結果

問題 No.1661 Sum is Prime (Hard Version)
ユーザー tokusakuraitokusakurai
提出日時 2021-08-27 22:00:27
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 206 ms / 3,000 ms
コード長 4,717 bytes
コンパイル時間 2,203 ms
コンパイル使用メモリ 206,136 KB
実行使用メモリ 46,040 KB
最終ジャッジ日時 2023-08-13 08:56:19
合計ジャッジ時間 5,969 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge14
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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 87 ms
45,900 KB
testcase_01 AC 87 ms
45,856 KB
testcase_02 AC 151 ms
45,812 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 AC 87 ms
45,872 KB
testcase_05 AC 85 ms
45,676 KB
testcase_06 AC 87 ms
45,916 KB
testcase_07 AC 87 ms
45,892 KB
testcase_08 AC 87 ms
45,848 KB
testcase_09 AC 86 ms
45,824 KB
testcase_10 AC 87 ms
45,972 KB
testcase_11 AC 86 ms
45,848 KB
testcase_12 AC 135 ms
45,912 KB
testcase_13 AC 134 ms
46,040 KB
testcase_14 AC 143 ms
45,892 KB
testcase_15 AC 170 ms
45,896 KB
testcase_16 AC 152 ms
45,756 KB
testcase_17 AC 145 ms
45,976 KB
testcase_18 AC 105 ms
45,852 KB
testcase_19 AC 120 ms
45,800 KB
testcase_20 AC 104 ms
45,984 KB
testcase_21 AC 145 ms
45,800 KB
testcase_22 AC 206 ms
45,956 KB
testcase_23 AC 198 ms
45,900 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

diff # 

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;
//const int mod = 998244353;

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 {
  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)};
}

/**
 * @brief Kth-Root
 */
uint64_t kth_root(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;
}

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(int64_t i = 2; i * i <= n; i++) {
    if(!prime[i]) continue;
    for(int64_t j = i + i; j <= n; j += i) {
      prime[j] = false;
    }
  }
  return prime;
}

template< int64_t LIM = 100000000000LL >
struct PrimeCount {
private:
  int64_t sq;
  vector< bool > prime;
  vector< int > 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(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 p3(int64_t x, int64_t y) {
    int64_t x13 = kth_root(x, 3), ans = 0;
    if(y <= x13) {
      int64_t a = pi(y);
      int64_t pi_x13 = pi(x13);
      for(int64_t i = a + 1; i <= pi_x13; i++) {
        int64_t xi = x / primes[i - 1];
        int64_t bi = pi(kth_root(xi, 2));
        for(int j = i; j <= bi; j++) {
          ans += pi(xi / primes[j - 1]) - (j - 1);
        }
      }
    }
    return ans;
  }

  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(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(1e7 + 5), 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(n, 4);
    int64_t a = pi(m);
    return phi(n, a) + a - 1 - p2(n, m) - p3(n, m);
  }
};

int main() {
    long long L, R; cin >> L >> R;

    if(R == 1) {cout << "0\n"; return 0;}

    PrimeCount pc;
    cout << pc.pi(R)-pc.pi(L-1)+pc.pi(2*R-1)-pc.pi(2*L) << '\n';
}
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