結果

問題 No.409 ダイエット
コンテスト
ユーザー cutmdo
提出日時 2023-03-08 02:27:53
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 38 ms / 2,000 ms
コード長 5,341 bytes
コンパイル時間 11,259 ms
コンパイル使用メモリ 296,800 KB
最終ジャッジ日時 2025-02-11 06:40:47
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
other AC * 92
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 # 

//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,avx512f")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <stack>
#include <queue>
#include <bitset>
#include <numeric>
#include <cassert>
#include <memory>
#include <random>
#include <functional>
#include <complex>
#include <immintrin.h>
#include <stdexcept>
#ifdef DEBUG
#include "./CompetitiveProgrammingCpp/Utils/debug.hpp"
#include "./CompetitiveProgrammingCpp/Utils/Timer.hpp"
#include "./CompetitiveProgrammingCpp/Utils/sample.hpp"
#else
#define dump(...)
template<class T>constexpr inline auto d_val(T a, T b) { return a; }
#endif

/* macro */
#define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i)
#define RFOR(i, b, e) for(ll i = (ll)((e)-1); i >= (ll)(b); --i)
#define REP(i, n) FOR(i, 0, (n))
#define RREP(i, n) RFOR(i, 0, (n))
#define REPC(x,c) for(const auto& x:(c))
#define REPI2(it,b,e) for(auto it = (b); it != (e); ++it)
#define REPI(it,c) REPI2(it, (c).begin(), (c).end())
#define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend())
#define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);)
#define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end())
#define ALL(x) (x).begin(),(x).end()
#define cauto const auto&
/* macro func */
template<class T>
inline auto sort(T& t) { std::sort(ALL(t)); }
template<class T>
inline auto rsort(T& t) { std::sort((t).rbegin(), (t).rend()); }
template<class T>
inline auto unique(T& t) { (t).erase(unique((t).begin(), (t).end()), (t).end()); }
template<class T, class S>
inline auto chmax(T& t, const S& s) { if(s > t) { t = s; return true; } return false; }
template<class T, class S>
inline auto chmin(T& t, const S& s) { if(s < t) { t = s; return true; } return false; }
inline auto BR() { std::cout << "\n"; }

/* type define */
using ll = long long;
using VS = std::vector<std::string>;
using VL = std::vector<long long>;
using VVL = std::vector<VL>;
using VVVL = std::vector<VVL>;
using VVVVL = std::vector<VVVL>;
using VVVVVL = std::vector<VVVVL>;
using VD = std::vector<double>;
template<class T>
using V = std::vector<T>;
template<class T = ll, class U = T>
using P = std::pair<T, U>;
using PAIR = P<ll>;

/* using std */
using std::cout;
constexpr char endl = '\n';
using std::cin;
using std::pair;
using std::string;
using std::stack;
using std::queue;
using std::deque;
using std::vector;
using std::list;
using std::map;
using std::unordered_map;
using std::multimap;
using std::unordered_multimap;
using std::set;
using std::unordered_set;
using std::unordered_multiset;
using std::multiset;
using std::bitset;
using std::priority_queue;

/* Initial processing  */
struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing;

/* Remove the source of the bug */
auto pow(signed, signed) { assert(false); }

/* define hash */
namespace std {
template <>	class hash<std::pair<ll, ll>> { public:	size_t operator()(const std::pair<ll, ll>& x) const { return hash<ll>()(1000000000 * x.first + x.second); } };
}

/* input */
template<class T> std::istream& operator >> (std::istream& is, vector<T>& vec) { for(T& x : vec) is >> x; return is; }

/* constant value */
// constexpr ll MOD = 1000000007;
constexpr ll MOD = 998244353;

//=============================================================================================


class ConvexHullTrick {
    using T = long long;
    std::deque<std::pair<T, T>> lines;

    static auto func(const std::pair<T, T>& line, const T& x) {
        return x * line.first + line.second;
    }
    static auto check(const std::pair<T, T>& line1, const std::pair<T, T>& line2, const std::pair<T, T>& line3) {
        auto [a1, b1] = line1;
        auto [a2, b2] = line2;
        auto [a3, b3] = line3;
        return (a2 - a1) * (b3 - b2) >= (b2 - b1) * (a3 - a2);
    }

public:
    ConvexHullTrick() {}

    auto add(const std::pair<T, T>& line) {
        while(lines.size() > 1 &&
              check(*std::next(lines.rbegin()), *lines.rbegin(), line)) {
            lines.pop_back();
        }
        lines.emplace_back(line);
    }
    auto add(const T& a, const T& b) { add({a,b}); }

    auto query(const T& x) {
        while(lines.size() > 1 &&
              func(*lines.begin(), x) > func(*std::next(lines.begin()), x)) {
            lines.pop_front();
        }
        return func(*lines.begin(), x);
    }
};


signed main() {
    ll n, a, b, w;
    cin >> n >> a >> b >> w;
    VL d(n);
    cin >> d;

    constexpr ll mx = 1e18;

    auto cht = ConvexHullTrick();
    VL dp(n + 1, mx);
    auto update = [&](ll i, ll x) {
        chmin(dp[i], x);
        auto pa = -b * i;
        auto pb = a * i + i * (i + 1) / 2 * b + dp[i];
        cht.add(pa, pb);
    };

    update(0, w);
    FOR(i, 1, n + 1) {
        auto ad = d[i - 1] - a * i + a + i * (i - 1) / 2 * b;
        auto min = cht.query(i);
        update(i, ad + min);
    }

    ll ans = dp[n];
    REP(i, n) {
        ll k = n - i;
        chmin(ans, dp[i] + -a * k + k * (k + 1) / 2 * b);
    }

    cout << ans << endl;
    dump(dp);
}
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