#387444 (C++14) No.886 Direct

提出ソース

結果

問題	No.886 Direct
ユーザー	noshi91
提出日時	2019-10-06 20:33:33
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	280 ms / 4,000 ms
コード長	8,687 bytes
コンパイル時間	836 ms
コンパイル使用メモリ	83,360 KB
実行使用メモリ	75,824 KB
最終ジャッジ日時	2024-10-11 01:21:13
合計ジャッジ時間	4,575 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	1 ms 6,820 KB
testcase_03	AC	2 ms 6,820 KB
testcase_04	AC	2 ms 6,816 KB
testcase_05	AC	2 ms 6,816 KB
testcase_06	AC	2 ms 6,816 KB
testcase_07	AC	2 ms 6,820 KB
testcase_08	AC	2 ms 6,816 KB
testcase_09	AC	2 ms 6,820 KB
testcase_10	AC	2 ms 6,820 KB
testcase_11	AC	2 ms 6,820 KB
testcase_12	AC	2 ms 6,820 KB
testcase_13	AC	2 ms 6,816 KB
testcase_14	AC	2 ms 6,820 KB
testcase_15	AC	2 ms 6,816 KB
testcase_16	AC	2 ms 6,816 KB
testcase_17	AC	3 ms 6,820 KB
testcase_18	AC	3 ms 6,816 KB
testcase_19	AC	3 ms 6,820 KB
testcase_20	AC	2 ms 6,820 KB
testcase_21	AC	3 ms 6,820 KB
testcase_22	AC	3 ms 6,816 KB
testcase_23	AC	85 ms 37,584 KB
testcase_24	AC	97 ms 40,716 KB
testcase_25	AC	52 ms 26,768 KB
testcase_26	AC	75 ms 33,840 KB
testcase_27	AC	246 ms 70,684 KB
testcase_28	AC	216 ms 68,552 KB
testcase_29	AC	262 ms 75,772 KB
testcase_30	AC	280 ms 75,776 KB
testcase_31	AC	270 ms 75,768 KB
testcase_32	AC	258 ms 75,824 KB
testcase_33	AC	275 ms 75,772 KB
testcase_34	AC	279 ms 75,772 KB
testcase_35	AC	260 ms 75,748 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

raw source code

//#define NDEBUG
#include <cstddef>
#include <cstdint>
#include <iostream>
#include <vector>

namespace n91 {

  using i8 = std::int_fast8_t;
  using i32 = std::int_fast32_t;
  using i64 = std::int_fast64_t;
  using u8 = std::uint_fast8_t;
  using u32 = std::uint_fast32_t;
  using u64 = std::uint_fast64_t;
  using isize = std::ptrdiff_t;
  using usize = std::size_t;

  constexpr usize operator"" _z(unsigned long long x) noexcept {
    return static_cast<usize>(x);
  }

  class rep {
    const usize f, l;

  public:
    class itr {
      friend rep;
      usize i;
      constexpr itr(const usize x) noexcept : i(x) {}

    public:
      void operator++() noexcept { ++i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    constexpr rep(const usize first, const usize last) noexcept
      : f(first), l(last) {}
    constexpr itr begin() const noexcept { return itr(f); }
    constexpr itr end() const noexcept { return itr(l); }
  };
  class revrep {
    const usize f, l;

  public:
    class itr {
      friend revrep;
      usize i;
      constexpr itr(usize x) noexcept : i(x) {}

    public:
      void operator++() noexcept { --i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    constexpr revrep(usize first, usize last) noexcept : f(--first), l(--last) {}
    constexpr itr begin() const noexcept { return itr(l); }
    constexpr itr end() const noexcept { return itr(f); }
  };
  template <class T> using vec_alias = std::vector<T>;
  template <class T> auto md_vec(const usize n, const T& value) {
    return std::vector<T>(n, value);
  }
  template <class... Args> auto md_vec(const usize n, Args... args) {
    return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
  }
  template <class T> constexpr T difference(const T& a, const T& b) {
    return a < b ? b - a : a - b;
  }
  template <class T> T scan() {
    T ret;
    std::cin >> ret;
    return ret;
  }

} // namespace n91

#include <cstdint>

namespace n91 {

  constexpr std::uint_fast64_t totient(std::uint_fast64_t x) noexcept {
    using u64 = std::uint_fast64_t;
    u64 ret = x;
    for (u64 i = static_cast<u64>(2); i * i <= x; ++i) {
      if (x % i == static_cast<u64>(0)) {
        ret -= ret / i;
        x /= i;
        while (x % i == static_cast<u64>(0)) {
          x /= i;
        }
      }
    }
    if (x != static_cast<u64>(1)) {
      ret -= ret / x;
    }
    return ret;
  }

  template <std::uint_fast64_t Modulus,
    std::uint_fast64_t InverseExp =
    totient(Modulus) - static_cast<std::uint_fast64_t>(1)>
    class modint {
    using u64 = std::uint_fast64_t;

    static_assert(Modulus < static_cast<u64>(1) << static_cast<u64>(32),
      "Modulus must be less than 2**32");

    u64 a;

    constexpr modint& negate() noexcept {
      if (a != static_cast<u64>(0)) {
        a = Modulus - a;
      }
      return *this;
    }

    public:
      constexpr modint(const u64 x = static_cast<u64>(0)) noexcept
        : a(x% Modulus) {}
      constexpr u64& value() noexcept { return a; }
      constexpr const u64& value() const noexcept { return a; }
      constexpr modint operator+() const noexcept { return modint(*this); }
      constexpr modint operator-() const noexcept { return modint(*this).negate(); }
      constexpr modint operator+(const modint rhs) const noexcept {
        return modint(*this) += rhs;
      }
      constexpr modint operator-(const modint rhs) const noexcept {
        return modint(*this) -= rhs;
      }
      constexpr modint operator*(const modint rhs) const noexcept {
        return modint(*this) *= rhs;
      }
      constexpr modint operator/(const modint rhs) const noexcept {
        return modint(*this) /= rhs;
      }
      constexpr modint& operator+=(const modint rhs) noexcept {
        a += rhs.a;
        if (a >= Modulus) {
          a -= Modulus;
        }
        return *this;
      }
      constexpr modint& operator-=(const modint rhs) noexcept {
        if (a < rhs.a) {
          a += Modulus;
        }
        a -= rhs.a;
        return *this;
      }
      constexpr modint& operator*=(const modint rhs) noexcept {
        a = a * rhs.a % Modulus;
        return *this;
      }
      constexpr modint& operator/=(modint rhs) noexcept {
        u64 exp = InverseExp;
        while (exp) {
          if (exp % static_cast<u64>(2) != static_cast<u64>(0)) {
            *this *= rhs;
          }
          rhs *= rhs;
          exp /= static_cast<u64>(2);
        }
        return *this;
      }
      constexpr bool operator==(const modint rhs) const noexcept {
        return a == rhs.a;
      }
      constexpr bool operator!=(const modint rhs) const noexcept {
        return a != rhs.a;
      }
  };

  template <class T, std::uint_fast64_t v> class modint_constant {
  public:
    static constexpr T value = static_cast<T>(v);

    using value_type = T;
  };

} // namespace n91

#include <cassert>
#include <cstddef>
#include <utility>
#include <vector>
#include <numeric>

namespace n91 {

  class prime_sieve {
  public:
    using size_type = std::size_t;

  private:
    std::vector<size_type> prime, factor;

  public:
    prime_sieve() {}
    explicit prime_sieve(const size_type size) : prime(), factor(size) {
      assert(size >= 2);
      std::iota(factor.begin(), factor.end(), static_cast<size_type>(0));
      factor[0] = 1;
      factor[1] = 0;
      for (size_type i{ 2 }; i != size; ++i) {
        const size_type fi = factor[i];
        if (fi == i) {
          prime.push_back(i);
        }
        for (const size_type p : prime) {
          if (p > fi) { break; }
          const size_type ip = i * p;
          if (ip >= size) { break; }
          factor[ip] = p;
        }
      }
    }
    size_type len() const noexcept { return factor.size(); }
    bool is_prime(const size_type i) const noexcept {
      assert(i < len());
      return factor[i] == i;
    }
    std::vector<size_type> factorize(size_type i) const noexcept {
      assert(i != 0);
      std::vector<size_type> ret;
      while (i != 1) {
        ret.push_back(factor[i]);
        i /= factor[i];
      }
      return std::move(ret);
    }
    template <class C> void divisor_zeta(C& c) const noexcept {
      const size_type n{ c.size() };
      assert(n <= len());
      for (size_type i{ 0 }; i != prime.size() && prime[i] < n; ++i) {
        for (size_type j{ 1 }; j * prime[i] < n; ++j) {
          c[j * prime[i]] += c[j];
        }
      }
    }
    template <class C> void divisor_mobius(C& c) const noexcept {
      const size_type n{ c.size() };
      assert(n <= len());
      for (size_type i{ 0 }; i != prime.size() && prime[i] < n; ++i) {
        for (size_type j{ (n - 1) / prime[i] }; j != 0; --j) {
          c[j * prime[i]] -= c[j];
        }
      }
    }
    template <class C> void multiple_zeta(C& c) const noexcept {
      const size_type n{ c.size() };
      assert(n <= len());
      for (size_type i{ 0 }; i != prime.size() && prime[i] < n; ++i) {
        for (size_type j{ (n - 1) / prime[i] }; j != 0; --j) {
          c[j] += c[j * prime[i]];
        }
      }
    }
    template <class C> void multiple_mobius(C& c) const noexcept {
      const size_type n{ c.size() };
      assert(n <= len());
      for (size_type i{ 0 }; i != prime.size() && prime[i] < n; ++i) {
        for (size_type j{ 1 }; j * prime[i] < n; ++j) {
          c[j] -= c[j * prime[i]];
        }
      }
    }
  };

} // namespace n91


#include <algorithm>
#include <iostream>
#include <numeric>
#include <queue>
#include <string>
#include <utility>

namespace n91 {

  constexpr usize lm(const usize a, const usize b) {
    if (b < a) {
      return a - b;
    }
    else {
      return 0_z;
    }
  }

  void main_() {
    using mint = modint<static_cast<u64>(1000000007)>;
    const usize h = scan<usize>();
    const usize w = scan<usize>();
    const usize n = std::max({ h, w, 2_z });
    std::vector<mint> a(n), b(n);
    for (const auto i : rep(1_z, n)) {
      a[i] = lm(h, i);
      b[i] = lm(w, i);
    }
    const prime_sieve ps{ n };
    ps.multiple_zeta(a);
    ps.multiple_zeta(b);
    for (const auto i : rep(0_z, n)) {
      a[i] *= b[i];
    }
    ps.multiple_mobius(a);
    mint ans = a[1_z] * static_cast<mint>(2);
    mint h_ = static_cast<mint>(h);
    mint w_ = static_cast<mint>(w);
    ans += (h_ - static_cast<mint>(1)) * w_ + h_ * (w_ - static_cast<mint>(1));
    std::cout << ans.value() << std::endl;
  }

} // namespace n91

int main() {
  n91::main_();
  return 0;
}

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結果

テストケース

ソースコード