#778343 (C++17(clang)) No.2012 Largest Triangle

• 問題: No.2012 Largest Triangle
• ユーザー: SSRS
• 提出日時: 2022-07-15 21:46:14
• 言語: C++17(clang) (17.0.6 + boost 1.83.0)
• 結果: AC
• 実行時間: 694 ms / 2,500 ms
• コード長: 2,524 bytes
• コンパイル時間: 1,479 ms
• コンパイル使用メモリ: 144,716 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-06-27 21:18:01
• 合計ジャッジ時間: 11,202 ms
• ジャッジサーバーID （参考情報）: judge3 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	241 ms; 5,376 KB
testcase_17	AC	238 ms; 5,376 KB
testcase_18	AC	241 ms; 5,376 KB
testcase_19	AC	236 ms; 5,376 KB
testcase_20	AC	237 ms; 5,376 KB
testcase_21	AC	234 ms; 5,376 KB
testcase_22	AC	240 ms; 5,376 KB
testcase_23	AC	236 ms; 5,376 KB
testcase_24	AC	237 ms; 5,376 KB
testcase_25	AC	236 ms; 5,376 KB
testcase_26	AC	691 ms; 5,376 KB
testcase_27	AC	678 ms; 5,376 KB
testcase_28	AC	686 ms; 5,376 KB
testcase_29	AC	694 ms; 5,376 KB
testcase_30	AC	689 ms; 5,376 KB
testcase_31	AC	379 ms; 5,376 KB
testcase_32	AC	382 ms; 5,376 KB
testcase_33	AC	378 ms; 5,376 KB
testcase_34	AC	372 ms; 5,376 KB
testcase_35	AC	374 ms; 5,376 KB
testcase_36	AC	3 ms; 5,376 KB
testcase_37	AC	3 ms; 5,376 KB
testcase_38	AC	3 ms; 5,376 KB
testcase_39	AC	3 ms; 5,376 KB
testcase_40	AC	3 ms; 5,376 KB
testcase_41	AC	135 ms; 5,376 KB

ソースコード

//https://atcoder.jp/contests/abc244/submissions/30254721
#include <algorithm>
#include <climits>
#include <cmath>
#include <iostream>
#include <vector>
#include <tuple>
using namespace std;
using ll = long long;
using Point = pair<ll, ll>;
const ll INF = LLONG_MAX / 4;
const double inv_phi = (sqrt(5) - 1) / 2;
void chmax(ll& a, ll b){ if(a < b) a = b; }

ll ccw(Point a, Point b, Point c){
    ll cross = (b.first - a.first) * (c.second - b.second) - (b.second - a.second) * (c.first - b.first);
    if(cross > 0) return 1;
    else if(cross == 0) return 0;
    else return -1;
}
struct ConvexHull{
    vector<Point> lower, upper;
    ConvexHull(Point p): lower{p}, upper{p}{}
    ConvexHull(const ConvexHull& a, const ConvexHull& b){
        vector<Point> v;
        merge(a.lower.begin(), a.lower.end(), b.lower.begin(), b.lower.end(), back_inserter(v));
        for(Point p : v){
            while(lower.size() >= 2 && ccw(lower.rbegin()[1], lower.back(), p) <= 0){
                lower.pop_back();
            }
            lower.push_back(p);
        }
        v.clear();
        merge(a.upper.begin(), a.upper.end(), b.upper.begin(), b.upper.end(), back_inserter(v));
        for(Point p : v){
            while(upper.size() >= 2 && ccw(upper.rbegin()[1], upper.back(), p) >= 0){
                upper.pop_back();
            }
            upper.push_back(p);
        }
    }
    ll get(ll A, ll B) const {
        auto& s = B < 0 ? lower : upper;
        // golden-section search
        auto f = [&](ll i){ return A * s[i].first + B * s[i].second; };
        ll l = 0, r = s.size() - 1, r2 = round(r * inv_phi), f_r2 = f(r2);
        while(abs(l - r) >= 6){
            ll l2 = r + llround((l - r) * inv_phi), f_l2 = f(l2);
            if(f_l2 < f_r2) tie(l, r) = tuple{r, l2};
            else tie(r, r2, f_r2) = tuple{r2, l2, f_l2};
        }
        ll ans = -INF;
        if(l > r) swap(l, r);
        for(ll i = l; i <= r; i++) chmax(ans, f(i));
        return ans;
    }
};
int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    ll Q;
    cin >> Q;
    vector<ConvexHull> S;
    ll ans = -INF;
    for(ll i = 1; i <= Q; i++){
        long long X, Y;
        cin >> X >> Y;
        S.emplace_back(pair{X, Y});
        for(ll j = 1; (i & j) == 0; j <<= 1){
            S.rbegin()[1] = ConvexHull(S.rbegin()[1], S.back());
            S.pop_back();
        }
        for(auto& s : S) chmax(ans, s.get(-Y, X));
        for(auto& s : S) chmax(ans, s.get(Y, -X));
    }
    cout << ans << '\n';
}