kyopro-lib

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:x: test/yosupo-judge/sum_of_totient_function/main.test.cpp

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Code

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

#include <iostream>
#include "Mylib/Number/Mint/mint.cpp"
#include "Mylib/Number/Totient/totient_sum.cpp"

namespace hl = haar_lib;

using mint = hl::modint<998244353>;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int64_t N;
  std::cin >> N;

  std::cout << hl::totient_sum<mint>(N) << "\n";

  return 0;
}
#line 1 "test/yosupo-judge/sum_of_totient_function/main.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_totient_function"

#include <iostream>
#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 2 "Mylib/Number/Totient/totient_sum.cpp"
#include <cmath>
#include <unordered_map>
#include <vector>
#line 2 "Mylib/Number/Totient/totient_table.cpp"
#include <numeric>
#line 4 "Mylib/Number/Totient/totient_table.cpp"

namespace haar_lib {
  std::vector<int> totient_table(int n) {
    std::vector<int> ret(n + 1);
    std::iota(ret.begin(), ret.end(), 0);

    for (int i = 2; i <= n; ++i) {
      if (ret[i] == i) {
        for (int j = i; j <= n; j += i) {
          ret[j] = ret[j] / i * (i - 1);
        }
      }
    }

    return ret;
  }
}  // namespace haar_lib
#line 6 "Mylib/Number/Totient/totient_sum.cpp"

namespace haar_lib {
  template <typename T>
  T totient_sum(int64_t N) {
    const int64_t K = (int64_t) pow(N, 0.66);

    std::vector<T> memo1(K + 1);
    auto table = totient_table(K);
    T sum      = 0;
    for (int i = 1; i <= K; ++i) {
      sum += table[i];
      memo1[i] = sum;
    }

    std::unordered_map<int64_t, T> memo2;

    auto f =
        [&](auto &f, int64_t x) -> T {
      if (x <= K) return memo1[x];
      if (memo2.find(x) != memo2.end()) return memo2[x];

      T ret = 0;

      const int64_t s = sqrt(x);

      for (int i = 2; i <= s; ++i) {
        if (x / i <= s) continue;
        ret -= f(f, x / i);
      }

      for (int i = 1; i <= s; ++i) {
        ret -= f(f, i) * (x / i - x / (i + 1));
      }

      ret += (T) x * (x + 1) / 2;

      return memo2[x] = ret;
    };

    return f(f, N);
  }
}  // namespace haar_lib
#line 6 "test/yosupo-judge/sum_of_totient_function/main.test.cpp"

namespace hl = haar_lib;

using mint = hl::modint<998244353>;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int64_t N;
  std::cin >> N;

  std::cout << hl::totient_sum<mint>(N) << "\n";

  return 0;
}
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