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#include "src/math/totient-enumeration.hpp"
std::vector< T > totient_enumeration(T n)
$i$ 番目の要素が $\phi(i)$ であるような長さ $n+1$ の vector を返す。
vector
math/totient を用いることで、 $\phi(n)$ を $O(\sqrt{n})$ で計算することができる。
math/totient
#pragma once #include "src/cpp-template/header/rep.hpp" #include <cassert> #include <limits> #include <vector> namespace luz { template < typename T > std::vector< T > totient_enumeration(T n) { static_assert(std::numeric_limits< T >::is_integer, "T must be integer"); assert(n >= 0); n += 1; std::vector< T > totients(n); for (T i: rep(0, n)) { totients[i] = i; } for (T i: rep(2, n)) { if (totients[i] != i) continue; for (T j = i; j < n; j += i) { totients[j] = totients[j] / i * (i - 1); } } return totients; } } // namespace luz
#line 2 "src/math/totient-enumeration.hpp" #line 2 "src/cpp-template/header/rep.hpp" #line 2 "src/cpp-template/header/size-alias.hpp" #include <cstddef> namespace luz { using isize = std::ptrdiff_t; using usize = std::size_t; } // namespace luz #line 4 "src/cpp-template/header/rep.hpp" #include <algorithm> namespace luz { struct rep { struct itr { usize i; constexpr itr(const usize i) noexcept: i(i) {} void operator++() noexcept { ++i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rep(const usize f, const usize l) noexcept : f(std::min(f, l)), l(l) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; struct rrep { struct itr { usize i; constexpr itr(const usize i) noexcept: i(i) {} void operator++() noexcept { --i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rrep(const usize f, const usize l) noexcept : f(l - 1), l(std::min(f, l) - 1) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; } // namespace luz #line 4 "src/math/totient-enumeration.hpp" #include <cassert> #include <limits> #include <vector> namespace luz { template < typename T > std::vector< T > totient_enumeration(T n) { static_assert(std::numeric_limits< T >::is_integer, "T must be integer"); assert(n >= 0); n += 1; std::vector< T > totients(n); for (T i: rep(0, n)) { totients[i] = i; } for (T i: rep(2, n)) { if (totients[i] != i) continue; for (T j = i; j < n; j += i) { totients[j] = totients[j] / i * (i - 1); } } return totients; } } // namespace luz