;
    }
  }

  // 木の根を求める
  int find(int x) {
    if (par[x] == x) {
      return x;
    } else {
      int root = find(par[x]);
      diff_weight[x] += diff_weight[par[x]];
      return par[x] = root;
    }
  }

  ll weight(int x) {
    find(x); // 経路圧縮
    return diff_weight[x];
  }

  // xからみたyの重み
  ll diff(int x, int y) {
    if (!same(x, y)) {
      return -INF;
    } else {
      return weight(y) - weight(x);
    }
  }

  // xからみたyの重みがwになるように併合
  bool unite(int x, int y, ll w) {
    w += weight(x);
    w -= weight(y);
    x = find(x);
    y = find(y);
    int numsum = num[x] + num[y];
    if (x == y) {
      if (diff(x, y) == w) {
        return true;
      } else {
        return false;
      }
    }
    if (ran[x] < ran[y]) {
      swap(x, y);
      w = -w;
    }
    par[y] = x;
    if (ran[x] == ran[y]) {
      ran[x]++;
    }
    diff_weight[y] = w;
    num[x] = num[y] = numsum;
    return true;
  }

  // xとyが同じ集合に属するか否か
  bool same(int x, int y) { return find(x) == find(y); }
};

int main() {
  int h, w;
  cin >> h >> w;
  int n;
  cin >> n;
  vector<vector<pll>> i2j(h), j2i(w);
  rep(i, n) {
    ll r, c, a;
    cin >> r >> c >> a;
    r--;
    c--;
    i2j[r].push_back(pll(c, a));
    j2i[c].push_back(pll(r, a));
  }

  WeightedUF uf(n + w);
  rep(i, h) {
    for (int j = 1; j < i2j[i].size(); j++) {
      if (not uf.unite(i2j[i][0].first, i2j[i][j].first,
                       i2j[i][j].second - i2j[i][0].second)) {
        cout << "No" << endl;
        return 0;
      }
    }
  }

  rep(j, w) {
    for (int i = 1; i < j2i[j].size(); i++) {
      if (not uf.unite(j2i[j][0].first + w, j2i[j][i].first + w,
                       j2i[j][i].second - j2i[j][0].second)) {
        cout << "No" << endl;
        return 0;
      }
    }
  }

  vl midx(h, -1), mjdx(w, -1);
  vl mival(h, INF), mjval(w, INF);
  rep(i, h) {
    int root = uf.find(i + w);
    if (mival[root - w] > uf.diff(root, i + w)) {
      mival[root - w] = uf.diff(root, i + w);
      midx[root - w] = i;
    }
  }

  rep(j, w) {
    int root = uf.find(j);
    if (mjval[root] > uf.diff(root, j)) {
      mjval[root] = uf.diff(root, j);
      mjdx[root] = j;
    }
  }
  DEBUG_VEC(midx);
  DEBUG_VEC(mjdx);

  ll mi = INF;
  rep(i, h) {
    rep(j, i2j[i].size()) {
      ll idx = i2j[i][j].first, val = i2j[i][j].second;
      // DEBUG(idx); DEBUG(val);
      int rooti = uf.find(i + w), rootj = uf.find(idx);
      // DEBUG(pii(rooti, rootj));
      val = val + uf.diff(i + w, rooti) + uf.diff(idx, rootj);
      int ii = midx[rooti - w], jj = mjdx[rootj];
      // DEBUG(pii(ii, jj));
      val = val + uf.diff(rooti, ii + w) + uf.diff(rootj, jj);
      // DEBUG(val);
      chmin(mi, val);
    }
  }
  if (mi < 0) {
    cout << "No" << endl;
  } else {
    cout << "Yes" << endl;
  }
}


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

using namespace std;

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                                           \
  cerr << #v << ":";                                                           \
  for (int i = 0; i < v.size(); i++)                                           \
    cerr << " " << v[i];                                                       \
  cerr << endl
#define DEBUG_MAT(v)                                                           \
  cerr << #v << endl;                                                          \
  for (int i = 0; i < v.size(); i++) {                                         \
    for (int j = 0; j < v[i].size(); j++) {                                    \
      cerr << v[i][j] << " ";                                                  \
    }                                                                          \
    cerr << endl;                                                              \
  }

typedef long long ll;

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) {
  return pair<S, T>(s.first - t.first, s.second - t.second);
}
template <class S, class T> ostream &operator<<(ostream &os, pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (n); i++)
#define rep1(i, n) for (int i = 1; i <= (n); i++)
#define rrep(i, n) for (int i = (n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const ll MOD = 1000000007;
// const ll MOD = 998244353;
const double pi = 3.14159265358979323846;
#define Sp(p) cout << setprecision(15) << fixed << p << endl;
int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
int dx2[8] = {1, 1, 0, -1, -1, -1, 0, 1}, dy2[8] = {0, 1, 1, 1, 0, -1, -1, -1};
#define fio()                                                                  \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);
// #define mp make_pair
// #define endl '\n'

class WeightedUF {
public:
  vi par, ran, num;
  vl diff_weight; // 親ノード(根ノードではない)との値の差分

  WeightedUF(int n) {
    par.resize(n);
    ran.resize(n);
    num.resize(n);
    diff_weight.resize(n);
    for (int i = 0; i < n; i++) {
      par[i] = i;
      ran[i] = 0;
      num[i] = 1;
      diff_weight[i] = 0;
    }
  }

  // 木の根を求める
  int find(int x) {
    if (par[x] == x) {
      return x;
    } else {
      int root = find(par[x]);
      diff_weight[x] += diff_weight[par[x]];
      return par[x] = root;
    }
  }

  ll weight(int x) {
    find(x); // 経路圧縮
    return diff_weight[x];
  }

  // xからみたyの重み
  ll diff(int x, int y) {
    if (!same(x, y)) {
      return -INF;
    } else {
      return weight(y) - weight(x);
    }
  }

  // xからみたyの重みがwになるように併合
  bool unite(int x, int y, ll w) {
    w += weight(x);
    w -= weight(y);
    x = find(x);
    y = find(y);
    int numsum = num[x] + num[y];
    if (x == y) {
      if (diff(x, y) == w) {
        return true;
      } else {
        return false;
      }
    }
    if (ran[x] < ran[y]) {
      swap(x, y);
      w = -w;
    }
    par[y] = x;
    if (ran[x] == ran[y]) {
      ran[x]++;
    }
    diff_weight[y] = w;
    num[x] = num[y] = numsum;
    return true;
  }

  // xとyが同じ集合に属するか否か
  bool same(int x, int y) { return find(x) == find(y); }
};

int main() {
  int h, w;
  cin >> h >> w;
  int n;
  cin >> n;
  vector<vector<pll>> i2j(h), j2i(w);
  rep(i, n) {
    ll r, c, a;
    cin >> r >> c >> a;
    r--;
    c--;
    i2j[r].push_back(pll(c, a));
    j2i[c].push_back(pll(r, a));
  }

  WeightedUF uf(h + w);
  rep(i, h) {
    for (int j = 1; j < i2j[i].size(); j++) {
      if (not uf.unite(i2j[i][0].first, i2j[i][j].first,
                       i2j[i][j].second - i2j[i][0].second)) {
        cout << "No" << endl;
        return 0;
      }
    }
  }

  rep(j, w) {
    for (int i = 1; i < j2i[j].size(); i++) {
      if (not uf.unite(j2i[j][0].first + w, j2i[j][i].first + w,
                       j2i[j][i].second - j2i[j][0].second)) {
        cout << "No" << endl;
        return 0;
      }
    }
  }

  vl midx(h, -1), mjdx(w, -1);
  vl mival(h, INF), mjval(w, INF);
  rep(i, h) {
    int root = uf.find(i + w);
    if (mival[root - w] > uf.diff(root, i + w)) {
      mival[root - w] = uf.diff(root, i + w);
      midx[root - w] = i;
    }
  }

  rep(j, w) {
    int root = uf.find(j);
    if (mjval[root] > uf.diff(root, j)) {
      mjval[root] = uf.diff(root, j);
      mjdx[root] = j;
    }
  }
  DEBUG_VEC(midx);
  DEBUG_VEC(mjdx);

  ll mi = INF;
  rep(i, h) {
    rep(j, i2j[i].size()) {
      ll idx = i2j[i][j].first, val = i2j[i][j].second;
      // DEBUG(idx); DEBUG(val);
      int rooti = uf.find(i + w), rootj = uf.find(idx);
      // DEBUG(pii(rooti, rootj));
      val = val + uf.diff(i + w, rooti) + uf.diff(idx, rootj);
      int ii = midx[rooti - w], jj = mjdx[rootj];
      // DEBUG(pii(ii, jj));
      val = val + uf.diff(rooti, ii + w) + uf.diff(rootj, jj);
      // DEBUG(val);
      chmin(mi, val);
    }
  }
  if (mi < 0) {
    cout << "No" << endl;
  } else {
    cout << "Yes" << endl;
  }
}