結果

問題 No.2613 Sum of Combination
ユーザー risujirohrisujiroh
提出日時 2024-01-19 23:22:45
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 542 ms / 4,500 ms
コード長 9,241 bytes
コンパイル時間 5,585 ms
コンパイル使用メモリ 314,412 KB
実行使用メモリ 17,536 KB
最終ジャッジ日時 2024-09-28 05:07:02
合計ジャッジ時間 19,205 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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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 2 ms
6,812 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 12 ms
6,940 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 3 ms
6,940 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 2 ms
6,944 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 2 ms
6,940 KB
testcase_13 AC 17 ms
6,940 KB
testcase_14 AC 17 ms
6,944 KB
testcase_15 AC 11 ms
6,940 KB
testcase_16 AC 17 ms
6,944 KB
testcase_17 AC 18 ms
6,940 KB
testcase_18 AC 17 ms
6,944 KB
testcase_19 AC 18 ms
6,944 KB
testcase_20 AC 3 ms
6,944 KB
testcase_21 AC 3 ms
6,944 KB
testcase_22 AC 33 ms
6,940 KB
testcase_23 AC 501 ms
15,872 KB
testcase_24 AC 516 ms
15,932 KB
testcase_25 AC 481 ms
13,972 KB
testcase_26 AC 530 ms
17,420 KB
testcase_27 AC 253 ms
10,664 KB
testcase_28 AC 536 ms
17,248 KB
testcase_29 AC 523 ms
16,528 KB
testcase_30 AC 539 ms
17,312 KB
testcase_31 AC 529 ms
16,292 KB
testcase_32 AC 522 ms
16,164 KB
testcase_33 AC 535 ms
17,404 KB
testcase_34 AC 532 ms
17,408 KB
testcase_35 AC 542 ms
17,380 KB
testcase_36 AC 529 ms
17,536 KB
testcase_37 AC 532 ms
17,536 KB
testcase_38 AC 526 ms
17,056 KB
testcase_39 AC 526 ms
17,104 KB
testcase_40 AC 529 ms
17,116 KB
testcase_41 AC 513 ms
17,244 KB
testcase_42 AC 539 ms
17,332 KB
testcase_43 AC 528 ms
17,408 KB
testcase_44 AC 511 ms
17,524 KB
testcase_45 AC 2 ms
6,944 KB
testcase_46 AC 2 ms
6,940 KB
testcase_47 AC 2 ms
6,944 KB
testcase_48 AC 2 ms
6,944 KB
testcase_49 AC 2 ms
6,940 KB
testcase_50 AC 513 ms
17,536 KB
testcase_51 AC 527 ms
17,412 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 # 

#if __INCLUDE_LEVEL__ == 0

#include __BASE_FILE__

namespace {

using atcoder::modint;

using Fp = atcoder::modint998244353;

void solve() {
  i64 n;
  int p;
  scan(n, p);
  modint::set_mod(p);
  std::vector<int> a;
  while (n) {
    a.push_back(static_cast<int>(n % p));
    n /= p;
  }
  ranges::reverse(a);
  const modint g = atcoder::internal::primitive_root_constexpr(p);
  std::vector<int> log(p);
  for (const int i : rep(p - 1)) {
    log[g.pow(i).val()] = i;
  }
  const auto mul = [&](const std::vector<Fp>& x, const std::vector<Fp>& y) -> std::vector<Fp> {
    std::vector<Fp> ret(p);
    // for (const int i : rep(1, p)) {
    //   for (const int j : rep(1, p)) {
    //     ret[(modint(i) * j).val()] += x[i] * y[j];
    //   }
    // }
    std::vector<Fp> nx(p - 1);
    std::vector<Fp> ny(p - 1);
    for (const int i : rep(1, p)) {
      nx[log[i]] = x[i];
      ny[log[i]] = y[i];
    }
    nx = atcoder::convolution(nx, ny);
    while (p - 1 < len(nx)) {
      nx[len(nx) - p] += nx.back();
      nx.pop_back();
    }
    for (const int i : rep(1, p)) {
      ret[i] = nx[log[i]];
    }
    return ret;
  };
  Comb<modint> comb(p - 1);
  std::vector f(2, std::vector<Fp>(p));
  f[1][1] = 1;
  for (const int e : a) {
    std::vector nf(2, std::vector<Fp>(p));
    {
      std::vector<Fp> tmp(p);
      for (const int i : rep(p)) {
        ++tmp[comb.binom(e, i).val()];
      }
      tmp = mul(f[0], tmp);
      for (const int i : rep(1, p)) {
        nf[0][i] += tmp[i];
      }
    }
    {
      std::vector<Fp> tmp(p);
      for (const int i : rep(e)) {
        ++tmp[comb.binom(e, i).val()];
      }
      tmp = mul(f[1], tmp);
      for (const int i : rep(1, p)) {
        nf[0][i] += tmp[i];
      }
    }
    {
      std::vector<Fp> tmp(p);
      ++tmp[comb.binom(e, e).val()];
      tmp = mul(f[1], tmp);
      for (const int i : rep(1, p)) {
        nf[1][i] += tmp[i];
      }
    }
    f = std::move(nf);
  }
  Fp ans = 0;
  for (const int i : rep(1, p)) {
    ans += i * (f[0][i] + f[1][i]);
  }
  print(ans);
}

}  // namespace

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

  solve();
}

#else  // __INCLUDE_LEVEL__

#include <bits/stdc++.h>

#include <atcoder/convolution>

template <class T>
std::vector<T> make_vector_for_overwrite(int n) {
  static_assert(std::is_trivially_destructible_v<T>);
  std::vector<T> v;
  static_assert(sizeof(v) == 3 * sizeof(T*));
  v.reserve(n);
  T*(&a)[3] = reinterpret_cast<T*(&)[3]>(v);
  assert(a[0] == a[1] && a[1] + n == a[2]);
  a[1] = a[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 (const int n : std::views::iota(1, max_n + 1)) {
      fact_[n] = fact_[n - 1] * n;
    }
    recip_fact_[max_n] = 1 / fact_[max_n];
    for (const int n : std::views::iota(1, max_n + 1) | std::views::reverse) {
      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) {
      const 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 = std::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:
  std::vector<T> fact_;
  std::vector<T> recip_fact_;
};

template <class T, class U = T>
bool chmin(T& x, U&& y) {
  return y < x && (x = std::forward<U>(y), true);
}

template <class T, class U = T>
bool chmax(T& x, U&& y) {
  return x < y && (x = std::forward<U>(y), true);
}

template <std::signed_integral T = int>
T inf() {
  T ret;
  std::memset(&ret, 0x3f, sizeof(ret));
  return ret;
}

template <std::floating_point T>
T inf() {
  return std::numeric_limits<T>::infinity();
}

template <class T>
concept Range = std::ranges::range<T> && !std::convertible_to<T, std::string_view>;

template <class T>
concept TupleLike = std::__is_tuple_like<T>::value && !Range<T>;

namespace std {

istream& operator>>(istream& is, Range auto&& r) {
  for (auto&& e : r) {
    is >> e;
  }
  return is;
}

istream& operator>>(istream& is, TupleLike auto&& t) {
  return apply([&](auto&... xs) -> istream& { return (is >> ... >> xs); }, t);
}

ostream& operator<<(ostream& os, Range auto&& r) {
  string_view sep = "";
  for (auto&& e : r) {
    os << exchange(sep, " ") << e;
  }
  return os;
}

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

#define DEF_INC_OR_DEC(op) \
  auto& operator op(Range auto&& r) { \
    for (auto&& e : r) { \
      op e; \
    } \
    return r; \
  } \
  auto& operator op(TupleLike auto&& t) { \
    apply([](auto&... xs) { (op xs, ...); }, t); \
    return t; \
  }

DEF_INC_OR_DEC(++)
DEF_INC_OR_DEC(--)

#undef DEF_INC_OR_DEC

}  // namespace std

namespace atcoder {

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

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

}  // namespace atcoder

void scan(auto&&... xs) { std::cin >> std::tie(xs...); }
void print(auto&&... xs) { std::cout << std::tie(xs...) << '\n'; }

#define FWD(...) static_cast<decltype(__VA_ARGS__)&&>(__VA_ARGS__)

template <class F>
class fix {
 public:
  explicit fix(F f) : f_(std::move(f)) {}

  decltype(auto) operator()(auto&&... xs) const { return f_(std::ref(*this), FWD(xs)...); }

 private:
  F f_;
};

template <class T>
concept LambdaExpr = std::is_placeholder_v<std::remove_cvref_t<T>> != 0 ||
                     std::is_bind_expression_v<std::remove_cvref_t<T>>;

auto operator++(LambdaExpr auto&& x, int) {
  return std::bind([](auto&& x) -> decltype(auto) { return FWD(x)++; }, FWD(x));
}

auto operator--(LambdaExpr auto&& x, int) {
  return std::bind([](auto&& x) -> decltype(auto) { return FWD(x)--; }, FWD(x));
}

#define DEF_UNARY_OP(op) \
  auto operator op(LambdaExpr auto&& x) { \
    return std::bind([](auto&& x) -> decltype(auto) { return op FWD(x); }, FWD(x)); \
  }

DEF_UNARY_OP(++)
DEF_UNARY_OP(--)
DEF_UNARY_OP(+)
DEF_UNARY_OP(-)
DEF_UNARY_OP(~)
DEF_UNARY_OP(!)
DEF_UNARY_OP(*)
DEF_UNARY_OP(&)

#undef DEF_UNARY_OP

#define DEF_BINARY_OP(op) \
  template <class T1, class T2> \
    requires LambdaExpr<T1> || LambdaExpr<T2> \
  auto operator op(T1&& x, T2&& y) { \
    return std::bind([](auto&& x, auto&& y) -> decltype(auto) { return FWD(x) op FWD(y); }, \
                     FWD(x), FWD(y)); \
  }

DEF_BINARY_OP(+=)
DEF_BINARY_OP(-=)
DEF_BINARY_OP(*=)
DEF_BINARY_OP(/=)
DEF_BINARY_OP(%=)
DEF_BINARY_OP(^=)
DEF_BINARY_OP(&=)
DEF_BINARY_OP(|=)
DEF_BINARY_OP(<<=)
DEF_BINARY_OP(>>=)
DEF_BINARY_OP(+)
DEF_BINARY_OP(-)
DEF_BINARY_OP(*)
DEF_BINARY_OP(/)
DEF_BINARY_OP(%)
DEF_BINARY_OP(^)
DEF_BINARY_OP(&)
DEF_BINARY_OP(|)
DEF_BINARY_OP(<<)
DEF_BINARY_OP(>>)
DEF_BINARY_OP(==)
DEF_BINARY_OP(!=)
DEF_BINARY_OP(<)
DEF_BINARY_OP(>)
DEF_BINARY_OP(<=)
DEF_BINARY_OP(>=)
DEF_BINARY_OP(&&)
DEF_BINARY_OP(||)

#undef DEF_BINARY_OP

template <class T1, class T2>
  requires LambdaExpr<T1> || LambdaExpr<T2>
auto at(T1&& x, T2&& y) {
  return std::bind([](auto&& x, auto&& y) -> decltype(auto) { return FWD(x)[FWD(y)]; }, FWD(x),
                   FWD(y));
}

template <int I>
auto get(LambdaExpr auto&& x) {
  return std::bind([](auto&& x) -> decltype(auto) { return std::get<I>(FWD(x)); }, FWD(x));
}

inline auto rep(int l, int r) { return std::views::iota(std::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); }

using namespace std::literals;
using namespace std::placeholders;

namespace ranges = std::ranges;
namespace views = std::views;

using i64 = std::int64_t;

#define len(...) static_cast<int>(ranges::size(__VA_ARGS__))

#endif  // __INCLUDE_LEVEL__
0