#582140 (C++17) No.1294 マウンテン数列

• 問題: No.1294 マウンテン数列
• ユーザー: kcvlex
• 提出日時: 2020-11-20 23:14:42
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 258 ms / 2,000 ms
• コード長: 8,807 bytes
• コンパイル時間: 1,719 ms
• コンパイル使用メモリ: 150,344 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-07-23 13:48:42
• 合計ジャッジ時間: 4,266 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	4 ms; 6,816 KB
testcase_01	AC	3 ms; 6,940 KB
testcase_02	AC	4 ms; 6,940 KB
testcase_03	AC	4 ms; 6,940 KB
testcase_04	AC	4 ms; 6,940 KB
testcase_05	AC	34 ms; 6,940 KB
testcase_06	AC	45 ms; 6,940 KB
testcase_07	AC	3 ms; 6,940 KB
testcase_08	AC	3 ms; 6,940 KB
testcase_09	AC	3 ms; 6,944 KB
testcase_10	AC	252 ms; 6,940 KB
testcase_11	AC	258 ms; 6,940 KB
testcase_12	AC	255 ms; 6,944 KB
testcase_13	AC	249 ms; 6,940 KB
testcase_14	AC	215 ms; 6,940 KB
testcase_15	AC	245 ms; 6,944 KB
testcase_16	AC	214 ms; 6,940 KB

ソースコード

#include <limits>
#include <initializer_list>
#include <utility>
#include <bitset>
#include <tuple>
#include <type_traits>
#include <functional>
#include <string>
#include <array>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <iterator>
#include <algorithm>
#include <complex>
#include <random>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <regex>
#include <cassert>
#include <cstddef>
#include <variant>

#define endl codeforces

#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)

using ll = std::int64_t;
using ull = std::uint64_t;
using pii = std::pair<int, int>;
using tii = std::tuple<int, int, int>;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
using size_type = ssize_t;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;

template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }

template <typename T, std::size_t Head, std::size_t... Tail> 
struct multi_dim_array { using type = std::array<typename multi_dim_array<T, Tail...>::type, Head>; };

template <typename T, std::size_t Head> 
struct multi_dim_array<T, Head> { using type = std::array<T, Head>; };

template <typename T, std::size_t... Args> using mdarray = typename multi_dim_array<T, Args...>::type;

template <typename T, typename F, typename... Args> 
void fill_seq(T &t, F f, Args... args) { 
    if constexpr (std::is_invocable<F, Args...>::value) { 
        t = f(args...); 
    } else { 
        for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); 
    } 
}

template <typename T> vec<T> make_v(size_type sz) { return vec<T>(sz); }

template <typename T, typename... Tail> 
auto make_v(size_type hs, Tail&&... ts) { 
    auto v = std::move(make_v<T>(std::forward<Tail>(ts)...)); 
    return vec<decltype(v)>(hs, v); 
}

namespace init__ { 
struct InitIO { 
    InitIO() { 
        std::cin.tie(nullptr); 
        std::ios_base::sync_with_stdio(false); 
        std::cout << std::fixed << std::setprecision(30); 
    } 
} init_io; 
}

template <typename T>
T ceil_pow2(T bound) {
    T ret = 1;
    while (ret < bound) ret *= 2;
    return ret;
}

template <typename T>
T ceil_div(T a, T b) { return a / b + !!(a % b); }


namespace math {

template <typename T>
constexpr T mul_id_ele() {
    if constexpr (std::is_fundamental<T>::value) {
        return T(1);
    } else {
        return T::mul_id_ele();
    }
}

template <typename T>
constexpr T add_id_ele() {
    if constexpr (std::is_fundamental<T>::value) {
        return T(0);
    } else {
        return T::add_id_ele();
    }
}

template <typename T>
constexpr T pow(const T &n, ll k) {
    T ret = mul_id_ele<T>();
    T cur = n;
    while (k) {
        if (k & 1) ret *= cur;
        cur *= cur;
        k /= 2;
    }
    return ret;
}


template <typename T>
typename std::enable_if<std::is_integral<T>::value, T>::type
gcd(T a, T b) { return b ? gcd(a % b, b) : a; }

}

namespace math {

template <ull Mod>
struct Modint {

    constexpr Modint(ll x) noexcept : x((Mod + x % static_cast<ll>(Mod)) % Mod) { }
    constexpr Modint() noexcept : Modint(0) { }
    
    constexpr static Modint add_id_ele() { 
        return Modint(0); 
    }
    
    constexpr static Modint mul_id_ele() {
        return Modint(1);
    }
    
    constexpr ll value() const noexcept { 
        return static_cast<ll>(x);
    }

    constexpr Modint& operator+=(const Modint &oth) noexcept {
        x += oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator-=(const Modint &oth) noexcept {
        x += Mod - oth.value();
        if (Mod <= x) x -= Mod;
        return *this;
    }

    constexpr Modint& operator*=(const Modint &oth) noexcept {
        x *= oth.value();
        x %= Mod;
        return *this;
    }

    constexpr Modint& operator/=(const Modint &oth) noexcept {
        x *= oth.inv().value();
        x %= Mod;
        return *this;
    }

    constexpr Modint operator+(const Modint &oth) const noexcept {
        return Modint(x) += oth;
    }

    constexpr Modint operator-(const Modint &oth) const noexcept {
        return Modint(x) -= oth;
    }

    constexpr Modint operator*(const Modint &oth) const noexcept {
        return Modint(x) *= oth;
    }

    constexpr Modint operator/(const Modint &oth) const noexcept {
        return Modint(x) /= oth;
    }

    constexpr Modint operator-() const noexcept {
        return Modint((x != 0) * (Mod - x)); 
    }

    constexpr bool operator==(const Modint &oth) const noexcept {
        return value() == oth.value();
    }

    template <typename T>
    constexpr typename std::enable_if<std::is_integral<T>::value, const Modint&>::type
    operator=(T t) noexcept {
        (*this) = Modint(std::forward<T>(t)); 
        return *this;
    }

    constexpr Modint inv() const noexcept {
        return ::math::pow(*this, Mod - 2);
    }

    constexpr ull mod() const noexcept {
        return Mod;
    }

private:
    ull x;
};

template <ull Mod>
Modint<Mod> inv(Modint<Mod> m) {
    return m.inv();
}

template <ull Mod>
std::istream& operator>>(std::istream &is, Modint<Mod> &m) {
    ll v;
    is >> v;
    m = v;
    return is;
}

template <ull Mod>
std::ostream& operator<<(std::ostream &os, Modint<Mod> m) {
    os << m.value();
    return os;
}

}

namespace tree {

template <typename T>
class BIT {
    vec<T> data;

public:
    const T id_ele;

    BIT() : id_ele() { }

    BIT(size_type sz, T id_ele) : id_ele(id_ele) {
        data = vec<T>(ceil_pow2(sz) + 1, id_ele);
    }

    /*
    template <typename F>
    BIT(F f, size_type sz, T id_ele) : id_ele(id_ele) {
        data = vec<T>(ceil_pow2(sz) + 1, id_ele);
        for (size_type i = 0; i < sz; i++) {
            data[i + 1] = f(i);
            size_type par = i + (i & -i);
            if (par < size_type(data.size())) data[par] += data[i + 1];
        }
    }

    BIT(vec<T> d, T id_ele) : data(d), id_ele(id_ele) {
        size_type sz = data.size();
        data.resize(ceil_pow2(sz));
    }
    */

    // [0, pos)
    T sum(size_type pos) const noexcept {
        T ret = id_ele;
        for (; 0 < pos; pos -= pos & -pos) ret += data[pos];
        return ret;
    }

    // [l, r)
    T sum(size_type l, size_type r) const noexcept { 
        return sum(r) - sum(l); 
    }

    void add(ll pos, T delta) noexcept {
        for (++pos; pos < size_type(data.size()); pos += pos & -pos) data[pos] += delta;
    }

    // sum(ret) < bound <= sum(ret+1)
    size_type lower_bound(T bound) const noexcept {
        if (data.back() < bound) return data.size();
        T sum = id_ele;
        size_type ret = 0;
        for (size_type i = size_type(data.size() - 1) / 2; 0 < i; i /= 2) {
            if (sum + data[ret + i] < bound) {
                ret += i;
                sum += data[ret];
            }
        }
        return ret;
    }

    const vec<T>& raw() const {
        return data;
    }
};

}

constexpr ll mod = 998'244'353;
constexpr size_type SIZE = 2510;
using mint = math::Modint<mod>;

int main() {
    ll n;
    std::cin >> n;
    vec<ll> av(n);
    for (ll &e : av) std::cin >> e;

    vec<mint> count(SIZE, 0);
    for (ll i = 1; i <= SIZE; i++) {
        tree::BIT<mint> bt(SIZE, 0);
        bt.add(0, 1);
        ll pre = av[0];
        bool ok = true;
        for (ll j = 1; j < n - 1; j++) {
            ll cur = av[j];
            // cur - bound <= i
            // cur - i <= bound
            if (i < cur - pre) {
                ok = false;
                break;
            }
            ll bound = std::max<ll>(1, cur - i);
            mint tmp = bt.sum(bound, SIZE);
            bt.add(pre, tmp + 1);
            pre = cur;
        }
        ll cur = av.back();
        if (!ok) continue;
        ll bound = std::max<ll>(1, cur - i);
        count[i] = bt.sum(bound, SIZE);
        if (cur - pre <= i) count[i] += 1;
        count[i] *= 2;
    }

    mint ans = 0;
    for (ll i = 1; i <= SIZE; i++) ans += (mint(i) * (count[i] - count[i - 1]));
    std::cout << ans << '\n';
    return 0;
}