Problem p02556 (C++) — buggy submission, verdict: Time Limit Exceeded

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
constexpr long long INF = 1LL << 60;
constexpr long long MOD = 1000000007;
double PI = acos(-1.0);
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n - 1); i >= 0; --i)
#define perm(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define ALL(obj) (obj).begin(), (obj).end()
#define RALL(obj) (obj).rbegin(), (obj).rend()
#define pb push_back
#define to_s to_string
#define len(v) (ll) v.size()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define print(x) cout << (x) << '\\n'
#define drop(x) cout << (x) << '\\n', exit(0)
#define debug(x) cout << #x << ": " << (x) << '\\n'
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> tpl;
typedef vector<ll> vec;
typedef vector<vector<ll>> vec2;
typedef vector<vector<vector<ll>>> vec3;
template <class S, class T> inline bool chmax(S &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class S, class T> inline bool chmin(S &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
inline ll msb(ll v) { return 1 << (31 - __builtin_clzll(v)); }
inline ll devc(ll x, ll y) { return (x + y - 1) / y; }
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a * (b / gcd(a, b)); }

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T1, typename T2, typename T3>
ostream &operator<<(ostream &os, const tuple<T1, T2, T3> &t) {
  os << get<0>(t) << " " << get<1>(t) << " " << get<2>(t);
  return os;
}

template <typename T1, typename T2, typename T3>
istream &operator>>(istream &is, tuple<T1, T2, T3> &t) {
  is >> get<0>(t) >> get<1>(t) >> get<2>(t);
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); ++i) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v)
    is >> in;
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const set<T> &st) {
  int ct = 0;
  for (auto &s : st)
    cout << s << (++ct != st.size() ? " " : "");
  return os;
}

template <typename T>
constexpr set<T> &operator|=(set<T> &st1, const set<T> &st2) {
  for (auto &s : st2)
    st1.insert(s);
  return st1;
}

template <typename T>
constexpr set<T> &operator-=(set<T> &st1, const set<T> &st2) {
  for (auto &s : st2)
    if (st1.count(s))
      st1.erase(s);
  return st1;
}

template <typename T>
constexpr set<T> &operator&=(set<T> &st1, const set<T> &st2) {
  auto itr = st1.begin();
  while (itr != st1.end()) {
    if (!st2.count(*itr))
      itr = st1.erase(itr);
    else
      ++itr;
  }
  return st1;
}

template <typename T>
constexpr set<T> operator|(const set<T> &st1, const set<T> &st2) {
  set<T> res = st1;
  res |= st2;
  return res;
}

template <typename T>
constexpr set<T> operator-(const set<T> &st1, const set<T> &st2) {
  set<T> res = st1;
  res -= st2;
  return res;
}

template <typename T>
constexpr set<T> operator&(const set<T> &st1, const set<T> &st2) {
  set<T> res = st1;
  res &= st2;
  return res;
}

/*---------------------------------    Tools
 * ------------------------------------------*/
template <typename T> vector<T> cumsum(const vector<T> &X) {
  vector<T> res(X.size() + 1, 0);
  for (int i = 0; i < X.size(); ++i)
    res[i + 1] += res[i] + X[i];
  return res;
}

template <typename S, typename T, typename F>
pair<T, T> bisearch(S left, T right, F f) {
  while (abs(right - left) > 1) {
    T mid = (right + left) / 2;
    if (f(mid))
      right = mid;
    else
      left = mid;
  }
  return {left, right};
}

template <typename S, typename T, typename F>
double trisearch(S left, T right, F f, int maxLoop = 90) {
  double low = left, high = right;
  while (maxLoop--) {
    double mid_left = high / 3 + low * 2 / 3;
    double mid_right = high * 2 / 3 + low / 3;
    if (f(mid_left) >= f(mid_right))
      low = mid_left;
    else
      high = mid_right;
  }
  return (low + high) * 0.5;
}

template <typename F> ll ternarySearch(ll L, ll R, F f) { //[L, R)
  ll lo = L - 1, hi = R - 1;
  while (lo + 1 != hi) {
    ll mi = (lo + hi) / 2;
    if (f(mi) <= f(mi + 1))
      hi = mi;
    else
      lo = mi;
  }
  return hi;
}

/*------------------------------- Main Code Here
 * -----------------------------------------*/

int main() {
  ll N;
  cin >> N;
  vec X;
  vec Y;
  rep(i, N) {
    ll x, y;
    cin >> x >> y;
    X.pb(x + y);
    Y.pb(x - y);
  }
  sort(ALL(X));
  sort(ALL(Y));
  ll ans = abs(X.front() - X.back());
  chmax(ans, abs(Y.front() - Y.back()));
  print(ans);

  return 0;
}

Error: TLE

Fixed submission:

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
constexpr long long INF = 1LL << 60;
constexpr long long MOD = 1000000007;
double PI = acos(-1.0);
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n - 1); i >= 0; --i)
#define perm(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define ALL(obj) (obj).begin(), (obj).end()
#define RALL(obj) (obj).rbegin(), (obj).rend()
#define pb push_back
#define to_s to_string
#define len(v) (ll) v.size()
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define print(x) cout << (x) << '\\n'
#define drop(x) cout << (x) << '\\n', exit(0)
#define debug(x) cout << #x << ": " << (x) << '\\n'
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> tpl;
typedef vector<ll> vec;
typedef vector<vector<ll>> vec2;
typedef vector<vector<vector<ll>>> vec3;
template <class S, class T> inline bool chmax(S &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class S, class T> inline bool chmin(S &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
inline ll msb(ll v) { return 1 << (31 - __builtin_clzll(v)); }
inline ll devc(ll x, ll y) { return (x + y - 1) / y; }
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a * (b / gcd(a, b)); }

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T1, typename T2, typename T3>
ostream &operator<<(ostream &os, const tuple<T1, T2, T3> &t) {
  os << get<0>(t) << " " << get<1>(t) << " " << get<2>(t);
  return os;
}

template <typename T1, typename T2, typename T3>
istream &operator>>(istream &is, tuple<T1, T2, T3> &t) {
  is >> get<0>(t) >> get<1>(t) >> get<2>(t);
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); ++i) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v)
    is >> in;
  return is;
}

template <typename T> ostream &operator<<(ostream &os, const set<T> &st) {
  int ct = 0;
  for (auto &s : st)
    cout << s << (++ct != st.size() ? " " : "");
  return os;
}

template <typename T>
constexpr set<T> &operator|=(set<T> &st1, const set<T> &st2) {
  for (auto &s : st2)
    st1.insert(s);
  return st1;
}

template <typename T>
constexpr set<T> &operator-=(set<T> &st1, const set<T> &st2) {
  for (auto &s : st2)
    if (st1.count(s))
      st1.erase(s);
  return st1;
}

template <typename T>
constexpr set<T> &operator&=(set<T> &st1, const set<T> &st2) {
  auto itr = st1.begin();
  while (itr != st1.end()) {
    if (!st2.count(*itr))
      itr = st1.erase(itr);
    else
      ++itr;
  }
  return st1;
}

template <typename T>
constexpr set<T> operator|(const set<T> &st1, const set<T> &st2) {
  set<T> res = st1;
  res |= st2;
  return res;
}

template <typename T>
constexpr set<T> operator-(const set<T> &st1, const set<T> &st2) {
  set<T> res = st1;
  res -= st2;
  return res;
}

template <typename T>
constexpr set<T> operator&(const set<T> &st1, const set<T> &st2) {
  set<T> res = st1;
  res &= st2;
  return res;
}

/*---------------------------------    Tools
 * ------------------------------------------*/
template <typename T> vector<T> cumsum(const vector<T> &X) {
  vector<T> res(X.size() + 1, 0);
  for (int i = 0; i < X.size(); ++i)
    res[i + 1] += res[i] + X[i];
  return res;
}

template <typename S, typename T, typename F>
pair<T, T> bisearch(S left, T right, F f) {
  while (abs(right - left) > 1) {
    T mid = (right + left) / 2;
    if (f(mid))
      right = mid;
    else
      left = mid;
  }
  return {left, right};
}

template <typename S, typename T, typename F>
double trisearch(S left, T right, F f, int maxLoop = 90) {
  double low = left, high = right;
  while (maxLoop--) {
    double mid_left = high / 3 + low * 2 / 3;
    double mid_right = high * 2 / 3 + low / 3;
    if (f(mid_left) >= f(mid_right))
      low = mid_left;
    else
      high = mid_right;
  }
  return (low + high) * 0.5;
}

template <typename F> ll ternarySearch(ll L, ll R, F f) { //[L, R)
  ll lo = L - 1, hi = R - 1;
  while (lo + 1 != hi) {
    ll mi = (lo + hi) / 2;
    if (f(mi) <= f(mi + 1))
      hi = mi;
    else
      lo = mi;
  }
  return hi;
}

/*---------------------------------   Geometry
 * -----------------------------------------*/
using ld = long double;
using Point = complex<ld>;
const ld EPS = 1e-10;

ld cross(const Point &a, const Point &b) {
  return a.real() * b.imag() - a.imag() * b.real();
}
ld dot(const Point &a, const Point &b) {
  return a.real() * b.real() + a.imag() * b.imag();
}

struct Line : vector<Point> {
  Line(Point a = Point(0.0, 0.0), Point b = Point(0.0, 0.0)) {
    this->push_back(a);
    this->push_back(b);
  }
  friend ostream &operator<<(ostream &s, const Line &l) {
    return s << '{' << l[0] << ',' << l[1] << '}';
  }
};

/* ∠ABC */
double degree(Point A, Point B, Point C) {
  if (B == C)
    return 0;
  return arg((A - B) / (C - B));
}

/* counter-clockwise */
/*
                    CCW

 -- BEHIND -- [a -- ON -- b] --- FRONT --

                    CW
 */
/*  AB, ACの関係性を調べる*/
/* 同一直線上 : positive, 非同一直線上 : negative*/
/* 同一直線上だが、CはAB上に無い : 3 */
/* 同一直線上でCはAB上の点 : 2 */
/* 同一直線上で逆向きにCが存在 : 1 */
/* AB -> ACが反時計周り : -1 */
/* AB -> ACが時計周り : -2 */
// VERIFIED : http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
enum CCW_RESULT { CCW = +1, CW = -1, BACK = +2, FRONT = -2, ON = 0 };
int ccw(Point A, Point B, Point C) {
  B -= A, C -= A;
  if (cross(B, C) > EPS)
    return CCW;
  if (cross(B, C) < -EPS)
    return CW;
  if (dot(B, C) < 0)
    return BACK;
  if (norm(B) < norm(C))
    return FRONT;
  return ON;
}

/* perpendicular bisector */
Line bisector(const Line &L) {
  Point X = L[0], Y = L[1];
  Point C = (X + Y) / ld(2.0);
  Point D = C + (X - Y) * Point(0.0, 1.0);
  return Line(C, D);
}

/* 二直線間の角度, 平行, 垂直 */
// VERIFIED : http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
double lineAngle(const Line &L1, const Line &L2) {
  return degree(Point(L1[1] - L1[0]), Point(0.0, 0.0), Point(L2[1] - L2[0]));
}

bool isParallel(const Line &L1, const Line &L2) {
  return abs(sin(lineAngle(L1, L2))) <= EPS;
}

bool isOrthogonal(const Line &L1, const Line &L2) {
  return abs(cos(lineAngle(L1, L2))) <= EPS;
}

/* cross point */
/* 二直線の交点 */
// VERIFIED : http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C
Point crosspoint(const Line &L1, const Line &L2) {
  if (isParallel(L1, L2))
    return Point(-INF, -INF);
  Point A = L1[0], B = L1[1];
  Point C = L2[0], D = L2[1];
  return A +
         (B - A) * (imag((A - C) * conj(C - D)) / imag((C - D) * conj(B - A)));
}

/* Line Segment Crossed? */
/* 線分の交差判定 */
// VERIFIED : http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B
bool isSegmentCrossed(const Line &L1, const Line &L2) {
  Point A = L1[0], B = L1[1];
  Point C = L2[0], D = L2[1];

  if (isParallel(L1, L2)) {
    if (ccw(A, B, C) == 2 or ccw(A, B, D) == 2 or ccw(C, D, A) == 2 or
        ccw(C, D, B) == 2)
      return true;
    return false;
  }

  double t = imag((A - C) * conj(C - D)) / imag((C - D) * conj(B - A));
  double s = imag((C - A) * conj(A - B)) / imag((A - B) * conj(D - C));
  return t + EPS >= 0 and t - EPS <= 1 and s + EPS >= 0 and s - EPS <= 1;
}

/* foot of a perpendicular line　*/
/* 垂線の足 */
// TODO : バグってる
Point foot(const Point &A, const Line &L) {
  return (A + L[0] + L[1] - (A * L[0] * conj(L[1]))) / ld(2.0);
};

// 凸包
// VERIFIED : http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A
vector<Point> ConvexHull(vector<Point> &X) {
  sort(ALL(X), [](Point A, Point B) {
    return A.real() != B.real() ? A.real() < B.real() : A.imag() < B.imag();
  });
  int k = 0;
  int n = X.size();
  vector<Point> res(2 * n);
  for (int i = 0; i < n; ++i) {
    while (k > 1 and ccw(res[k - 2], res[k - 1], X[i]) == CW)
      --k;
    res[k++] = X[i];
  }
  for (int i = n - 2, t = k; i >= 0; --i) {
    while (k > t and ccw(res[k - 2], res[k - 1], X[i]) == CW)
      --k;
    res[k++] = X[i];
  }
  res.resize(k - 1);
  return res;
}

ll RotatingCalipers(vector<Point> &CH) {
  ll N = CH.size();
  if (N == 2)
    return abs(CH[0].real() - CH[1].real()) + abs(CH[0].imag() - CH[1].imag());
  int i = 0, j = 0; // 任意の方向に対する最遠点対

  auto comp_x = [](Point a, Point b) -> bool {
    return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag();
  };

  // x軸方向に対する最遠点対を求める
  for (int k = 0; k < N; ++k) {
    if (!comp_x(CH[i], CH[k]))
      i = k;
    if (comp_x(CH[j], CH[k]))
      j = k;
  }

  // 回転させながら距離の最大値を更新していく
  ll res = 0;
  int si = i, sj = j;
  while (i != sj || j != si) {
    ll dist =
        abs(CH[i].real() - CH[j].real()) + abs(CH[i].imag() - CH[j].imag());
    chmax(res, dist);

    if (cross(CH[(i + 1) % N] - CH[i], CH[(j + 1) % N] - CH[j]) < 0) {
      i = (i + 1) % N;
    } else {
      j = (j + 1) % N;
    }
  }
  return res;
}

/*------------------------------- Main Code Here
 * -----------------------------------------*/

int main() {
  ll N;
  cin >> N;

  vector<Point> ps;

  rep(i, N) {
    ll x, y;
    cin >> x >> y;
    ps.pb(Point(x, y));
  }

  vector<Point> CH = ConvexHull(ps);
  print(RotatingCalipers(CH));

  return 0;
}