結果

問題 No.1300 Sum of Inversions
ユーザー kcvlexkcvlex
提出日時 2020-11-27 21:56:05
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 210 ms / 2,000 ms
コード長 8,630 bytes
コンパイル時間 2,157 ms
コンパイル使用メモリ 157,156 KB
実行使用メモリ 17,528 KB
最終ジャッジ日時 2023-10-01 05:36:10
合計ジャッジ時間 9,606 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
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 1 ms
4,376 KB
testcase_03 AC 151 ms
16,068 KB
testcase_04 AC 149 ms
15,804 KB
testcase_05 AC 104 ms
10,944 KB
testcase_06 AC 169 ms
16,620 KB
testcase_07 AC 167 ms
16,248 KB
testcase_08 AC 190 ms
16,856 KB
testcase_09 AC 185 ms
16,972 KB
testcase_10 AC 79 ms
10,360 KB
testcase_11 AC 86 ms
10,500 KB
testcase_12 AC 149 ms
16,008 KB
testcase_13 AC 148 ms
15,768 KB
testcase_14 AC 209 ms
17,376 KB
testcase_15 AC 193 ms
16,964 KB
testcase_16 AC 151 ms
16,264 KB
testcase_17 AC 72 ms
10,544 KB
testcase_18 AC 97 ms
10,860 KB
testcase_19 AC 120 ms
15,652 KB
testcase_20 AC 137 ms
15,536 KB
testcase_21 AC 127 ms
15,652 KB
testcase_22 AC 103 ms
11,184 KB
testcase_23 AC 175 ms
16,736 KB
testcase_24 AC 118 ms
11,268 KB
testcase_25 AC 99 ms
10,976 KB
testcase_26 AC 93 ms
10,832 KB
testcase_27 AC 111 ms
10,796 KB
testcase_28 AC 195 ms
17,104 KB
testcase_29 AC 122 ms
15,528 KB
testcase_30 AC 210 ms
16,964 KB
testcase_31 AC 126 ms
11,204 KB
testcase_32 AC 126 ms
11,200 KB
testcase_33 AC 75 ms
17,320 KB
testcase_34 AC 87 ms
17,460 KB
testcase_35 AC 83 ms
17,408 KB
testcase_36 AC 85 ms
17,528 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 <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;
using mint = math::Modint<mod>;

int main() {
    ll n;
    std::cin >> n;
    vec<ll> av(n);
    for (auto &e : av) std::cin >> e;
    vec<ll> ord(n);
    std::iota(ALL(ord), 0);
    std::stable_sort(ALL(ord), [&](ll i, ll j) { return av[i] < av[j]; });

    auto sz = n + 10;
    tree::BIT<mint> bt1(sz, mint(0));
    tree::BIT<ll> used(sz, 0);
    vec<mint> sum1(n), cnt(n);
    for (ll i : ord) {
        sum1[i] = bt1.sum(i, sz);
        bt1.add(i, av[i]);
        cnt[i] = used.sum(i, sz);
        used.add(i, 1);
    }

    tree::BIT<mint> bt2(sz, mint(0));
    tree::BIT<mint> cnt_bt(sz, mint(0));
    mint ans = 0;
    for (ll i : ord) {
        mint c = cnt_bt.sum(i, sz);
        mint s = bt2.sum(i, sz);
        mint addv = (c * av[i]) + s;
        ans += addv;
        cnt_bt.add(i, cnt[i]);
        bt2.add(i, sum1[i] + mint(cnt[i] * av[i]));
    }

    std::cout << ans << "\n";
    return 0;
}
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