Problem p03995 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout << fixed << setprecision(10)
#define ALL(a) (a).begin(), (a).end()
#define ALLR(a) (a).rbegin(), (a).rend()
#define spa << " " <<
#define test cout << "test" << endl;
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i, n, m) for (ll i = (n); i < (ll)(m); i++)
#define rrep(i, n, m) for (ll i = (m)-1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}
void pmod(ll &a, ll b) { a = (a + b) % MOD; }
void pmod(ll &a, ll b, ll c) { a = (b + c) % MOD; }
void qmod(ll &a, ll b) { a = (a * b) % MOD; }
void qmod(ll &a, ll b, ll c) { a = (b * c) % MOD; }
ll median(ll a, ll b, ll c) {
  return a + b + c - max({a, b, c}) - min({a, b, c});
}
void ans1(bool x) {
  if (x)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
void ans2(bool x) {
  if (x)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
void ans3(bool x) {
  if (x)
    cout << "Yay!" << endl;
  else
    cout << ":(" << endl;
}
template <typename T1, typename T2> void ans(bool x, T1 y, T2 z) {
  if (x)
    cout << y << endl;
  else
    cout << z << endl;
}
template <typename T> void debug(vector<vector<T>> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    cout << v[i][0];
    for (ll j = 1; j < w; j++)
      cout spa v[i][j];
    cout << endl;
  }
};
void debug(vector<string> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    for (ll j = 0; j < w; j++)
      cout << v[i][j];
    cout << endl;
  }
};
template <typename T> void debug(vector<T> &v, ll n) {
  if (n != 0)
    cout << v[0];
  for (ll i = 1; i < n; i++)
    cout spa v[i];
  cout << endl;
};
template <typename T> vector<vector<T>> vec(ll x, ll y, T w) {
  vector<vector<T>> v(x, vector<T>(y, w));
  return v;
}
ll gcd(ll x, ll y) {
  ll r;
  while (y != 0 && (r = x % y) != 0) {
    x = y;
    y = r;
  }
  return y == 0 ? x : y;
}
vector<ll> dx = {1, 0, -1, 0, 1, 1, -1, -1};
vector<ll> dy = {0, 1, 0, -1, 1, -1, 1, -1};
template <typename T> vector<T> make_v(size_t a, T b) {
  return vector<T>(a, b);
}
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}
ostream &operator<<(ostream &os, pair<ll, ll> &p) {
  return os << p.first << " " << p.second;
}
struct UnionFind {
  vector<ll> data;
  vector<ll> difweight;
  UnionFind(ll size) {
    data.assign(size, -1);
    difweight.assign(size, 0);
  }
  bool unite(ll x, ll y, ll w) { // y=x+w
    w += weight(x);
    w -= weight(y);
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y), w = -w;
      data[x] += data[y];
      data[y] = x;
      difweight[y] = w;
    }
    return x != y;
  }
  bool find(ll x, ll y) { return root(x) == root(y); }
  ll diff(ll x, ll y) { return weight(y) - weight(x); }
  ll weight(ll x) {
    root(x);
    return difweight[x];
  }
  ll root(ll x) {
    if (data[x] < 0) {
      return x;
    } else {
      ll tmp = root(data[x]);
      difweight[x] += difweight[data[x]];
      return data[x] = tmp;
    }
  }
  ll size(ll x) { return -data[root(x)]; }
  ll debug() {
    rep(i, 0, data.size()) {
      root(i);
      cout << i spa data[i] spa difweight[i] spa weight(i) << endl;
    }
    cout << endl;
  }
};
int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res = 0, buf = 0;
  bool judge = true;
  ll h, w;
  cin >> h >> w;
  ll n;
  cin >> n;
  vector<vector<P>> v(h);
  rep(i, 0, n) {
    ll x, y, a;
    cin >> x >> y >> a;
    x--;
    y--;
    v[x].EB(y, a);
  }
  UnionFind uf(w);
  rep(i, 0, h) {
    sort(ALL(v[i]));
    rep(j, 0, (ll)v[i].size() - 1) {
      auto x1 = v[i][j], x2 = v[i][j + 1];
      if (uf.find(v[i][j].fi, v[i][j + 1].fi)) {
        if (uf.diff(x1.fi, x2.fi) != x2.se - x1.se)
          judge = false;
      } else {
        uf.unite(x1.fi, x2.fi, x2.se - x1.se);
      }
    }
  }
  vector<ll> val(w, INF);
  rep(i, 0, w) { chmin(val[uf.root(i)], uf.weight(i)); }
  rep(i, 0, h) {
    for (auto z : v[i]) {
      if (z.se < uf.weight(z.fi) - val[uf.root(i)])
        judge = false;
    }
  }
  ans1(judge);
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout << fixed << setprecision(10)
#define ALL(a) (a).begin(), (a).end()
#define ALLR(a) (a).rbegin(), (a).rend()
#define spa << " " <<
#define test cout << "test" << endl;
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i, n, m) for (ll i = (n); i < (ll)(m); i++)
#define rrep(i, n, m) for (ll i = (m)-1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}
void pmod(ll &a, ll b) { a = (a + b) % MOD; }
void pmod(ll &a, ll b, ll c) { a = (b + c) % MOD; }
void qmod(ll &a, ll b) { a = (a * b) % MOD; }
void qmod(ll &a, ll b, ll c) { a = (b * c) % MOD; }
ll median(ll a, ll b, ll c) {
  return a + b + c - max({a, b, c}) - min({a, b, c});
}
void ans1(bool x) {
  if (x)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
void ans2(bool x) {
  if (x)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
void ans3(bool x) {
  if (x)
    cout << "Yay!" << endl;
  else
    cout << ":(" << endl;
}
template <typename T1, typename T2> void ans(bool x, T1 y, T2 z) {
  if (x)
    cout << y << endl;
  else
    cout << z << endl;
}
template <typename T> void debug(vector<vector<T>> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    cout << v[i][0];
    for (ll j = 1; j < w; j++)
      cout spa v[i][j];
    cout << endl;
  }
};
void debug(vector<string> &v, ll h, ll w) {
  for (ll i = 0; i < h; i++) {
    for (ll j = 0; j < w; j++)
      cout << v[i][j];
    cout << endl;
  }
};
template <typename T> void debug(vector<T> &v, ll n) {
  if (n != 0)
    cout << v[0];
  for (ll i = 1; i < n; i++)
    cout spa v[i];
  cout << endl;
};
template <typename T> vector<vector<T>> vec(ll x, ll y, T w) {
  vector<vector<T>> v(x, vector<T>(y, w));
  return v;
}
ll gcd(ll x, ll y) {
  ll r;
  while (y != 0 && (r = x % y) != 0) {
    x = y;
    y = r;
  }
  return y == 0 ? x : y;
}
vector<ll> dx = {1, 0, -1, 0, 1, 1, -1, -1};
vector<ll> dy = {0, 1, 0, -1, 1, -1, 1, -1};
template <typename T> vector<T> make_v(size_t a, T b) {
  return vector<T>(a, b);
}
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}
ostream &operator<<(ostream &os, pair<ll, ll> &p) {
  return os << p.first << " " << p.second;
}
struct UnionFind {
  vector<ll> data;
  vector<ll> difweight;
  UnionFind(ll size) {
    data.assign(size, -1);
    difweight.assign(size, 0);
  }
  bool unite(ll x, ll y, ll w) { // y=x+w
    w += weight(x);
    w -= weight(y);
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y), w = -w;
      data[x] += data[y];
      data[y] = x;
      difweight[y] = w;
    }
    return x != y;
  }
  bool find(ll x, ll y) { return root(x) == root(y); }
  ll diff(ll x, ll y) { return weight(y) - weight(x); }
  ll weight(ll x) {
    root(x);
    return difweight[x];
  }
  ll root(ll x) {
    if (data[x] < 0) {
      return x;
    } else {
      ll tmp = root(data[x]);
      difweight[x] += difweight[data[x]];
      return data[x] = tmp;
    }
  }
  ll size(ll x) { return -data[root(x)]; }
  ll debug() {
    rep(i, 0, data.size()) {
      root(i);
      cout << i spa data[i] spa difweight[i] spa weight(i) << endl;
    }
    cout << endl;
  }
};
int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res = 0, buf = 0;
  bool judge = true;
  ll h, w;
  cin >> h >> w;
  ll n;
  cin >> n;
  vector<vector<P>> v(h);
  rep(i, 0, n) {
    ll x, y, a;
    cin >> x >> y >> a;
    x--;
    y--;
    v[x].EB(y, a);
  }
  UnionFind uf(w);
  rep(i, 0, h) {
    sort(ALL(v[i]));
    rep(j, 0, (ll)v[i].size() - 1) {
      auto x1 = v[i][j], x2 = v[i][j + 1];
      if (uf.find(v[i][j].fi, v[i][j + 1].fi)) {
        if (uf.diff(x1.fi, x2.fi) != x2.se - x1.se)
          judge = false;
      } else {
        uf.unite(x1.fi, x2.fi, x2.se - x1.se);
      }
    }
  }
  vector<ll> val(w, INF);
  rep(i, 0, w) { chmin(val[uf.root(i)], uf.weight(i)); }
  rep(i, 0, h) {
    for (auto z : v[i]) {
      if (z.se < uf.weight(z.fi) - val[uf.root(z.fi)])
        judge = false;
    }
  }
  ans1(judge);
  return 0;
}