結果

問題 No.1193 Penguin Sequence
コンテスト
ユーザー otera
提出日時 2020-08-25 05:46:34
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 392 ms / 2,000 ms
コード長 6,845 bytes
コンパイル時間 6,032 ms
コンパイル使用メモリ 137,728 KB
最終ジャッジ日時 2025-01-13 13:46:03
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 # 

/**
 *    author:  otera    
**/
#include<iostream>
#include<string> 
#include<cstdio>
#include<cstring>
#include<vector>
#include<cmath>
#include<algorithm> 
#include<functional>
#include<iomanip>
#include<queue>
#include<deque>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
using namespace std;

#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
typedef long double ld;
const int inf=1e9+7;
const ll INF=1LL<<60 ;
const ll mod=1e9+7 ;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef complex<ld> Point;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<int, int> P;
typedef pair<ld, ld> LDP;
typedef pair<ll, ll> LP;
#define fr first
#define sc second
#define all(c) c.begin(),c.end()
#define pb push_back
#define debug(x)  cerr << #x << " = " << (x) << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

// modint: mod 計算を int を扱うように扱える構造体
template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b; swap(a, b);
            u -= t * v; swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr istream& operator >> (istream &is, Fp<MOD>& x) noexcept {
        return is >> x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

// 二項係数ライブラリ
template<class T> struct BiCoef {
    vector<T> fact_, inv_, finv_;
    constexpr BiCoef() {}
    constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
        init(n);
    }
    constexpr void init(int n) noexcept {
        fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
        int MOD = fact_[0].getmod();
        for(int i = 2; i < n; i++){
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            finv_[i] = finv_[i-1] * inv_[i];
        }
    }
    constexpr T com(int n, int k) const noexcept {
        if (n < k || n < 0 || k < 0) return 0;
        return fact_[n] * finv_[k] * finv_[n-k];
    }
    constexpr T fact(int n) const noexcept {
        if (n < 0) return 0;
        return fact_[n];
    }
    constexpr T inv(int n) const noexcept {
        if (n < 0) return 0;
        return inv_[n];
    }
    constexpr T finv(int n) const noexcept {
        if (n < 0) return 0;
        return finv_[n];
    }
};

//const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Fp<MOD>;
BiCoef<mint> bc;

template <class Abel> struct BIT {
private:
	vector<Abel> node; int n;
    Abel UNITY_SUM = 0; //to be set
public:
	BIT(int n_) {
		n = n_; node.resize(n, UNITY_SUM);
	}
	//0-indexed
	void add(int a, Abel w) {
		for (int i = a; i < n; i |= i + 1)node[i] += w;
	}
	//[0,a)
	Abel sum(int a) {
		Abel ret = UNITY_SUM;
		for (int i = a - 1; i >= 0; i = (i&(i + 1)) - 1)ret += node[i];
		return ret;
	}
	//[a,b)
	Abel sum(int a, int b) {
		return sum(b) - sum(a);
	}
	//k-th number (k is 0-indexed)
    int get(int k) {
        ++k;
        int res = 0;
        int n = 1; while(n < (int)node.size()) n *= 2;
        for(int i = n / 2; i > 0; i /= 2) {
            if(res + i < (int)node.size() && node[res + i - 1] < k) {
                k -= node[res + i - 1];
                res += i;
            }
        }
        return res; //0-indexed
    }
    //debug
    void print() {
        for(int i = 0; i < n; ++i) cout << sum(i, i + 1) << ",";
        cout << endl;
    }
};

template<typename T>
vector<T> compress(vector<T> A){
    sort(A.begin(), A.end());
    A.erase(unique(A.begin(), A.end()), A.end());
    return A;
}

void solve() {
    bc.init(200200);
	int n; cin >> n;
    vector<int> a(n);
    rep(i, n) {
        cin >> a[i];
    }
    auto comp = compress(a);
    int sz = (int)comp.size();
    BIT<int> bit(sz);
    int cnt = 0;
    rep(i, n) {
        int x = lower_bound(all(comp), a[i]) - comp.begin();
        cnt += i - bit.sum(x + 1);
        bit.add(x, 1);
    }
    mint sum = 1;
    for(int i = 1; i <= n; ++ i) {
        sum *= bc.com(n, i);
    }
    int cnt2 = 0;
    sort(all(a));
    BIT<int> bit2(sz);
    rep(i, n) {
        int x = lower_bound(all(comp), a[i]) - comp.begin();
        cnt2 += bit2.sum(x);
        bit2.add(x, 1);
    }
    // cerr << cnt2 << endl;
    mint ans = 0;
    //同じ操作
    for(int i = 1; i <= n; ++ i) {
        ans += (mint)cnt * sum / bc.com(n, i) * bc.com(n - 2, i - 2);
    }
    //違う操作
    for(int i = 1; i <= n; ++ i) {
        ans += (mint)cnt2 * sum / n / n * (mint)i * (mint)((n + i + 1) * (n - i - 1 + 1) / 2);
    }
    cout << ans << endl;
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//int t; cin >> t; rep(i, t)solve();
	solve();
    return 0;
}
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