結果
| 問題 |
No.2012 Largest Triangle
|
| コンテスト | |
| ユーザー |
 srtubaki
|
| 提出日時 | 2022-07-16 02:05:02 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 123 ms / 2,500 ms |
| コード長 | 7,254 bytes |
| コンパイル時間 | 2,639 ms |
| コンパイル使用メモリ | 206,260 KB |
| 最終ジャッジ日時 | 2025-01-30 09:26:52 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 41 |
ソースコード
#pragma region template
#include <bits/stdc++.h>
using namespace std;
// clang-format off
using ll = long long; using vl = vector<ll>; using vvl = vector<vl>;
using ld = long double; using vld = vector<ld>; using vvld = vector<vld>;
using pll = pair<ll, ll>; using vpll = vector<pll>; using vvpll = vector<vpll>;
using vb = vector<bool>; using vvb = vector<vector<bool>>;
using vs = vector<string>;
using mll = map<ll, ll>;
template <class T> using V = vector<T>; template <class T> using VV = V<V<T>>; template <class T> using VVV = V<VV<T>>;
template <class T> using max_heap = priority_queue<T>;
template <class T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
constexpr ll inf = 3001001000100100100LL;
#define endl '\n'
#define _overload(_1, _2, _3, name, ...) name
#define rep(...) _overload(__VA_ARGS__, _rep, _rep2,)(__VA_ARGS__)
#define repc(...) _overload(__VA_ARGS__, _repc, _repc2,)(__VA_ARGS__)
#define repr(...) _overload(__VA_ARGS__, _repr, _repr2,)(__VA_ARGS__)
#define reprc(...) _overload(__VA_ARGS__, _reprc, _reprc2,)(__VA_ARGS__)
#define _rep(i,k,n) for(ll i=(k) , i##_xxxx=(n); i < i##_xxxx; ++i)
#define _repc(i,k,n) for(ll i=(k) , i##_xxxx=(n); i <=i##_xxxx; ++i)
#define _repr(i,k,n) for(ll i=(n)-1, i##_xxxx=(k); i >=i##_xxxx; --i)
#define _reprc(i,k,n) for(ll i=(n) , i##_xxxx=(k); i >=i##_xxxx; --i)
#define _rep2(i,n) _rep(i,0,n)
#define _repc2(i,n) _repc(i,1,n)
#define _repr2(i,n) _repr(i,0,n)
#define _reprc2(i,n) _reprc(i,1,n)
#define rall(o) rbegin(o), rend(o)
#define all(o) begin(o), end(o)
template <class C> ll sz(const C& c) { return static_cast<ll>(c.size()); }
template <class T> bool chmax(T& m, const T& v){ if (m < v){ m = v; return true; } return false; }
template <class T> bool chmin(T& m, const T& v){ if (v < m){ m = v; return true; } return false; }
template <class T> T cdiv(const T& a, const T& b){ return (a + b - 1) / b; }
template <class T> T rdiv(const T& a, const T& b){ return (a + b / 2) / b; }
template <class T, class S> string join(const T& v, const S& sep ){ stringstream ss; bool f = false; for (const auto& e : v){ if (f) ss << sep; f = true; ss << e;} return ss.str(); }
template <class T, class S, class... U> string join(const T& v, const S& sep, const U& ...args){ stringstream ss; bool f = false; for (const auto& c : v){ if (f) ss << sep; f = true; ss << join(c, args...); } return ss.str(); }
template <class T> ostream& operator<<(ostream& os, const vector<T>& seq){ os << '[' << join(seq, ",") << ']'; return os; } template <class T> ostream& operator<<(ostream& os, const vector<vector<T>>& seq){ os << '[' << join(seq, ",\n ") << ']'; return os; }
template <class T> ostream& operator<<(ostream& os, const deque<T>& seq){ os << '[' << join(seq, ",") << ']'; return os; }
template <class T> ostream& operator<<(ostream& os, const set<T>& seq){ os << '{' << join(seq, ",") << '}'; return os; }
template <class T , class TH> ostream& operator<<(ostream& os, const unordered_set<T, TH>& seq){ os << '{' << join(seq, ",") << '}'; return os; }
template <class TK, class TV> ostream& operator<<(ostream& os, const map<TK, TV>& seq){ os << '{'; bool f = false; for (const auto& e : seq){ if (f) os << ','; f = true; os << e.first << ":" << e.second; } os << '}'; return os; }
template <class T1, class T2> ostream& operator<<(ostream& os, const pair<T1, T2>& pa){ os << '(' << pa.first << ',' << pa.second << ')'; return os; }
#if LOCAL
#define debug(...) _debug(__VA_ARGS__, __LINE__)
#else
#define debug(...)
#endif
void print() { std::cout << '\n'; }
template <class S> void print(const S& a){ std::cout << a << '\n'; }
template <class S> void _debug(const S& a){ std::cerr << "(L:" << std::setw(3) << a << ")\n"; }
template <class S, class... T> void print(const S& a, const T&... args){ std::cout << a << ' '; print(args...); }
template <class S, class... T> void _debug(const S& a, const T&... args){ std::cerr << a << ' '; _debug(args...); }
struct setup_main { setup_main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); std::cout << fixed << setprecision(15); } } setup_main_;
// clang-format on
#pragma endregion
template <class T>
struct Point {
T x, y;
bool operator<(const Point& b) const { return x < b.x or (x == b.x and y < b.y); }
Point operator-() const { return Point{-x, -y}; }
Point operator+() const { return *this; }
Point& operator+=(const Point& b) { x += b.x, y += b.y; return *this; }
Point& operator-=(const Point& b) { x -= b.x, y -= b.y; return *this; }
Point& operator*=(const T& c) { x *= c, y *= c; return *this; }
friend Point operator+(const Point& a, const Point& b) { return Point(a) += b; }
friend Point operator-(const Point& a, const Point& b) { return Point(a) -= b; }
friend Point operator*(const Point& a, const Point& b) { return Point(a) -= b; }
T cross(const Point& b) const { return (x * b.y - b.x * y); }
friend T cross(const Point& a, const Point& b) { return a.cross(b); }
friend ostream& operator<<(ostream& os, const Point& p) {
os << make_pair(p.x, p.y);
return os;
}
};
// 凸包
template <class T>
vector<Point<T>> convex_calc(vector<Point<T>>& P) {
vector<Point<ll>> S;
for (auto&& p1 : P) {
while (sz(S) >= 2) {
Point<T> p2 = S.back();
S.pop_back();
Point<T> p3 = S.back();
if (cross(p2 - p1, p3 - p2) < 0) {
S.push_back(p2);
break;
}
}
S.push_back(p1);
}
return S;
}
template <class T>
vector<Point<T>> convex_hull_upper(vector<Point<T>> P) {
sort(all(P));
return convex_calc(P);
}
template <class T>
vector<Point<T>> convex_hull_lower(vector<Point<T>> P) {
sort(rall(P));
return convex_calc(P);
}
template <class T>
vector<Point<T>> convex_hull(vector<Point<T>> P) {
sort(all(P));
vector<Point<T>> u = convex_calc(P);
reverse(all(P));
vector<Point<T>> l = convex_calc(P);
rep(i, 1, l.size() - 1) u.push_back(l[i]);
return u;
}
/*/
凸包上の点だけ考えれば良い
底辺を決め打って、高さを3分探索
倍加すると探索が楽
/*/
void solve(ll N, vector<ll> X, vector<ll> Y) {
vector<Point<ll>> P(N);
rep(i, N) P[i] = {X[i], Y[i]};
rep(i, N) P.push_back(-P[i]);
P = convex_hull(P);
ll ans = 0;
N = sz(P) / 2;
rep(i, N) {
Point<ll> p = P[i];
auto f = [&](Point<ll> pl, Point<ll> pr) { return abs(cross(p, pl)) < abs(cross(p, pr)); };
ll l = i, r = i + N;
while (r - l > 2) {
ll ml = l + (r - l) / 3, mr = r - (r - l) / 3;
if (f(P[ml], P[mr]))
l = ml;
else
r = mr;
}
chmax(ans, abs(cross(p, P[l])));
chmax(ans, abs(cross(p, P[(r + l) / 2])));
chmax(ans, abs(cross(p, P[r])));
}
print(ans);
}
int main() {
int N;
cin >> N;
vector<ll> x(N), y(N);
rep(i, N) {
cin >> x[i] >> y[i];
}
solve(N, x, y);
}