結果

問題 No.1193 Penguin Sequence
コンテスト
ユーザー emthrm
提出日時 2020-08-22 16:00:29
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 409 ms / 2,000 ms
コード長 5,845 bytes
コンパイル時間 4,418 ms
コンパイル使用メモリ 205,548 KB
最終ジャッジ日時 2025-01-13 09:56:39
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt(): val(0) {}
  ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(ll exponent) const {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; }
  ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; }
  ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; }
  ModInt &operator/=(const ModInt &x) {
    // assert(__gcd(static_cast<int>(x.val), mod) == 1);
    unsigned a = x.val, b = mod; int u = 1, v = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(u -= tmp * v, v);
    }
    return *this *= u;
  }
  bool operator==(const ModInt &x) const { return val == x.val; }
  bool operator!=(const ModInt &x) const { return val != x.val; }
  bool operator<(const ModInt &x) const { return val < x.val; }
  bool operator<=(const ModInt &x) const { return val <= x.val; }
  bool operator>(const ModInt &x) const { return val > x.val; }
  bool operator>=(const ModInt &x) const { return val >= x.val; }
  ModInt &operator++() { if (++val == mod) val = 0; return *this; }
  ModInt operator++(int) { ModInt res = *this; ++*this; return res; }
  ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; }
  ModInt operator--(int) { ModInt res = *this; --*this; return res; }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  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; }
  friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; }
  friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val; // "val!" and "mod" must be disjoint.
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) const {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) const {
    if (n < 0 || k < 0) return ModInt(0);
    return k == 0 ? ModInt(1) : nCk(n + k - 1, k);
  }
};

template <typename Abelian>
struct BIT0based {
  BIT0based(int n, const Abelian UNITY = 0) : n(n), UNITY(UNITY), dat(n, UNITY) {}

  void add(int idx, Abelian val) {
    while (idx < n) {
      dat[idx] += val;
      idx |= idx + 1;
    }
  }

  Abelian sum(int idx) const {
    Abelian res = UNITY;
    --idx;
    while (idx >= 0) {
      res += dat[idx];
      idx = (idx & (idx + 1)) - 1;
    }
    return res;
  }

  Abelian sum(int left, int right) const {
    return left < right ? sum(right) - sum(left) : UNITY;
  }

  Abelian operator[](const int idx) const { return sum(idx, idx + 1); }

  int lower_bound(Abelian val) const {
    if (val <= UNITY) return 0;
    int res = 0, exponent = 1;
    while (exponent <= n) exponent <<= 1;
    for (int mask = exponent >> 1; mask > 0; mask >>= 1) {
      if (res + mask - 1 < n && dat[res + mask - 1] < val) {
        val -= dat[res + mask - 1];
        res += mask;
      }
    }
    return res;
  }

private:
  int n;
  const Abelian UNITY;
  vector<Abelian> dat;
};

int main() {
  int n; cin >> n;
  vector<int> a(n); REP(i, n) cin >> a[i];
  vector<int> b(a);
  sort(ALL(b));
  b.erase(unique(ALL(b)), b.end());
  REP(i, n) a[i] = lower_bound(ALL(b), a[i]) - b.begin();
  int m = b.size();
  vector mp(m, 0);
  REP(i, n) ++mp[a[i]];
  ll mx = 0;
  int small = 0;
  REP(i, m) {
    mx += 1LL * (n - small - mp[i]) * mp[i];
    small += mp[i];
  }
  Combinatorics com(n);
  ModInt mul = 1;
  FOR(i, 1, n + 1) mul *= com.nCk(n, i);
  ModInt tmp = 0, ans = 0;
  FOR(i, 1, n + 1) {
    ans += mul * mx * tmp * com.nCk(n - 1, i - 1) / com.nCk(n, i);
    tmp += com.nCk(n - 1, i - 1) / com.nCk(n, i);
  }
  ModInt tmp2 = 0;
  FOR(i, 1, n + 1) tmp2 += mul * com.nCk(n - 2, i - 2) / com.nCk(n, i);
  BIT0based<int> bit(m);
  REP(i, n) {
    ans += tmp2 * bit.sum(a[i] + 1, m);
    bit.add(a[i], 1);
  }
  cout << ans << '\n';
  return 0;
}
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