結果

問題 No.1193 Penguin Sequence
コンテスト
ユーザー Mister
提出日時 2020-08-22 15:54:45
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 453 ms / 2,000 ms
コード長 6,180 bytes
コンパイル時間 1,539 ms
コンパイル使用メモリ 110,268 KB
最終ジャッジ日時 2025-01-13 09:53:29
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 38
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 <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <functional>

template <int MOD>
struct ModInt {
    using lint = long long;
    int val;

    // constructor
    ModInt(lint v = 0) : val(v % MOD) {
        if (val < 0) val += MOD;
    };

    // unary operator
    ModInt operator+() const { return ModInt(val); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt inv() const { return this->pow(MOD - 2); }

    // arithmetic
    ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; }
    ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; }
    ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; }
    ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; }
    ModInt pow(lint n) const {
        auto x = ModInt(1);
        auto b = *this;
        while (n > 0) {
            if (n & 1) x *= b;
            n >>= 1;
            b *= b;
        }
        return x;
    }

    // compound assignment
    ModInt& operator+=(const ModInt& x) {
        if ((val += x.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator-=(const ModInt& x) {
        if ((val -= x.val) < 0) val += MOD;
        return *this;
    }
    ModInt& operator*=(const ModInt& x) {
        val = lint(val) * x.val % MOD;
        return *this;
    }
    ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); }

    // compare
    bool operator==(const ModInt& b) const { return val == b.val; }
    bool operator!=(const ModInt& b) const { return val != b.val; }
    bool operator<(const ModInt& b) const { return val < b.val; }
    bool operator<=(const ModInt& b) const { return val <= b.val; }
    bool operator>(const ModInt& b) const { return val > b.val; }
    bool operator>=(const ModInt& b) const { return val >= b.val; }

    // I/O
    friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept {
        lint v;
        is >> v;
        x = v;
        return is;
    }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; }
};

template <class T>
struct Combination {
    int max_n;
    std::vector<T> f, invf;

    explicit Combination(int n)
        : max_n(n), f(n + 1), invf(n + 1) {
        f[0] = 1;
        for (int i = 1; i <= n; ++i) {
            f[i] = f[i - 1] * i;
        }

        invf[max_n] = f[max_n].inv();
        for (int i = max_n - 1; i >= 0; --i) {
            invf[i] = invf[i + 1] * (i + 1);
        }
    }

    T fact(int n) const { return n < 0 ? T(0) : f[n]; }
    T invfact(int n) const { return n < 0 ? T(0) : invf[n]; }
    T perm(int a, int b) const {
        return a < b || b < 0 ? T(0) : f[a] * invf[a - b];
    }
    T binom(int a, int b) const {
        return a < b || b < 0 ? T(0) : f[a] * invf[a - b] * invf[b];
    }
};

template <class T>
std::map<T, int> compress(std::vector<T>& v) {
    std::sort(v.begin(), v.end());
    v.erase(std::unique(v.begin(), v.end()), v.end());

    std::map<T, int> rev;
    for (int i = 0; i < (int)v.size(); ++i) rev[v[i]] = i;
    return rev;
}

template <class T>
struct SegmentTree {
    using Merger = std::function<T(T, T)>;

    int length;
    std::vector<T> dat;
    T unit;
    Merger merge;

    SegmentTree() = default;

    SegmentTree(int n, const T& unit, const Merger& merge)
        : length(1), unit(unit), merge(merge) {
        while (length < n) length <<= 1;
        dat.assign(length * 2, unit);
    }

    template <class Container>
    SegmentTree(const Container& elems, const T& unit, const Merger& merge)
        : length(1), unit(unit), merge(merge) {
        int n = elems.size();
        while (length < n) length <<= 1;

        dat.assign(length * 2, unit);

        std::copy(elems.begin(), elems.end(), dat.begin() + length);

        for (int nidx = length - 1; nidx >= 1; --nidx) {
            T vl = dat[nidx * 2 + 0];
            T vr = dat[nidx * 2 + 1];
            dat[nidx] = merge(vl, vr);
        }
    }

    void update(int nidx, const T& elem) {
        nidx += length;
        dat[nidx] = elem;

        while (nidx > 0) {
            nidx >>= 1;
            T vl = dat[nidx * 2 + 0];
            T vr = dat[nidx * 2 + 1];
            dat[nidx] = merge(vl, vr);
        }
    }

    T fold(int ql, int qr) const {
        ql = std::max(ql, 0);
        qr = std::min(qr, length);
        ql += length, qr += length;

        T lacc = unit, racc = unit;
        while (ql < qr) {
            if (ql & 1) {
                lacc = merge(lacc, dat[ql]);
                ++ql;
            }
            if (qr & 1) {
                --qr;
                racc = merge(dat[qr], racc);
            }
            ql >>= 1, qr >>= 1;
        }

        return merge(lacc, racc);
    }

    T get(int idx) const { return dat[idx + length]; }
    T fold_all() const { return dat[1]; }
};

constexpr int MOD = 998244353;
using mint = ModInt<MOD>;
const Combination<mint> C(400000);

void solve() {
    int n;
    std::cin >> n;

    std::vector<int> xs(n);
    for (auto& x : xs) std::cin >> x;

    int m;
    {
        auto nxs = xs;
        auto xrev = compress(nxs);

        m = nxs.size();
        for (auto& x : xs) x = xrev[x];
    }

    SegmentTree<int>
        seg(m, 0, [](auto a, auto b) { return a + b; });
    mint rev = 0;
    for (auto x : xs) {
        rev += seg.fold(x + 1, m);
        seg.update(x, seg.get(x) + 1);
    }

    mint ans = 0;
    {
        mint pat = 0;
        for (int l = 2; l <= n; ++l) {
            pat += C.binom(n - 2, l - 2) / C.binom(n, l);
        }
        ans += pat * rev;
    }

    mint allrev = 0;
    for (auto x : xs) {
        allrev += seg.fold(x + 1, m);
    }

    {
        mint pat = 0, sum = 0;
        for (int r = 1; r <= n; ++r) {
            mint p = C.binom(n - 1, r - 1) / C.binom(n, r);
            pat += sum * p;
            sum += p;
        }
        ans += pat * allrev;
    }

    mint tot = 1;
    for (int i = 1; i <= n; ++i) tot *= C.binom(n, i);

    std::cout << ans * tot << "\n";
}

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}
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