test/verify/yosupo-counting-primes.test.cpp

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• Last update: 2024-04-24 02:34:04+09:00
• Problem: https://judge.yosupo.jp/problem/counting_primes

Depends on

• Kth Root Integer (math/number-theory/kth-root-integer.hpp)
• Prime Count(素数の個数) (math/number-theory/prime-count.hpp)
• Prime Table(素数テーブル) (math/number-theory/prime-table.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/counting_primes

#include "../../template/template.hpp"

#include "../../math/number-theory/prime-count.hpp"

int main() {
  int64_t n;
  cin >> n;
  PrimeCount<> pc;
  cout << pc.pi(n) << "\n";
}

#line 1 "test/verify/yosupo-counting-primes.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/counting_primes

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yosupo-counting-primes.test.cpp"

#line 1 "math/number-theory/kth-root-integer.hpp"
uint64_t kth_root_integer(uint64_t a, int k) {
  if(k == 1) return a;
  auto check = [&](uint32_t x) {
    uint64_t mul = 1;
    for(int j = 0; j < k; j++) {
      if(__builtin_mul_overflow(mul, x, &mul)) return false;
    }
    return mul <= a;
  };
  uint64_t ret = 0;
  for(int i = 31; i >= 0; i--) {
    if(check(ret | (1u << i))) ret |= 1u << i;
  }
  return ret;
}
#line 1 "math/number-theory/prime-table.hpp"
/**
 * @brief Prime Table(素数テーブル)
 * 
 */
vector< bool > prime_table(int n) {
  vector< bool > prime(n + 1, true);
  if(n >= 0) prime[0] = false;
  if(n >= 1) prime[1] = false;
  for(int i = 2; i * i <= n; i++) {
    if(!prime[i]) continue;
    for(int j = i * i; j <= n; j += i) {
      prime[j] = false;
    }
  }
  return prime;
}
#line 3 "math/number-theory/prime-count.hpp"

/**
 * @brief Prime Count(素数の個数)
 */
template< int64_t LIM = 100000000000LL >
struct PrimeCount {
private:
  int64_t sq;
  vector< bool > prime;
  vector< int64_t > prime_sum, primes;

  int64_t p2(int64_t x, int64_t y) {
    if(x < 4) return 0;
    int64_t a = pi(y);
    int64_t b = pi(kth_root_integer(x, 2));
    if(a >= b) return 0;
    int64_t sum = (a - 2) * (a + 1) / 2 - (b - 2) * (b + 1) / 2;
    for(int64_t i = a; i < b; i++) sum += pi(x / primes[i]);
    return sum;
  }

  int64_t phi(int64_t m, int64_t n) {
    if(m < 1) return 0;
    if(n > m) return 1;
    if(n < 1) return m;
    if(m <= primes[n - 1] * primes[n - 1]) return pi(m) - n + 1;
    if(m <= primes[n - 1] * primes[n - 1] * primes[n - 1] && m <= sq) {
      int64_t sx = pi(kth_root_integer(m, 2));
      int64_t ans = pi(m) - (sx + n - 2) * (sx - n + 1) / 2;
      for(int64_t i = n; i < sx; ++i) ans += pi(m / primes[i]);
      return ans;
    }
    return phi(m, n - 1) - phi(m / primes[n - 1], n - 1);
  }

public:

  PrimeCount() : sq(kth_root_integer(LIM, 2)), prime_sum(sq + 1) {
    prime = prime_table(sq);
    for(int i = 1; i <= sq; i++) prime_sum[i] = prime_sum[i - 1] + prime[i];
    primes.reserve(prime_sum[sq]);
    for(int i = 1; i <= sq; i++) if(prime[i]) primes.push_back(i);
  }

  int64_t pi(int64_t n) {
    if(n <= sq) return prime_sum[n];
    int64_t m = kth_root_integer(n, 3);
    int64_t a = pi(m);
    return phi(n, a) + a - 1 - p2(n, m);
  }
};
#line 6 "test/verify/yosupo-counting-primes.test.cpp"

int main() {
  int64_t n;
  cin >> n;
  PrimeCount<> pc;
  cout << pc.pi(n) << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	Grothendieck_prime_00	AC	9 ms	6 MB
g++	example_00	AC	9 ms	6 MB
g++	example_01	AC	9 ms	6 MB
g++	max_00	AC	218 ms	6 MB
g++	max_01	AC	218 ms	6 MB
g++	max_02	AC	218 ms	6 MB
g++	max_03	AC	218 ms	6 MB
g++	max_04	AC	218 ms	6 MB
g++	random_00	AC	213 ms	6 MB
g++	random_01	AC	127 ms	6 MB
g++	random_02	AC	131 ms	6 MB
g++	random_03	AC	102 ms	6 MB
g++	random_04	AC	53 ms	6 MB
g++	small_00	AC	8 ms	6 MB
g++	small_01	AC	8 ms	6 MB
g++	small_02	AC	9 ms	6 MB
g++	small_03	AC	8 ms	6 MB
g++	small_04	AC	8 ms	6 MB
g++	small_prime_00	AC	8 ms	6 MB
g++	small_prime_01	AC	8 ms	6 MB
g++	very_small_00	AC	8 ms	6 MB
g++	very_small_01	AC	8 ms	6 MB
g++	very_small_02	AC	8 ms	6 MB
g++	very_small_03	AC	8 ms	6 MB
g++	very_small_04	AC	8 ms	6 MB
clang++	Grothendieck_prime_00	AC	8 ms	6 MB
clang++	example_00	AC	8 ms	6 MB
clang++	example_01	AC	8 ms	6 MB
clang++	max_00	AC	228 ms	6 MB
clang++	max_01	AC	228 ms	6 MB
clang++	max_02	AC	227 ms	6 MB
clang++	max_03	AC	227 ms	6 MB
clang++	max_04	AC	228 ms	6 MB
clang++	random_00	AC	228 ms	6 MB
clang++	random_01	AC	133 ms	6 MB
clang++	random_02	AC	139 ms	6 MB
clang++	random_03	AC	108 ms	6 MB
clang++	random_04	AC	56 ms	6 MB
clang++	small_00	AC	9 ms	6 MB
clang++	small_01	AC	8 ms	6 MB
clang++	small_02	AC	8 ms	6 MB
clang++	small_03	AC	8 ms	6 MB
clang++	small_04	AC	9 ms	6 MB
clang++	small_prime_00	AC	8 ms	6 MB
clang++	small_prime_01	AC	8 ms	6 MB
clang++	very_small_00	AC	8 ms	6 MB
clang++	very_small_01	AC	8 ms	6 MB
clang++	very_small_02	AC	9 ms	6 MB
clang++	very_small_03	AC	8 ms	6 MB
clang++	very_small_04	AC	8 ms	6 MB

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