test/yosupo-judge/sum_of_exponential_times_polynomial_limit/main.test.cpp

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• Last update: 2021-05-10 06:09:59+09:00
• Problem: https://judge.yosupo.jp/problem/sum_of_exponential_times_polynomial_limit
• Link: View error logs on GitHub Actions

Depends on

• Sum of exponential times polynomial limit (\sum_{i=0}^{\infty} r^i i^d) (Mylib/Math/sum_of_exponential_times_polynomial_limit.cpp)
• Modint (Mylib/Number/Mint/mint.cpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_exponential_times_polynomial_limit"

#include <iostream>
#include "Mylib/Math/sum_of_exponential_times_polynomial_limit.cpp"
#include "Mylib/Number/Mint/mint.cpp"

namespace hl = haar_lib;

constexpr int mod = 998244353;
using mint        = hl::modint<mod>;

int main() {
  int r, d;
  std::cin >> r >> d;
  std::cout << hl::sum_of_exponential_times_polynomial_limit<mint>(r, d) << "\n";

  return 0;
}

#line 1 "test/yosupo-judge/sum_of_exponential_times_polynomial_limit/main.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_exponential_times_polynomial_limit"

#include <iostream>
#line 2 "Mylib/Math/sum_of_exponential_times_polynomial_limit.cpp"
#include <cstdint>
#include <vector>

namespace haar_lib {
  template <typename T>
  T sum_of_exponential_times_polynomial_limit(int64_t r, int d) {
    T ret   = 0;
    T r_pow = 1;
    int m   = T::mod();

    std::vector<T> s(d + 1);
    std::vector<T> invs(d + 2);
    invs[1] = 1;

    for (int i = 2; i <= d + 1; ++i) {
      invs[i] = (m / i) * (m - invs[m % i]);
    }

    for (int i = 0; i <= d; ++i) {
      if (i > 0) s[i] += s[i - 1];
      s[i] += T::pow(i, d) * r_pow;
      r_pow *= r;
    }

    T t = 1;
    for (int i = 0; i <= d; ++i) {
      ret += t * s[d - i];
      t *= invs[i + 1] * (-r) * (d + 1 - i);
    }

    ret /= T::pow(1 - r, d + 1);

    return ret;
  }
}  // namespace haar_lib
#line 3 "Mylib/Number/Mint/mint.cpp"
#include <utility>

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod() { return M; }

    constexpr modint() : val_(0) {}
    constexpr modint(int64_t n) {
      if (n >= M)
        val_ = n % M;
      else if (n < 0)
        val_ = n % M + M;
      else
        val_ = n;
    }

    constexpr auto &operator=(const modint &a) {
      val_ = a.val_;
      return *this;
    }
    constexpr auto &operator+=(const modint &a) {
      if (val_ + a.val_ >= M)
        val_ = (uint64_t) val_ + a.val_ - M;
      else
        val_ += a.val_;
      return *this;
    }
    constexpr auto &operator-=(const modint &a) {
      if (val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto &operator*=(const modint &a) {
      val_ = (uint64_t) val_ * a.val_ % M;
      return *this;
    }
    constexpr auto &operator/=(const modint &a) {
      val_ = (uint64_t) val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
    constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
    constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
    constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }

    constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
    constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }

    constexpr auto &operator++() {
      *this += 1;
      return *this;
    }
    constexpr auto &operator--() {
      *this -= 1;
      return *this;
    }

    constexpr auto operator++(int) {
      auto t = *this;
      *this += 1;
      return t;
    }
    constexpr auto operator--(int) {
      auto t = *this;
      *this -= 1;
      return t;
    }

    constexpr static modint pow(int64_t n, int64_t p) {
      if (p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for (; p; (e *= e) %= M, p >>= 1)
        if (p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a) {
      int64_t b = M, u = 1, v = 0;

      while (b) {
        int64_t t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }

      u %= M;
      if (u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }

    constexpr auto pow(int64_t p) const { return pow(val_, p); }
    constexpr auto inv() const { return inv(val_); }

    friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }

    friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
    friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
    friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
    friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }

    friend std::istream &operator>>(std::istream &s, modint &a) {
      s >> a.val_;
      return s;
    }
    friend std::ostream &operator<<(std::ostream &s, const modint &a) {
      s << a.val_;
      return s;
    }

    template <int N>
    static auto div() {
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept { return val_; }
    explicit operator int64_t() const noexcept { return val_; }
  };
}  // namespace haar_lib
#line 6 "test/yosupo-judge/sum_of_exponential_times_polynomial_limit/main.test.cpp"

namespace hl = haar_lib;

constexpr int mod = 998244353;
using mint        = hl::modint<mod>;

int main() {
  int r, d;
  std::cin >> r >> d;
  std::cout << hl::sum_of_exponential_times_polynomial_limit<mint>(r, d) << "\n";

  return 0;
}

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