結果

問題 No.1193 Penguin Sequence
ユーザー heno239heno239
提出日時 2020-08-22 14:15:01
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 333 ms / 2,000 ms
コード長 4,079 bytes
コンパイル時間 1,327 ms
コンパイル使用メモリ 124,056 KB
実行使用メモリ 22,728 KB
最終ジャッジ日時 2024-10-15 08:30:05
合計ジャッジ時間 12,075 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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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 300 ms
22,728 KB
testcase_01 AC 333 ms
22,724 KB
testcase_02 AC 333 ms
22,656 KB
testcase_03 AC 332 ms
22,596 KB
testcase_04 AC 332 ms
22,724 KB
testcase_05 AC 333 ms
22,728 KB
testcase_06 AC 331 ms
22,724 KB
testcase_07 AC 332 ms
22,724 KB
testcase_08 AC 333 ms
22,656 KB
testcase_09 AC 333 ms
22,728 KB
testcase_10 AC 332 ms
22,600 KB
testcase_11 AC 194 ms
21,376 KB
testcase_12 AC 196 ms
21,376 KB
testcase_13 AC 288 ms
22,208 KB
testcase_14 AC 272 ms
22,080 KB
testcase_15 AC 316 ms
22,468 KB
testcase_16 AC 281 ms
21,120 KB
testcase_17 AC 18 ms
19,780 KB
testcase_18 AC 42 ms
20,224 KB
testcase_19 AC 329 ms
22,656 KB
testcase_20 AC 263 ms
22,016 KB
testcase_21 AC 214 ms
21,572 KB
testcase_22 AC 49 ms
20,164 KB
testcase_23 AC 180 ms
21,184 KB
testcase_24 AC 160 ms
21,060 KB
testcase_25 AC 82 ms
20,164 KB
testcase_26 AC 33 ms
19,908 KB
testcase_27 AC 280 ms
22,084 KB
testcase_28 AC 201 ms
21,316 KB
testcase_29 AC 288 ms
22,272 KB
testcase_30 AC 110 ms
20,548 KB
testcase_31 AC 94 ms
20,296 KB
testcase_32 AC 229 ms
21,700 KB
testcase_33 AC 165 ms
20,928 KB
testcase_34 AC 136 ms
20,676 KB
testcase_35 AC 168 ms
21,188 KB
testcase_36 AC 134 ms
20,676 KB
testcase_37 AC 275 ms
22,084 KB
testcase_38 AC 18 ms
19,712 KB
testcase_39 AC 18 ms
19,712 KB
testcase_40 AC 18 ms
19,780 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<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#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++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acosl(-1.0);

ll mod_pow(ll x, ll n, ll m) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

ul gcd(ul a, ul b) {
	if (a < b)swap(a, b);
	while (b) {
		ul r = a % b; a = b; b = r;
	}
	return a;
}
struct BIT {
private:
	vector<ll> node; int n;
public:
	BIT(int n_) {
		n = n_; node.resize(n, 0);
	}
	//0-indexed
	void add(int a, ll w) {
		for (int i = a; i < n; i |= i + 1)node[i] += w;
	}
	//[0,a)
	ll sum(int a) {
		ll ret = 0;
		for (int i = a - 1; i >= 0; i = (i & (i + 1)) - 1)ret += node[i];
		return ret;
	}
	//[a,b)
	ll sum(int a, int b) {
		return sum(b) - sum(a);
	}
};
void solve() {
	int n; cin >> n;
	vector<int> a(n);
	rep(i, n)cin >> a[i];
	vector<int> v = a; sort(all(v));
	v.erase(unique(all(v)), v.end());
	rep(i, n) {
		a[i] = lower_bound(all(v), a[i]) - v.begin();
	}
	BIT bt(v.size());
	modint num = 0;
	modint rnum = 0;
	rep(i, n) {
		num += bt.sum(a[i]+1,v.size());
		rnum += bt.sum(0, a[i]);
		bt.add(a[i], 1);
	}
	

	modint xsum = 1;
	rep1(i, n)xsum *= comb(n, i);


	modint sum = 0;
	for (int x = 2; x <= n; x++) {
		sum += comb(n-2, x - 2) / comb(n, x);
	}
	//cout << sum * xsum << "\n";
	modint csum = 0;
	modint sum2 = 0;
	for (int i = 1; i <= n; i++) {
		modint b = comb(n-1, i - 1) / comb(n, i);
		sum2 += csum * b;
		csum += b;
	}
	
	//cout << xsum * sum2 << "\n";
	//cout << num << " " << rnum << "\n";
	modint ans = num * xsum * sum+(num+rnum)*xsum*sum2;
	cout << ans << "\n";
}

signed main() {
    ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	init_f();
	//expr();
	//int t; cin >> t; rep(i, t)
	//while (cin >> n >> m>>s1>>s2>>t, n)
	solve();
	return 0;
}
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