Tifa's CP Library

:heavy_check_mark: lsieve2 (src/code/nt/lsieve2.hpp)

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#ifndef TIFALIBS_MATH_LSIEVE2
#define TIFALIBS_MATH_LSIEVE2

#include "../util/util.hpp"

namespace tifa_libs::math {

class lsieve2 {
  vecpt<u32> pr;
  vecu fr;

 public:
  explicit constexpr lsieve2(u32 n) : fr(n + 1) {
    for (u32 i = 2, x = n / 2, p1, p2, e; i <= n; x = n / (++i)) {
      if (!fr[i]) {
        for (p1 = 1, p2 = i, e = 0; p1 <= x; p1 = p2, p2 *= i, ++e) fr[p2] = 1;
        pr.emplace_back(i, e);
      }
      for (u32 t = 0; t < pr.size(); ++t)
        if (u32 p = pr[t].first; p > x) break;
        else if (i % p) fr[p * i] = i;
        else {
          fr[p * i] = fr[i];
          break;
        }
    }
  }

  // @param F: T(u32, u32)
  // @param %fpi(p, i) = $f(p^i)$
  // @return v[i] = f(i), for i in [0, n]
  template <class T, class F>
  requires requires(F f, u32 p, u32 i) {
    { f(p, i) } -> std::same_as<T>;
  }
  constexpr vec<T> run(F fpi, T init = T{1}) {
    vec<T> v(fr.size());
    v[1] = init;
    for (u32 i = 0; i < pr.size(); ++i)
      for (u32 p = pr[i].first, e = pr[i].second, pe = p, ex = 1; ex <= e; ++ex, pe *= p) v[pe] = fpi(p, ex);
    for (u32 i = 2; i < fr.size(); ++i) v[i] = v[i / fr[i]] * v[fr[i]];
    return v;
  }
};

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/nt/lsieve2.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/nt/lsieve2.hpp"

namespace tifa_libs::math {

class lsieve2 {
  vecpt<u32> pr;
  vecu fr;

 public:
  explicit constexpr lsieve2(u32 n) : fr(n + 1) {
    for (u32 i = 2, x = n / 2, p1, p2, e; i <= n; x = n / (++i)) {
      if (!fr[i]) {
        for (p1 = 1, p2 = i, e = 0; p1 <= x; p1 = p2, p2 *= i, ++e) fr[p2] = 1;
        pr.emplace_back(i, e);
      }
      for (u32 t = 0; t < pr.size(); ++t)
        if (u32 p = pr[t].first; p > x) break;
        else if (i % p) fr[p * i] = i;
        else {
          fr[p * i] = fr[i];
          break;
        }
    }
  }

  // @param F: T(u32, u32)
  // @param %fpi(p, i) = $f(p^i)$
  // @return v[i] = f(i), for i in [0, n]
  template <class T, class F>
  requires requires(F f, u32 p, u32 i) {
    { f(p, i) } -> std::same_as<T>;
  }
  constexpr vec<T> run(F fpi, T init = T{1}) {
    vec<T> v(fr.size());
    v[1] = init;
    for (u32 i = 0; i < pr.size(); ++i)
      for (u32 p = pr[i].first, e = pr[i].second, pe = p, ex = 1; ex <= e; ++ex, pe *= p) v[pe] = fpi(p, ex);
    for (u32 i = 2; i < fr.size(); ++i) v[i] = v[i / fr[i]] * v[fr[i]];
    return v;
  }
};

}  // namespace tifa_libs::math


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