#778605 (C++17) No.2012 Largest Triangle

提出ソース

結果

問題	No.2012 Largest Triangle
ユーザー	haruki_K
提出日時	2022-07-15 22:23:42
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	200 ms / 2,500 ms
コード長	10,002 bytes
コンパイル時間	2,623 ms
コンパイル使用メモリ	220,720 KB
実行使用メモリ	7,296 KB
最終ジャッジ日時	2024-06-27 21:19:43
合計ジャッジ時間	6,432 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	2 ms 6,944 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,944 KB
testcase_16	AC	58 ms 6,944 KB
testcase_17	AC	60 ms 6,944 KB
testcase_18	AC	59 ms 6,944 KB
testcase_19	AC	58 ms 6,944 KB
testcase_20	AC	58 ms 6,944 KB
testcase_21	AC	59 ms 6,944 KB
testcase_22	AC	59 ms 6,944 KB
testcase_23	AC	57 ms 6,940 KB
testcase_24	AC	59 ms 6,944 KB
testcase_25	AC	58 ms 6,940 KB
testcase_26	AC	197 ms 7,040 KB
testcase_27	AC	194 ms 7,040 KB
testcase_28	AC	195 ms 7,168 KB
testcase_29	AC	197 ms 7,296 KB
testcase_30	AC	200 ms 7,040 KB
testcase_31	AC	85 ms 6,940 KB
testcase_32	AC	86 ms 6,940 KB
testcase_33	AC	86 ms 6,940 KB
testcase_34	AC	84 ms 6,944 KB
testcase_35	AC	86 ms 6,940 KB
testcase_36	AC	2 ms 6,940 KB
testcase_37	AC	2 ms 6,940 KB
testcase_38	AC	3 ms 6,944 KB
testcase_39	AC	3 ms 6,940 KB
testcase_40	AC	2 ms 6,944 KB
testcase_41	AC	45 ms 7,296 KB

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ソースコード

raw source code

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#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 repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#define oj_local(x, y) (x)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
    repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
    return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
    repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
    return false;
}
template <class vec> int sort_unique(vec &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(s.back() + *l++);
    return s;
}
template <class It> auto suffix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(*--r + s.back());
    reverse(s.begin(), s.end());
    return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
// <<<
// >>> convex hull trick

template <class T, class Comp> struct CHT {
    struct Line {
        T a, b;
        mutable Line const *right;
        Line(T a, T b) : a(a), b(b), right(nullptr) { }
        T operator()(pair<T, T> const& p) const { return a*p.first + b*p.second; }
        bool operator<(Line const& l) const { return a < l.a; }
        bool operator<(pair<T, T> const& p) const {
            return right and Comp()((*right)(p), (*this)(p));
        }
#ifdef LOCAL
        friend string to_s(Line l) { return to_s(make_pair(l.a, l.b)); }
#endif
    };
    multiset<Line, less<>> s;

    static bool bad(Line const& l1, Line const& l2, Line const& l3) {
        using S = conditional_t<is_floating_point_v<T>, long double, __int128_t>;
        S a1 = l2.a - l1.a, b1 = l2.b - l1.b;
        S a2 = l3.a - l2.a, b2 = l3.b - l2.b;
        return not Comp()(a2*b1, a1*b2);
    }

    using It = typename multiset<Line, less<>>::iterator;
    const Line *ptr(It &it) { return it == s.end() ? nullptr : &*it; }
    bool del(It &it, It &jt, It &kt) {
        it->right = &*jt, jt->right = ptr(kt);
        if (kt == s.end()) return false;
        if (bad(*it, *jt, *kt)) {
            s.erase(jt);
            it->right = &*kt;
            return true;
        }
        return false;
    }

    CHT() {}
    CHT(CHT const& rhs) : s(rhs.s) {
        for (auto it = s.begin(), jt = it; it != s.end(); it = jt) {
            it->right = ptr(++jt);
        }
    }
    int size() const { return s.size(); }

    T get(T x, T y) const {
        assert(s.size());
        assert(y > 0);
        pair<T, T> p(x, y);
        auto it = s.lower_bound(p);
        return (*it)(p);
    }
    T get(T x) const { return get(x, 1); }
    void add(T a, T b) {
        Line l(a, b);
        auto it = s.lower_bound(l);
        if (it != s.end() and it->a == a) {
            if (not Comp()(b, it->b)) return;
            it = s.erase(it);
        }
        if (it != s.end() and it != s.begin() and bad(*prev(it), l, *it)) return;
        auto jt = it, kt = it;
        it = s.insert(it, l);
        while (kt != s.end() and del(it, jt, ++kt)) jt = kt;
        if (it == s.begin()) return;
        kt = it, jt = --it, jt->right = &*kt;
        while (it != s.begin() and del(--it, jt, kt)) jt = it;
    }
};
template <class T> using CHT_min = CHT<T, less<>>;
template <class T> using CHT_max = CHT<T, greater<>>;

template <class T> struct CHT_pair {
    CHT_min<T> cht_min;
    CHT_max<T> cht_max;
    void add(T a, T b) {
        cht_min.add(a, b);
        cht_max.add(a, b);
    }
    T get_min(T x, T y) const {
        if (y > 0) {
            return (*cht_min.s.lower_bound(pair(x, y)))(pair(x, y));
        } else {
            return (*cht_max.s.lower_bound(pair(-x, -y)))(pair(x, y));
        }
    }
    T get_max(T x, T y) const {
        if (y > 0) {
            return (*cht_max.s.lower_bound(pair(x, y)))(pair(x, y));
        } else {
            return (*cht_min.s.lower_bound(pair(-x, -y)))(pair(x, y));
        }
    }
};

// <<<

int32_t main() {
    int n; cin >> n;
    vector<int> x(n), y(n);
    rep (i, n) cin >> x[i] >> y[i];

    CHT_pair<int> cht;
    rep (i, n) cht.add(x[i], y[i]);

    int ma = 0;
    rep (i, n) {
        chmax(ma, cht.get_max(y[i], -x[i]));
        chmax(ma, cht.get_max(-y[i], x[i]));
    }
    cout << ma << '\n';

}

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結果

テストケース

ソースコード