結果

問題 No.2458 Line Up Charged Balls
ユーザー 👑 hitonanodehitonanode
提出日時 2023-09-01 22:03:44
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 90 ms / 2,000 ms
コード長 10,810 bytes
コンパイル時間 1,987 ms
コンパイル使用メモリ 188,696 KB
実行使用メモリ 5,660 KB
最終ジャッジ日時 2023-09-01 22:03:49
合計ジャッジ時間 4,697 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge13
このコードへのチャレンジ
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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
4,380 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 2 ms
4,380 KB
testcase_03 AC 2 ms
4,380 KB
testcase_04 AC 2 ms
4,376 KB
testcase_05 AC 53 ms
5,476 KB
testcase_06 AC 57 ms
5,472 KB
testcase_07 AC 2 ms
4,380 KB
testcase_08 AC 2 ms
4,380 KB
testcase_09 AC 79 ms
5,116 KB
testcase_10 AC 22 ms
4,380 KB
testcase_11 AC 2 ms
4,380 KB
testcase_12 AC 2 ms
4,376 KB
testcase_13 AC 45 ms
4,376 KB
testcase_14 AC 43 ms
4,380 KB
testcase_15 AC 21 ms
4,380 KB
testcase_16 AC 69 ms
5,312 KB
testcase_17 AC 75 ms
5,380 KB
testcase_18 AC 71 ms
5,368 KB
testcase_19 AC 83 ms
5,476 KB
testcase_20 AC 79 ms
5,420 KB
testcase_21 AC 67 ms
5,480 KB
testcase_22 AC 73 ms
5,660 KB
testcase_23 AC 89 ms
5,484 KB
testcase_24 AC 74 ms
5,420 KB
testcase_25 AC 89 ms
5,384 KB
testcase_26 AC 81 ms
5,352 KB
testcase_27 AC 90 ms
5,368 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

/*
Convex Hull Trick
- y = ax + b が順次追加されつつ，最大値/最小値クエリに答える
- y = c(x - a)^2 + b 型の関数を表す(a, b)たちが順次追加されつつ，最小値クエリに答える
Verify:
CF 1179D https://codeforces.com/contest/1179/submission/59448330
CF 1137E https://codeforces.com/contest/1137/submission/59448399
*/
#include <limits>
#include <set>
#include <utility>
#include <vector>
// Convex Hull Trick
// Implementation Idea:
// https://github.com/satanic0258/Cpp_snippet/blob/master/src/technique/ConvexHullTrick.cpp
// #include <boost/multiprecision/cpp_int.hpp>
// using mpint = boost::multiprecision::cpp_int;
namespace CHT {
using T_CHT = long long;
static const T_CHT T_MIN = std::numeric_limits<T_CHT>::lowest() + 1;
struct Line {
    T_CHT a, b; // y = ax + b
    mutable std::pair<T_CHT, T_CHT>
        rp; // (numerator, denominator) `x` coordinate of the crossing point with next line
    Line(T_CHT a, T_CHT b) : a(a), b(b), rp(T_MIN, T_MIN) {}
    static std::pair<T_CHT, T_CHT> cross(const Line &ll, const Line &lr) {
        return std::make_pair(ll.b - lr.b, lr.a - ll.a); // `ll.a < lr.a` is assumed implicitly
    }
    bool operator<(const Line &r) const {
        if (b == T_MIN) {
            return r.rp.first == T_MIN ? true : a * r.rp.second < r.rp.first;
        } else if (r.b == T_MIN) {
            return rp.first == T_MIN ? false : !(r.a * rp.second < rp.first);
        } else {
            return a < r.a;
        }
    }
};
template <typename T_MP> struct Lines : std::multiset<Line> {
    bool flg_min; // true iff for minimization
    inline bool isNeedless(iterator itr) {
        if (size() == 1) return false;
        auto nxt = std::next(itr);
        if (itr == begin())
            return itr->a == nxt->a and itr->b <= nxt->b;
        else {
            auto prv = std::prev(itr);
            if (nxt == end())
                return itr->a == prv->a and itr->b <= prv->b;
            else
                return T_MP(prv->b - itr->b) * (nxt->a - itr->a) >=
                       T_MP(itr->b - nxt->b) * (itr->a - prv->a);
        }
    }
    void add_line(T_CHT a, T_CHT b) {
        if (flg_min) a = -a, b = -b;
        auto itr = insert({a, b});
        if (isNeedless(itr))
            erase(itr);
        else {
            while (std::next(itr) != end() and isNeedless(std::next(itr))) {
                erase(std::next(itr));
            }
            while (itr != begin() and isNeedless(std::prev(itr))) { erase(std::prev(itr)); }
            if (std::next(itr) != end()) { itr->rp = CHT::Line::cross(*itr, *std::next(itr)); }
            if (itr != begin()) { std::prev(itr)->rp = CHT::Line::cross(*std::prev(itr), *itr); }
        }
    }
    Lines(bool is_minimizer) : flg_min(is_minimizer) {}
    std::pair<T_CHT, T_CHT> get(T_CHT x) {
        auto itr = lower_bound({x, CHT::T_MIN});
        T_CHT retval = CHT::T_MIN, reta = CHT::T_MIN;
        if (itr != end()) { retval = itr->a * x + itr->b, reta = itr->a; }
        if (itr != begin()) {
            T_CHT tmp = std::prev(itr)->a * x + std::prev(itr)->b;
            if (tmp >= retval) { retval = tmp, reta = std::max(reta, std::prev(itr)->a); }
        }
        return std::make_pair(flg_min ? -retval : retval, flg_min ? -reta : reta);
    }
};
} // namespace CHT

template <typename T_MP> struct ConvexHullTrick {
    using T_CHT = CHT::T_CHT;
    CHT::Lines<T_MP> lines;
    ConvexHullTrick(bool is_minimizer) : lines(is_minimizer) {}
    void add_line(T_CHT a, T_CHT b) { lines.add_line(a, b); } // Add y = ax + b
    std::pair<T_CHT, T_CHT> get(T_CHT x) { return lines.get(x); }
    void add_convex_parabola(T_CHT c, T_CHT a, T_CHT b) {
        add_line(c * a * (-2), c * a * a + b);
    } // Add y = c(x - a)^2 + b
    T_CHT parabola_lower_bound(T_CHT c, T_CHT x) { return lines.get(x).first + c * x * x; }
};


int main() {
    int N;
    cin >> N;
    vector<lint> Q(N);
    cin >> Q;
    dbg(Q);

    ConvexHullTrick<__int128> cht(false);
    lint ret = 0;
    REP(i, N) {
        lint got = 0;
        if (i) chmax(got, cht.get(Q[i]).first);
        chmax(ret, got);
        cht.add_line(Q.at(i), got);
    }
    cout << ret << '\n';
}
0