結果

問題 No.2616 中央番目の中央値
コンテスト
ユーザー Today03
提出日時 2024-01-27 00:52:59
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 185 ms / 2,000 ms
コード長 4,562 bytes
コンパイル時間 2,101 ms
コンパイル使用メモリ 198,952 KB
最終ジャッジ日時 2025-02-18 23:58:45
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 * 37
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ソースコード

diff # 

#include <bits/stdc++.h>
#ifdef LOCAL
#include "./debug.cpp"
#else
#define debug(...)
#define print_line
#endif
using namespace std;
using ll = long long;

#include <iostream>

/**
 * @brief Modint
 */

template <long long MOD>
struct modint {
    long long value;
    modint(long long x = 0) {
        if (x >= 0) {
            value = x % MOD;
        } else {
            value = MOD - (-x) % MOD;
        }
    }
    modint operator-() const {
        return modint(-value);
    }
    modint operator+() const {
        return modint(*this);
    }
    modint &operator+=(const modint &other) {
        value += other.value;
        if (value >= MOD) {
            value -= MOD;
        }
        return *this;
    }
    modint &operator-=(const modint &other) {
        value += MOD - other.value;
        if (value >= MOD) {
            value -= MOD;
        }
        return *this;
    }
    modint &operator*=(const modint other) {
        value = value * other.value % MOD;
        return *this;
    }
    modint &operator/=(modint other) {
        (*this) *= other.inv();
        return *this;
    }
    modint operator+(const modint &other) const {
        return modint(*this) += other;
    }
    modint operator-(const modint &other) const {
        return modint(*this) -= other;
    }
    modint operator*(const modint &other) const {
        return modint(*this) *= other;
    }
    modint operator/(const modint &other) const {
        return modint(*this) /= other;
    }
    modint pow(long long x) const {
        modint ret(1), mul(value);
        while (x > 0) {
            if (x % 2 == 1) {
                ret *= mul;
            }
            mul *= mul;
            x /= 2;
        }
        return ret;
    }
    modint inv() const {
        return pow(MOD - 2);
    }
    bool operator==(const modint &other) const {
        return value == other.value;
    }
    bool operator!=(const modint &other) const {
        return value != other.value;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &x) {
        return os << x.value;
    }
    friend std::istream &operator>>(std::istream &is, modint &x) {
        long long v;
        is >> v;
        x = modint<MOD>(v);
        return is;
    }
};
using mod998 = modint<998244353>;
using mod107 = modint<1000000007>;
using mint = mod998;

#include <vector>
#include <iostream>

/**
 * @brief Fenwick Tree
 * @docs docs/data_structure/fenwick_tree.md
 */

template <typename T>
struct fenwick_tree {
    fenwick_tree(int n) {
        this->n = n;
        dat.resize(n);
    }
    void add(int i, T x) {
        i++;
        while (i <= n) {
            dat[i - 1] += x;
            i += i & -i;
        }
    }
    T operator[](int i) {
        return sum(i, i + 1);
    }
    T sum(int l, int r) {
        return sum(r) - sum(l);
    }
    friend std::ostream &operator<<(ostream &os, fenwick_tree A) {
        int n = A.n;
        os << "[ ";
        for (int i = 0; i < n; i++) {
            os << A[i];
            if (i != n - 1) {
                os << ", ";
            }
        }
        os << " ]";
        return os;
    }

private:
    int n;
    std::vector<T> dat;
    T sum(int r) {
        T ret = 0;
        while (r > 0) {
            ret += dat[r - 1];
            r -= r & -r;
        }
        return ret;
    }
};

#include <vector>

/**
 * @brief Combination
 */

template <typename T>
struct combination {
    std::vector<T> fact, factinv;
    combination(int n) {
        fact.resize(n + 1);
        factinv.resize(n + 1);
        fact[0] = 1;
        for (int i = 1; i <= n; i++) {
            fact[i] = fact[i - 1] * i;
        }
        for (int i = 0; i <= n; i++) {
            factinv[i] = fact[i].inv();
        }
    }
    T nCr(long long n, long long r) {
        if (n < 0 || r < 0 || n - r < 0) {
            return 0;
        }
        return fact[n] * factinv[r] * factinv[n - r];
    }
    T nPr(long long n, long long r) {
        if (n < 0 || r < 0 || n - r < 0) {
            return 0;
        }
        return fact[n] * factinv[n - r];
    }
};

int main() {
    int N;
    cin >> N;
    vector<int> P(N);
    for (int i = 0; i < N; i++) cin >> P[i], P[i]--;

    combination<mint> C(N);
    fenwick_tree<int> FT(N);
    mint ans = 0;
    for (int i = 0; i < N; i++) {
        int ls = FT.sum(0, P[i]);
        int lb = FT.sum(P[i] + 1, N);
        int rs = P[i] - ls;
        int rb = N - i - 1 - rs;

        ans += C.nCr(rb + ls, ls) * C.nCr(lb + rs, rs);
        FT.add(P[i], 1);
    }

    cout << ans << endl;
}
0