結果

問題 No.2616 中央番目の中央値
ユーザー ゆにぽけ
提出日時 2024-01-26 21:50:14
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 76 ms / 2,000 ms
コード長 4,784 bytes
コンパイル時間 1,329 ms
コンパイル使用メモリ 129,532 KB
最終ジャッジ日時 2025-02-18 23:09:59
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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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 #
プレゼンテーションモードにする

#include <iostream>
#include <vector>
#include <algorithm>
#include <array>
#include <iterator>
#include <string>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <cmath>
#include <ctime>
#include <iomanip>
#include <numeric>
#include <stack>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <random>
#include <utility>
#include <functional>
using namespace std;
template<int m> struct modint
{
    private:
    unsigned int value;
    static constexpr int mod() {return m;}
    public:
    constexpr modint(const long long x = 0) noexcept
    {
        long long y = x;
        if(y < 0 || y >= mod())
        {
            y %= mod();
            if(y < 0) y += mod();
        }
        value = (unsigned int)y;
    }
    constexpr unsigned int val() noexcept {return value;}
    constexpr modint &operator+=(const modint &other) noexcept
    {
        value += other.value;
        if(value >= mod()) value -= mod();
        return *this;
    }
    constexpr modint &operator-=(const modint &other) noexcept
    {
        unsigned int x = value;
        if(x < other.value) x += mod();
        x -= other.value;
        value = x;
        return *this;
    }
    constexpr modint &operator*=(const modint &other) noexcept
    {
        unsigned long long x = value;
        x *= other.value;
        value = (unsigned int) (x % mod());
        return *this;
    }
    constexpr modint &operator/=(const modint &other) noexcept
    {
        return *this *= other.inverse();
    }
    constexpr modint inverse() const noexcept
    {
        assert(value);
        long long a = value,b = mod(),x = 1,y = 0;
        while(b)
        {
            long long q = a/b;
            a -= q*b; swap(a,b);
            x -= q*y; swap(x,y);
        }
        return modint(x);
    }
    constexpr modint power(long long N) const noexcept
    {
        assert(N >= 0);
        modint p = *this,ret = 1;
        while(N)
        {
            if(N & 1) ret *= p;
            p *= p;
            N >>= 1;
        }
        return ret;
    }
    constexpr modint operator+() {return *this;}
    constexpr modint operator-() {return modint() - *this;}
    constexpr modint &operator++(int) noexcept {return *this += 1;}
    constexpr modint &operator--(int) noexcept {return *this -= 1;}
    friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
    friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
    friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
    friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
    friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
using mint = modint<998244353>;
/* using mint = modint<1000000007>; */
template<class S>
struct combination
{
    private:
    vector<S> f,invf;
    public:
    combination(int N = 0) : f(1,1),invf(1,1)
    {
        update(N);
    }
    void update(int N)
    {
        if((int)f.size() > N) return;
        int pi = (int)f.size();
        N = max(N,pi*2);
        f.resize(N+1),invf.resize(N+1);
        for(int i = pi;i <= N;i++) f[i] = f[i-1]*i;
        invf[N] = S(1)/f[N];
        for(int i = N-1;i >= pi;i--) invf[i] = invf[i+1]*(i+1);
    }
    S factorial(int N)
    {
        update(N);
        return f[N];
    }
    S invfactorial(int N)
    {
        update(N);
        return invf[N];
    }
    S P(int N,int K)
    {
        assert(0 <= K && K <= N);
        update(N);
        return f[N]*invf[N-K];
    }
    S C(int N,int K)
    {
        assert(0 <= K && K <= N);
        update(N);
        return f[N]*invf[K]*invf[N-K];
    }
};
combination<mint> C;
template<class T> struct BinaryIndexedTree
{
    private:
    int N;
    vector<T> node;
    public:
    BinaryIndexedTree() : N(0) {}
    BinaryIndexedTree(int N) : N(N), node(N) {}
    void add(int pos,T x)
    {
        assert(0 <= pos && pos < N);
        pos++;
        while(pos <= N)
        {
            node[pos-1] += x;
            pos += pos & -pos;
        }
    }
    T sum(int l,int r)
    {
        assert(0 <= l && l <= N && r <= N);
        return sum(r) - sum(l);
    }
    T sum(int r)
    {
        T ret = 0;
        while(r > 0)
        {
            ret += node[r-1];
            r -= r & -r;
        }
        return ret;
    }
    T sum() {return sum(N);}
    
};
void Main()
{
    int N;
    cin >> N;
    vector<int> P(N);
    for(int i = 0;i < N;i++)
    {
        cin >> P[i];
        P[i]--;
    }
    BinaryIndexedTree<int> BIT(N);
    mint ans = 0;
    for(int i = 0;i < N;i++)
    {
        int ld = BIT.sum(P[i]),lu = i - ld;
        int rd = P[i] - ld,ru = N - P[i] - 1 - lu;
        //ru = N - P[i] - 1 - i + ld
        //lu = i - ld,rd = P[i] - ld
        /* for(int i = 0;i <= min(ld,ru);i++) a += C.C(ld,i) * C.C(ru,i); */
        /* for(int i = 0;i <= min(lu,rd);i++) b += C.C(lu,i) * C.C(rd,i); */
        mint a = C.factorial(ld + ru) * C.invfactorial(ld) * C.invfactorial(ru);
        mint b = C.factorial(lu + rd) * C.invfactorial(lu) * C.invfactorial(rd);
        ans += a * b;
        /* cout << lu << " " << ru << endl; */
        /* cout << ld << " " << rd << endl; */
        //x + y == z + w
        //x + z == y + w
        //y == z && x == w
        BIT.add(P[i],1);
    }
    cout << ans << endl;
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int tt = 1;
    /* cin >> tt; */
    while(tt--) Main();
}
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