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 04:35:51
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 142 ms / 2,000 ms
コード長 6,034 bytes
コンパイル時間 12,603 ms
コンパイル使用メモリ 314,756 KB
最終ジャッジ日時 2025-02-11 06:41:26
ジャッジサーバーID
（参考情報） 		judge3 / judge3
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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 LiChaoTree {
    using T = long long;
    using Line = std::pair<T, T>;
    constexpr static T INF = std::numeric_limits< T >::max() / 2;

    int m_size;
    std::vector<T> m_x;
    std::vector<Line> m_node;
    std::unordered_map<T, T> m_xtoi;

    static inline int calcSize(int n) { int size = 1; while(size < n) { size <<= 1; }return size; }
    auto f(const Line& line, const T& x)const { return line.first * x + line.second; }

    auto add(const Line& line_, int k, int l, int r) {
        auto line = line_;

        auto m = (l + r) / 2;
        if(f(line, m_x[m]) < f(m_node[k], m_x[m])) { std::swap(line, m_node[k]); }
        if(l + 1 == r) { return; }
        if(line.first > m_node[k].first) {
            add(line, (k << 1) + 1, l, m);
        } else if(line.first < m_node[k].first) {
            add(line, (k << 1) + 2, m, r);
        }
    }

public:
    LiChaoTree(const std::vector<T>& x_) :m_size(calcSize(x_.size())) {
        auto x = x_;
        std::sort(x.begin(), x.end());
        x.erase(std::unique(x.begin(), x.end()), x.end());
        m_x = decltype(m_x)(m_size);
        for(size_t i = 0; i < x.size(); ++i) {
            m_x[i] = x[i];
            m_xtoi.emplace(x[i], i);
        }
        for(size_t i = x.size(); i < m_size; ++i) { m_x[i] = m_x[i - 1] + 1; }
        m_node = decltype(m_node)(m_size << 1, {0,INF});
    }

    auto add(const Line& line) { add(line, 0, 0, m_size); }
    auto add(const T& a, const T& b) { add({a,b}); }

    auto query(const T& x) {
        auto k = m_xtoi[x] + m_size;
        auto ret = INF;
        while(k > 0) {
            ret = std::min(ret, f(m_node[k - 1], x));
            k >>= 1;
        }
        return ret;
    }
};

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

    VL xs(n);
    std::iota(ALL(xs), 1);
    LiChaoTree lct(xs);

    constexpr ll mx = 1e18;
    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];
        lct.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 = lct.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;
}
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