tests/math/meissel-lehmer/libchecker.test.cpp

View this file on GitHub
Last update: 2025-06-26 16:44:42+09:00
Problem: https://judge.yosupo.jp/problem/counting_primes

Depends on

Code

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#include "../../../library/fastio.hpp"
#include "../../../library/math/meissel-lehmer.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/counting_primes"

int main() {
  ll n;
  asalib::FastIO >> n;
  asalib::FastIO << asalib::math::meissel_lehmer(n) << '\n';
  return 0;
}

#line 1 "tests/math/meissel-lehmer/libchecker.test.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#line 2 "library/fastio.hpp"

#line 5 "library/fastio.hpp"
#include <concepts>
#line 11 "library/fastio.hpp"
#include <type_traits>
using namespace std;

// TODO: 何も入力がない場合にも対応する？

namespace asalib {
  namespace _internal {
    class FastIO {
      private:
      using uint = unsigned int;
      static constexpr uint BUFFER_SIZE = 1 << 20;
      static constexpr uint MAX_TOKEN_SIZE = 64;

      // ===== Read ===== //

      private:
      array<char, BUFFER_SIZE> read_buffer;
      array<char, BUFFER_SIZE>::iterator read_ptr;
      uint read_size = 0;

      inline void load() {
        // まだ読んでないデータを前に持ってくる
        memcpy(read_buffer.begin(), read_ptr, read_size - (read_ptr - read_buffer.begin()));
        read_size -= read_ptr - read_buffer.begin();
        read_ptr = read_buffer.begin();
        // stdin から読み込み
        read_size += fread(read_buffer.begin() + read_size, 1, BUFFER_SIZE - read_size, stdin);
      }

      inline void skip_space() {
        // 制御文字 + space
        // DEL (127 = 0x7F) がコーナーケースだがまあ使わんやろ
        while (*read_ptr <= ' ') ++read_ptr;
      }

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _read_uint(T& x) {
        x = 0;
        while (true) {
          uint64_t v;
          memcpy(&v, read_ptr, 8);
          // '0' -> 0 処理
          // こっちを先にやることで制御文字系もはじく
          v -= 0x30'30'30'30'30'30'30'30;
          // ASCII 範囲外
          if (v & 0x80'80'80'80'80'80'80'80) break;
          // 桁ごとの数字から数値に
          v = (v * 10 + (v >> 8)) & 0x00ff00ff00ff00ff;
          v = (v * 100 + (v >> 16)) & 0x0000ffff0000ffff;
          v = (v * 10000 + (v >> 32)) & 0x00000000ffffffff;
          x = 1'0000'0000 * x + v;
          read_ptr += 8;
        }
        while (true) {
          uint32_t v;
          memcpy(&v, read_ptr, 4);
          v -= 0x30'30'30'30;
          if (v & 0x80'80'80'80) break;
          v = (v * 10 + (v >> 8)) & 0x00ff00ff;
          v = (v * 100 + (v >> 16)) & 0x0000ffff;
          x = 1'0000 * x + v;
          read_ptr += 4;
        }
        while (true) {
          uint16_t v;
          memcpy(&v, read_ptr, 2);
          v -= 0x3030;
          if (v & 0x8080) break;
          v = (v * 10 + (v >> 8)) & 0x00ff;
          x = 100 * x + v;
          read_ptr += 2;
        }
        if (*read_ptr > ' ') x = 10 * x + (*read_ptr++ & 0x0f);
      }

      inline void read_commonop() {
        // そろそろ限界なら読み込み
        if ((read_ptr - read_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) load();
        skip_space();
      }

      public:
      FastIO& operator>>(char& x) {
        read_commonop();
        x = *read_ptr++;
        return *this;
      }

      FastIO& operator>>(string& x) {
        read_commonop();
        x.clear();
        while (*read_ptr > ' ') {
          x += *read_ptr++;
          if (read_ptr == read_buffer.end()) load();
        }
        return *this;
      }

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      FastIO& operator>>(T& x) {
        read_commonop();
        constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
        if constexpr (is_signed) {
          if (*read_ptr == '-') {
            ++read_ptr;
            _read_uint(x);
            x = -x;
            return *this;
          }
        }
        _read_uint(x);
        return *this;
      }

      // ===== Write ===== //

      private:
      array<char, BUFFER_SIZE> write_buffer;
      array<char, BUFFER_SIZE>::iterator write_ptr;
      static constexpr uint MAX_PRECOMPUTE_NUM = 1'0000;
      static constexpr uint MAX_PRECOMPUTE_NUM_DIGIT = 4;

      static constexpr array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits = [] {
        array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits {};
        for (uint i = 0; i < MAX_PRECOMPUTE_NUM; ++i) {
          uint x = i;
          for (int j = MAX_PRECOMPUTE_NUM_DIGIT - 1; j >= 0; --j) {
            digits[i * MAX_PRECOMPUTE_NUM_DIGIT + j] = '0' + (x % 10);
            x /= 10;
          }
        }
        return digits;
      }();

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      static constexpr array<T, numeric_limits<T>::digits10 + 1> Pow10 = [] {
        array<T, numeric_limits<T>::digits10 + 1> pow10 {};
        pow10[0] = 1;
        for (uint i = 1; i < pow10.size(); ++i) pow10[i] = pow10[i - 1] * 10;
        return pow10;
      }();

      inline void write_commonop() {
        // そろそろ限界なら書き込む
        if ((write_ptr - write_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) flush();
      }

      inline void putchar(const char& x) { *write_ptr++ = x; }

      template<typename T, int NumDig>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _write_uint_top(const T& x) {
        // leading-zero を書き込まないようにする
        if constexpr (NumDig > 1) {
          if (x < Pow10<T>[NumDig - 1]) {
            _write_uint_top<T, NumDig - 1>(x);
            return;
          }
        }
        copy_n(digits.begin() + (x + 1) * MAX_PRECOMPUTE_NUM_DIGIT - NumDig, NumDig, write_ptr);
        write_ptr += NumDig;
      }

      template<typename T, int NumDig>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _write_uint(const T& x) {
        if constexpr (NumDig >= 0) {
          if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x / MAX_PRECOMPUTE_NUM);
          copy_n(digits.begin() + x % MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT, MAX_PRECOMPUTE_NUM_DIGIT, write_ptr);
          write_ptr += MAX_PRECOMPUTE_NUM_DIGIT;
        }
      }

      template<typename T, int NumDig>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      inline void _write_uint_root(const T& x) {
        if constexpr (is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) {
          // 128bit 除算はおそいので 64bit 除算を使う
          if (x < Pow10<T>[16]) {
            _write_uint_root<uint64_t, NumDig>(x);
          }
          else if (x < Pow10<T>[32]) {
            _write_uint_root<uint64_t, NumDig>(x / Pow10<T>[16]);
            _write_uint<uint64_t, 16>(x % Pow10<T>[16]);
          }
          else {
            _write_uint_root<uint64_t, NumDig>(x / Pow10<T>[32]);
            _write_uint<uint64_t, 16>(x % Pow10<T>[32] / Pow10<T>[16]);
            _write_uint<uint64_t, 16>(x % Pow10<T>[16]);
          }
          return;
        }

        if constexpr (NumDig < numeric_limits<T>::digits10) {
          if (x >= Pow10<T>[NumDig]) {
            _write_uint_root<T, NumDig + MAX_PRECOMPUTE_NUM_DIGIT>(x);
            return;
          }
        }
        _write_uint_top<T, MAX_PRECOMPUTE_NUM_DIGIT>(x / Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
        if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x % Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
      }

      public:
      inline void flush() {
        fwrite(write_buffer.begin(), 1, write_ptr - write_buffer.begin(), stdout);
        write_ptr = write_buffer.begin();
      }

      FastIO& operator<<(const char& x) {
        write_commonop();
        putchar(x);
        return *this;
      }

      FastIO& operator<<(const string& x) {
        write_commonop();
        uint idx = 0;
        while (idx < x.size()) {
          const uint siz = min(BUFFER_SIZE - (uint) (write_ptr - write_buffer.begin()), (uint) x.size() - idx);
          copy_n(x.begin() + idx, siz, write_ptr);
          write_ptr += siz;
          idx += siz;
          if (write_ptr == write_buffer.end()) flush();
        }
        return *this;
      }

      template<typename T>
        requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
      FastIO& operator<<(const T& x) {
        write_commonop();
        constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
        if constexpr (is_signed) {
          if (x < 0) {
            putchar('-');
            _write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(-x);
            return *this;
          }
        }
        _write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(x);
        return *this;
      }

      // ===== Common ====== //

      public:
      FastIO() {
        read_ptr = read_buffer.begin();
        write_ptr = write_buffer.begin();
        load();
      }

      ~FastIO() { flush(); }
    };
  }  // namespace _internal

  _internal::FastIO FastIO;
}  // namespace asalib
#line 2 "library/math/meissel-lehmer.hpp"

#line 9 "library/math/meissel-lehmer.hpp"
using namespace std;

#line 2 "library/data-structure/bit.hpp"

#line 6 "library/data-structure/bit.hpp"
using namespace std;

#line 2 "library/_internal/types.hpp"

#line 4 "library/_internal/types.hpp"
using namespace std;

#line 2 "library/_internal/modint-base.hpp"

#line 5 "library/_internal/modint-base.hpp"
using namespace std;

namespace asalib {
  namespace _internal {
    class modint_base {};

    template<typename T>
    concept is_modint = is_base_of_v<modint_base, T>;
  }  // namespace _internal
}  // namespace asalib
#line 7 "library/_internal/types.hpp"

namespace asalib {
  namespace _internal {
    // ---------- concept definition ---------- //
    template<class T>
    concept integral_like = integral<T> || is_modint<T>;

    template<class T>
    concept floating_like = floating_point<T>;

    template<class T>
    concept numeric_like = integral_like<T> || floating_like<T>;

    // ---------- function definition ---------- //
    template<class T>
    T plus(T a, T b) { return a + b; }

    template<class T>
    T minus(T a, T b) { return a - b; }

    // ---------- constant definition ---------- //
    template<class T>
    T zero() { return 0; }
  }  // namespace _internal
}  // namespace asalib
#line 9 "library/data-structure/bit.hpp"

namespace asalib {
  namespace ds {
    template<_internal::numeric_like T, T (*op)(T, T) = _internal::plus<T>, T (*invop)(T, T) = _internal::minus<T>, T (*e)() = _internal::zero<T>>
    class BIT {
      public:
      BIT(): _n(0) {}
      explicit BIT(size_t n) {
        _n = n;
        data.reserve(n);
        data.resize(n, 0);
      }

      void add(size_t i, T x) {
        assert(0 <= i && i < _n);
        ++i;
        while (i <= _n) {
          data[i - 1] = op(data[i - 1], x);
          i += i & -i;
        }
      }

      T sum(size_t l, size_t r) const {
        assert(0 <= l && l <= r && r <= _n);
        return invop(_sum(r), _sum(l));
      }

      private:
      size_t _n;
      vector<T> data;
      T _sum(size_t i) const {
        T s = e();
        while (i > 0) {
          s = op(s, data[i - 1]);
          i -= i & -i;
        }
        return s;
      }
    };
  }  // namespace ds
}  // namespace asalib
#line 12 "library/math/meissel-lehmer.hpp"

namespace asalib {
  namespace math {
    template<integral T>
    constexpr T meissel_lehmer(T n) {
      // n <= 2 だと y = 0 になってしまうのでここで返しておく
      if (n <= 2) [[unlikely]]
        return n == 2;
      T y = powl(n, 1.0 / 3.0) * powl(logl(n), 2.0 / 3.0);

      // 前計算
      T ny = n / y;
      if (n < 200) [[unlikely]]  // この場合は普通に求めちゃったほうが早い
        ny = n;

      constexpr T None = -1;
      vector<T> minim_prime(ny + 1, None);
      vector<T> prime(0);
      for (T i = 2; i <= ny; ++i) {
        if (minim_prime[i] == None) {
          minim_prime[i] = prime.size();
          prime.push_back(i);
        }
        for (T j = 0; j < (T) prime.size(); ++j) {
          if (i * prime[j] > ny || prime[j] > prime[minim_prime[i]]) break;
          minim_prime[i * prime[j]] = j;
        }
      }
      if (n < 200) [[unlikely]]
        return prime.size();

      T pi_ny = prime.size();
      T pi_y = 0;
      for (T p : prime) {
        if (p > y) break;
        ++pi_y;
      }
      T pi_n = pi_y - 1;

      // P_2 (n, a) を計算し引いていく
      for (T b = pi_y + 1, c = pi_ny; b <= pi_ny; ++b) {
        while (c >= b && prime[b - 1] * prime[c - 1] > n) --c;
        if (c < b) break;
        pi_n -= c - b + 1;
      }

      // phi(n, a) の計算
      vector<tuple<T, T, bool>> params(0);
      function<void(T, T, bool)> phi = [&](T x, T a, bool isMinus) {
        if (x == 0) return;
        else if (x <= ny)
          params.push_back({ x, a, isMinus });
        else if (a == 0)
          pi_n += x * (isMinus ? -1 : 1);
        else
          phi(x, a - 1, isMinus), phi(x / prime[a - 1], a - 1, !isMinus);
      };
      phi(n, pi_y, false);
      sort(params.begin(), params.end());

      asalib::ds::BIT<T> bit(pi_ny);
      T idx = 2;
      for (auto&& [n, a, isMinus] : params) {
        while (idx <= n) bit.add(minim_prime[idx++], 1);
        pi_n += (n - bit.sum(0, a)) * (isMinus ? -1 : 1);
      }

      return pi_n;
    }
  }  // namespace math
}  // namespace asalib
#line 9 "tests/math/meissel-lehmer/libchecker.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/counting_primes"

int main() {
  ll n;
  asalib::FastIO >> n;
  asalib::FastIO << asalib::math::meissel_lehmer(n) << '\n';
  return 0;
}