Problem p02840 (C++)

Buggy submission (status: Runtime Error):
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep1(i, n) for (int i = 1; i < (int)(n); ++i)
#define repeq(i, n) for (int i = 0; i <= (int)(n); ++i)
#define rep1eq(i, n) for (int i = 1; i <= (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define rrep1(i, n) for (int i = (int)(n)-1; i > 0; --i)
#define rrepeq(i, n) for (int i = (int)(n); i >= 0; --i)
#define rrep1eq(i, n) for (int i = (int)(n); i > 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
template <typename T> using Graph = vector<vector<T>>;
template <typename T> using Spacial = vector<vector<vector<T>>>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int MOD = 1e9 + 7;
const int MOD2 = 998244353;
const double EPS = 1e-9;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

template <typename T> struct is_pair : false_type {};
template <typename T1, typename T2> struct is_pair<pair<T1, T2>> : true_type {};
template <typename T> struct is_vector : false_type {};
template <typename T> struct is_vector<vector<T>> : true_type {};

template <typename T1, typename T2>
istream &operator>>(istream &istr, pair<T1, T2> &p) {
  istr >> p.first >> p.second;
  return istr;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &ostr, const pair<T1, T2> &p) {
  ostr << p.first << " " << p.second;
  return ostr;
}
template <typename T> istream &operator>>(istream &istr, vector<T> &vec) {
  for (auto itr = vec.begin(); itr != vec.end(); ++itr) {
    istr >> *itr;
  }
  return istr;
}
template <typename T> ostream &operator<<(ostream &ostr, const vector<T> &vec) {
  if (vec.empty())
    return ostr;
  bool vp = is_vector<T>() || is_pair<T>();
  ostr << vec.front();
  for (auto itr = ++vec.begin(); itr != vec.end(); ++itr) {
    ostr << (vp ? "\n" : " ") << *itr;
  }
  return ostr;
}

template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

int modpow(int a, long long n, int mod = MOD) {
  int ret = 1;
  do {
    if (n & 1)
      ret = 1LL * ret * a % mod;
    a = 1LL * a * a % mod;
  } while (n >>= 1);
  return ret;
}

template <typename T> T GCD(T a, T b) { return b ? GCD(b, a % b) : a; }
template <typename T> T LCM(T a, T b) { return a / GCD(a, b) * b; }

template <typename T1, typename T2>
bool CompareBySecond(pair<T1, T2> a, pair<T1, T2> b) {
  return a.second != b.second ? a.second < b.second : a.first < b.first;
}
template <typename T> bool CompareBySlope(pair<T, T> a, pair<T, T> b) {
  // counterclockwise from 12 o'clock direction
  if (a.first * b.first < 0)
    return a.first < b.first;
  if (a.first == 0)
    return a.second >= 0 || b.first > 0;
  if (b.first == 0)
    return b.second < 0 && a.first < 0;
  return a.second * b.first < a.first * b.second;
}

/* -------- <templates end> -------- */

void solve() {
  ll n, x, d;
  cin >> n >> x >> d;

  if (d == 0 && x == 0) {
    cout << 1 << endl;
    return;
  }

  if (d == 0) {
    cout << n + 1 << endl;
    return;
  }

  if (x == 0) {
    cout << n * (n - 1) / 2 + 1 << endl;
    return;
  }

  if (d < 0)
    x = -x, d = -d;

  ll cycle = d / GCD(abs(x), d);
  int diff = (x % d) * cycle / d;
  int sz = min(n, cycle);

  Graph<pll> dp(sz);
  repeq(i, n) {
    ll left = (ll)i * (i - 1) / 2;
    ll right = (ll)i * (n - i + n - 1) / 2 + 1;
    ll add = i / cycle * diff + x / d * i;
    dp[i % cycle].push_back(pll(left + add, right + add));
  }

  ll ans = 0;
  rep(i, sz) {
    sort(ALL(dp[i]));
    ll cnt = 0;
    ll left, right;
    tie(left, right) = dp[i][0];
    for (auto p = ++dp[i].begin(); p != dp[i].end(); ++p) {
      if (right < p->first) {
        cnt += right - left;
        tie(left, right) = *p;
      } else {
        chmax(right, p->second);
      }
    }
    cnt += right - left;
    ans += cnt;
  }
  cout << ans << endl;
}

/* -------- <programs end> -------- */

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  solve();
  return 0;
}


Fixed submission:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep1(i, n) for (int i = 1; i < (int)(n); ++i)
#define repeq(i, n) for (int i = 0; i <= (int)(n); ++i)
#define rep1eq(i, n) for (int i = 1; i <= (int)(n); ++i)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; --i)
#define rrep1(i, n) for (int i = (int)(n)-1; i > 0; --i)
#define rrepeq(i, n) for (int i = (int)(n); i >= 0; --i)
#define rrep1eq(i, n) for (int i = (int)(n); i > 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
template <typename T> using Graph = vector<vector<T>>;
template <typename T> using Spacial = vector<vector<vector<T>>>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int MOD = 1e9 + 7;
const int MOD2 = 998244353;
const double EPS = 1e-9;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

template <typename T> struct is_pair : false_type {};
template <typename T1, typename T2> struct is_pair<pair<T1, T2>> : true_type {};
template <typename T> struct is_vector : false_type {};
template <typename T> struct is_vector<vector<T>> : true_type {};

template <typename T1, typename T2>
istream &operator>>(istream &istr, pair<T1, T2> &p) {
  istr >> p.first >> p.second;
  return istr;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &ostr, const pair<T1, T2> &p) {
  ostr << p.first << " " << p.second;
  return ostr;
}
template <typename T> istream &operator>>(istream &istr, vector<T> &vec) {
  for (auto itr = vec.begin(); itr != vec.end(); ++itr) {
    istr >> *itr;
  }
  return istr;
}
template <typename T> ostream &operator<<(ostream &ostr, const vector<T> &vec) {
  if (vec.empty())
    return ostr;
  bool vp = is_vector<T>() || is_pair<T>();
  ostr << vec.front();
  for (auto itr = ++vec.begin(); itr != vec.end(); ++itr) {
    ostr << (vp ? "\n" : " ") << *itr;
  }
  return ostr;
}

template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}
template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

int modpow(int a, long long n, int mod = MOD) {
  int ret = 1;
  do {
    if (n & 1)
      ret = 1LL * ret * a % mod;
    a = 1LL * a * a % mod;
  } while (n >>= 1);
  return ret;
}

template <typename T> T GCD(T a, T b) { return b ? GCD(b, a % b) : a; }
template <typename T> T LCM(T a, T b) { return a / GCD(a, b) * b; }

template <typename T1, typename T2>
bool CompareBySecond(pair<T1, T2> a, pair<T1, T2> b) {
  return a.second != b.second ? a.second < b.second : a.first < b.first;
}
template <typename T> bool CompareBySlope(pair<T, T> a, pair<T, T> b) {
  // counterclockwise from 12 o'clock direction
  if (a.first * b.first < 0)
    return a.first < b.first;
  if (a.first == 0)
    return a.second >= 0 || b.first > 0;
  if (b.first == 0)
    return b.second < 0 && a.first < 0;
  return a.second * b.first < a.first * b.second;
}

/* -------- <templates end> -------- */

void solve() {
  ll n, x, d;
  cin >> n >> x >> d;

  if (d == 0 && x == 0) {
    cout << 1 << endl;
    return;
  }

  if (d == 0) {
    cout << n + 1 << endl;
    return;
  }

  if (x == 0) {
    cout << n * (n - 1) / 2 + 1 << endl;
    return;
  }

  if (d < 0)
    x = -x, d = -d;

  ll cycle = d / GCD(abs(x), d);
  int diff = (x % d) * cycle / d;
  int sz = min(n + 1, cycle);

  Graph<pll> dp(sz);
  repeq(i, n) {
    ll left = (ll)i * (i - 1) / 2;
    ll right = (ll)i * (n - i + n - 1) / 2 + 1;
    ll add = i / cycle * diff + x / d * i;
    dp[i % cycle].push_back(pll(left + add, right + add));
  }

  ll ans = 0;
  rep(i, sz) {
    sort(ALL(dp[i]));
    ll cnt = 0;
    ll left, right;
    tie(left, right) = dp[i][0];
    for (auto p = ++dp[i].begin(); p != dp[i].end(); ++p) {
      if (right < p->first) {
        cnt += right - left;
        tie(left, right) = *p;
      } else {
        chmax(right, p->second);
      }
    }
    cnt += right - left;
    ans += cnt;
  }
  cout << ans << endl;
}

/* -------- <programs end> -------- */

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  solve();
  return 0;
}