//===----------------------------------------------------------------------===// // // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // See https://llvm.org/LICENSE.txt for license information. // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // //===----------------------------------------------------------------------===// #ifndef _LIBCPP___ALGORITHM_LOWER_BOUND_H #define _LIBCPP___ALGORITHM_LOWER_BOUND_H #include <__algorithm/comp.h> #include <__algorithm/half_positive.h> #include <__algorithm/iterator_operations.h> #include <__config> #include <__functional/identity.h> #include <__functional/invoke.h> #include <__iterator/advance.h> #include <__iterator/distance.h> #include <__iterator/iterator_traits.h> #include <__type_traits/is_callable.h> #include <__type_traits/remove_reference.h> #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) # pragma GCC system_header #endif _LIBCPP_BEGIN_NAMESPACE_STD template _LIBCPP_NODISCARD _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Iter __lower_bound_bisecting( _Iter __first, const _Type& __value, typename iterator_traits<_Iter>::difference_type __len, _Comp& __comp, _Proj& __proj) { while (__len != 0) { auto __l2 = std::__half_positive(__len); _Iter __m = __first; _IterOps<_AlgPolicy>::advance(__m, __l2); if (std::__invoke(__comp, std::__invoke(__proj, *__m), __value)) { __first = ++__m; __len -= __l2 + 1; } else { __len = __l2; } } return __first; } // One-sided binary search, aka meta binary search, has been in the public domain for decades, and has the general // advantage of being \Omega(1) rather than the classic algorithm's \Omega(log(n)), with the downside of executing at // most 2*log(n) comparisons vs the classic algorithm's exact log(n). There are two scenarios in which it really shines: // the first one is when operating over non-random-access iterators, because the classic algorithm requires knowing the // container's size upfront, which adds \Omega(n) iterator increments to the complexity. The second one is when you're // traversing the container in order, trying to fast-forward to the next value: in that case, the classic algorithm // would yield \Omega(n*log(n)) comparisons and, for non-random-access iterators, \Omega(n^2) iterator increments, // whereas the one-sided version will yield O(n) operations on both counts, with a \Omega(log(n)) bound on the number of // comparisons. template _LIBCPP_NODISCARD _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator __lower_bound_onesided(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) { // step = 0, ensuring we can always short-circuit when distance is 1 later on if (__first == __last || !std::__invoke(__comp, std::__invoke(__proj, *__first), __value)) return __first; using _Distance = typename iterator_traits<_ForwardIterator>::difference_type; for (_Distance __step = 1; __first != __last; __step <<= 1) { auto __it = __first; auto __dist = __step - _IterOps<_AlgPolicy>::__advance_to(__it, __step, __last); // once we reach the last range where needle can be we must start // looking inwards, bisecting that range if (__it == __last || !std::__invoke(__comp, std::__invoke(__proj, *__it), __value)) { // we've already checked the previous value and it was less, we can save // one comparison by skipping bisection if (__dist == 1) return __it; return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj); } // range not found, move forward! __first = __it; } return __first; } template _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator __lower_bound(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) { const auto __dist = _IterOps<_AlgPolicy>::distance(__first, __last); return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj); } template _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value, _Compare __comp) { static_assert(__is_callable<_Compare, decltype(*__first), const _Tp&>::value, "The comparator has to be callable"); auto __proj = std::__identity(); return std::__lower_bound<_ClassicAlgPolicy>(__first, __last, __value, __comp, __proj); } template _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value) { return std::lower_bound(__first, __last, __value, __less<>()); } _LIBCPP_END_NAMESPACE_STD #endif // _LIBCPP___ALGORITHM_LOWER_BOUND_H