結果

問題 No.1960 Guruguru Permutation
ユーザー 👑 tute7627
提出日時 2022-05-19 00:01:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 17 ms / 2,000 ms
コード長 3,671 bytes
コンパイル時間 1,921 ms
コンパイル使用メモリ 198,788 KB
最終ジャッジ日時 2025-01-29 09:16:27
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 22
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 #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
template< int mod >
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
using modint = ModInt< 998244353 >;
/**
 * @brief Enumeration(組み合わせ)
 */
template< typename T >
struct Enumeration {
private:
  static vector< T > _fact, _finv, _inv;
  inline static void expand(size_t sz) {
    if(_fact.size() < sz + 1) {
      int pre_sz = max(1, (int) _fact.size());
      _fact.resize(sz + 1, T(1));
      _finv.resize(sz + 1, T(1));
      _inv.resize(sz + 1, T(1));
      for(int i = pre_sz; i <= (int) sz; i++) {
        _fact[i] = _fact[i - 1] * T(i);
      }
      _finv[sz] = T(1) / _fact[sz];
      for(int i = (int) sz - 1; i >= pre_sz; i--) {
        _finv[i] = _finv[i + 1] * T(i + 1);
      }
      for(int i = pre_sz; i <= (int) sz; i++) {
        _inv[i] = _finv[i] * _fact[i - 1];
      }
    }
  }
public:
  explicit Enumeration(size_t sz = 0) { expand(sz); }
  static inline T fact(int k) {
    expand(k);
    return _fact[k];
  }
  static inline T finv(int k) {
    expand(k);
    return _finv[k];
  }
  static inline T inv(int k) {
    expand(k);
    return _inv[k];
  }
  static T P(int n, int r) {
    if(r < 0 || n < r) return 0;
    return fact(n) * finv(n - r);
  }
  static T C(int p, int q) {
    if(q < 0 || p < q) return 0;
    return fact(p) * finv(q) * finv(p - q);
  }
  static T H(int n, int r) {
    if(n < 0 || r < 0) return 0;
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
template< typename T >
vector< T > Enumeration< T >::_fact = vector< T >();
template< typename T >
vector< T > Enumeration< T >::_finv = vector< T >();
template< typename T >
vector< T > Enumeration< T >::_inv = vector< T >();
int main(){
  Enumeration<modint>comb;
  int N, M, K;
  cin >> N >> M >> K;
  assert(1 <= N && N <= (int)2e5);
  assert(0 <= M && M <= N);
  assert(0 <= K && K <= N);
  if(M + K >= N){
    int common = M + K - N;
    N -= common;
    M -= common;
    K -= common;
  }
  modint ans = 0;
  for(int i = 0; i <= M; i++){
    ans += comb.C(M, i) * comb.P(K, i);
  }
  cout << ans * comb.P(N, N - M - K) << endl;
  return 0;
}
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