#921231 (C++23) No.2514 Twelvefold Way Returns

• 問題: No.2514 Twelvefold Way Returns
• ユーザー: risujiroh
• 提出日時: 2023-10-20 22:23:39
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 27 ms / 3,000 ms
• コード長: 5,678 bytes
• コンパイル時間: 3,472 ms
• コンパイル使用メモリ: 260,468 KB
• 実行使用メモリ: 4,348 KB
• 最終ジャッジ日時: 2023-10-20 22:24:19
• 合計ジャッジ時間: 5,322 ms
• ジャッジサーバーID （参考情報）: judge12 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,348 KB
testcase_01	AC	2 ms; 4,348 KB
testcase_02	AC	6 ms; 4,348 KB
testcase_03	AC	3 ms; 4,348 KB
testcase_04	AC	21 ms; 4,348 KB
testcase_05	AC	17 ms; 4,348 KB
testcase_06	AC	15 ms; 4,348 KB
testcase_07	AC	2 ms; 4,348 KB
testcase_08	AC	12 ms; 4,348 KB
testcase_09	AC	12 ms; 4,348 KB
testcase_10	AC	23 ms; 4,348 KB
testcase_11	AC	3 ms; 4,348 KB
testcase_12	AC	7 ms; 4,348 KB
testcase_13	AC	2 ms; 4,348 KB
testcase_14	AC	6 ms; 4,348 KB
testcase_15	AC	11 ms; 4,348 KB
testcase_16	AC	24 ms; 4,348 KB
testcase_17	AC	15 ms; 4,348 KB
testcase_18	AC	23 ms; 4,348 KB
testcase_19	AC	25 ms; 4,348 KB
testcase_20	AC	26 ms; 4,348 KB
testcase_21	AC	25 ms; 4,348 KB
testcase_22	AC	25 ms; 4,348 KB
testcase_23	AC	10 ms; 4,348 KB
testcase_24	AC	24 ms; 4,348 KB
testcase_25	AC	13 ms; 4,348 KB
testcase_26	AC	2 ms; 4,348 KB
testcase_27	AC	25 ms; 4,348 KB
testcase_28	AC	8 ms; 4,348 KB
testcase_29	AC	8 ms; 4,348 KB
testcase_30	AC	7 ms; 4,348 KB
testcase_31	AC	9 ms; 4,348 KB
testcase_32	AC	5 ms; 4,348 KB
testcase_33	AC	2 ms; 4,348 KB
testcase_34	AC	5 ms; 4,348 KB
testcase_35	AC	20 ms; 4,348 KB
testcase_36	AC	2 ms; 4,348 KB
testcase_37	AC	2 ms; 4,348 KB
testcase_38	AC	24 ms; 4,348 KB
testcase_39	AC	27 ms; 4,348 KB
testcase_40	AC	25 ms; 4,348 KB

ソースコード

#if __INCLUDE_LEVEL__ == 0

#include __BASE_FILE__

using Fp = atcoder::modint998244353;

using T = pair<Fp, Fp>;

namespace atcoder {

T operator+(const T& x, const T& y) {
  return {x.first + y.first, x.second + y.second};
}

T operator*(const T& x, const T& y) {
  return {x.first * y.first + x.second * y.second * 3,
          x.first * y.second + x.second * y.first};
}

T& operator*=(T& x, const T& y) { return x = x * y; }

}  // namespace atcoder

namespace {

Comb<Fp> comb(1000);

void solve() {
  int n, m;
  scan(n, m);

  T omega{-1 / Fp(2), Fp(atcoder::internal::primitive_root<Fp::mod()>)
                              .pow((Fp::mod() - 1) / 4) /
                          2};

  Fp ans = 0;
  for (int i : rep(m + 1)) {
    for (int j : rep(m - i + 1)) {
      int k = m - i - j;
      T t = power(T{i, 0} + T{j, 0} * omega + T{k, 0} * omega * omega, n);
      if (int r = (j * 2 + k) % 3) {
        t *= power(omega, r);
      }
      ans += comb.binom(m, i) * comb.binom(m - i, j) * t.first;
    }
  }
  ans /= Fp(3).pow(m);

  print(ans);
}

}  // namespace

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  solve();
}

#else  // __INCLUDE_LEVEL__

#include <bits/stdc++.h>

using namespace std;

#include <atcoder/modint>

template <class T>
vector<T> make_vector_for_overwrite(int n) {
  static_assert(is_trivially_destructible_v<T>);
  vector<T> v;
  v.reserve(n);
  auto p = (T**)&v;
  p[1] = p[2];
  return v;
}

template <class T>
class Comb {
 public:
  Comb() = default;

  explicit Comb(int max_n)
      : fact_(make_vector_for_overwrite<T>(max_n + 1)),
        recip_fact_(make_vector_for_overwrite<T>(max_n + 1)) {
    fact_[0] = 1;
    for (int n = 1; n <= max_n; ++n) {
      fact_[n] = fact_[n - 1] * n;
    }
    recip_fact_[max_n] = 1 / fact_[max_n];
    for (int n = max_n; 1 <= n; --n) {
      recip_fact_[n - 1] = n * recip_fact_[n];
    }
  }

  T recip(int n) const {
    assert(n);
    return n < 0 ? -recip(-n) : recip_fact_[n] * fact_[n - 1];
  }

  T fact(int n) const {
    assert(0 <= n);
    return fact_[n];
  }

  T recip_fact(int n) const { return n < 0 ? 0 : recip_fact_[n]; }

  T falling_fact(int n, int k) const {
    assert(0 <= n || n < k);
    if (n < 0) {
      T t = falling_fact(k - n - 1, k);
      return k & 1 ? -t : t;
    }
    return n < k ? 0 : recip_fact(n - k) * fact(n);
  }

  T recip_falling_fact(int n, int k) const {
    assert(n < 0 || k <= n);
    return falling_fact(n - k, -k);
  }

  T rising_fact(int n, int k) const {
    assert(n <= 0 || 0 < n + k);
    return falling_fact(n + k - 1, k);
  }

  T recip_rising_fact(int n, int k) const {
    assert(0 < n || n + k <= 0);
    return falling_fact(n - 1, -k);
  }

  T binom(int n, int k) const {
    if ((n < 0) ^ (k < 0) ^ (n < k)) {
      return 0;
    }
    if (n < 0 && k < 0) {
      k = n - k;
    }
    return recip_fact(k) * falling_fact(n, k);
  }

  T recip_binom(int n, int k) const {
    assert((0 <= n) ^ (0 <= k) ^ (k <= n));
    k = max(k, n - k);
    return recip_falling_fact(n, k) * fact(k);
  }

  T multiset(int n, int k) const { return binom(n + k - 1, k); }

  T recip_multiset(int n, int k) const {
    assert((0 < n) ^ (0 <= k) ^ (0 < n + k));
    return recip_binom(n + k - 1, k);
  }

 private:
  vector<T> fact_;
  vector<T> recip_fact_;
};

template <class T, class N>
constexpr T power(T x, N n) {
  assert(0 < n);
  while (n % 2 == 0) {
    x *= x;
    n >>= 1;
  }
  T ret = x;
  while (n >>= 1) {
    x *= x;
    if (n % 2) {
      ret *= x;
    }
  }
  return ret;
}

namespace std {

template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}

template <class... Ts>
istream& operator>>(istream& is, tuple<Ts...>& t) {
  return apply([&is](auto&... xs) -> istream& { return (is >> ... >> xs); }, t);
}

template <class R, enable_if_t<!is_convertible_v<R, string>>* = nullptr>
auto operator>>(istream& is, R&& r) -> decltype(is >> *begin(r)) {
  for (auto&& e : r) {
    is >> e;
  }
  return is;
}

template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << ' ' << p.second;
}

template <class... Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
  auto f = [&os](const auto&... xs) -> ostream& {
    [[maybe_unused]] auto sep = "";
    ((os << exchange(sep, " ") << xs), ...);
    return os;
  };
  return apply(f, t);
}

template <class R, enable_if_t<!is_convertible_v<R, string_view>>* = nullptr>
auto operator<<(ostream& os, R&& r) -> decltype(os << *begin(r)) {
  auto sep = "";
  for (auto&& e : r) {
    os << exchange(sep, " ") << e;
  }
  return os;
}

}  // namespace std

namespace atcoder {

template <class T, internal::is_modint_t<T>* = nullptr>
istream& operator>>(istream& is, T& x) {
  int v;
  is >> v;
  x = T::raw(v);
  return is;
}

template <class T, internal::is_modint_t<T>* = nullptr>
ostream& operator<<(ostream& os, const T& x) {
  return os << x.val();
}

}  // namespace atcoder

template <class... Ts>
void scan(Ts&&... xs) {
  (cin >> ... >> xs);
}

template <class... Ts>
void print(Ts&&... xs) {
  cout << tie(xs...) << '\n';
}

inline auto rep(int l, int r) { return views::iota(min(l, r), r); }
inline auto rep(int n) { return rep(0, n); }
inline auto rep1(int l, int r) { return rep(l, r + 1); }
inline auto rep1(int n) { return rep(1, n + 1); }
inline auto per(int l, int r) { return rep(l, r) | views::reverse; }
inline auto per(int n) { return per(0, n); }
inline auto per1(int l, int r) { return per(l, r + 1); }
inline auto per1(int n) { return per(1, n + 1); }

inline auto len = ranges::ssize;

#endif  // __INCLUDE_LEVEL__