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1//===----------------------------------------------------------------------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9#ifndef _LIBCPP___CXX03___ALGORITHM_LOWER_BOUND_H10#define _LIBCPP___CXX03___ALGORITHM_LOWER_BOUND_H11 12#include <__cxx03/__algorithm/comp.h>13#include <__cxx03/__algorithm/half_positive.h>14#include <__cxx03/__algorithm/iterator_operations.h>15#include <__cxx03/__config>16#include <__cxx03/__functional/identity.h>17#include <__cxx03/__iterator/advance.h>18#include <__cxx03/__iterator/distance.h>19#include <__cxx03/__iterator/iterator_traits.h>20#include <__cxx03/__type_traits/invoke.h>21#include <__cxx03/__type_traits/is_callable.h>22#include <__cxx03/__type_traits/remove_reference.h>23 24#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)25# pragma GCC system_header26#endif27 28_LIBCPP_BEGIN_NAMESPACE_STD29 30template <class _AlgPolicy, class _Iter, class _Type, class _Proj, class _Comp>31_LIBCPP_NODISCARD _LIBCPP_HIDE_FROM_ABI _Iter __lower_bound_bisecting(32 _Iter __first,33 const _Type& __value,34 typename iterator_traits<_Iter>::difference_type __len,35 _Comp& __comp,36 _Proj& __proj) {37 while (__len != 0) {38 auto __l2 = std::__half_positive(__len);39 _Iter __m = __first;40 _IterOps<_AlgPolicy>::advance(__m, __l2);41 if (std::__invoke(__comp, std::__invoke(__proj, *__m), __value)) {42 __first = ++__m;43 __len -= __l2 + 1;44 } else {45 __len = __l2;46 }47 }48 return __first;49}50 51// One-sided binary search, aka meta binary search, has been in the public domain for decades, and has the general52// advantage of being \Omega(1) rather than the classic algorithm's \Omega(log(n)), with the downside of executing at53// most 2*log(n) comparisons vs the classic algorithm's exact log(n). There are two scenarios in which it really shines:54// the first one is when operating over non-random-access iterators, because the classic algorithm requires knowing the55// container's size upfront, which adds \Omega(n) iterator increments to the complexity. The second one is when you're56// traversing the container in order, trying to fast-forward to the next value: in that case, the classic algorithm57// would yield \Omega(n*log(n)) comparisons and, for non-random-access iterators, \Omega(n^2) iterator increments,58// whereas the one-sided version will yield O(n) operations on both counts, with a \Omega(log(n)) bound on the number of59// comparisons.60template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp>61_LIBCPP_NODISCARD _LIBCPP_HIDE_FROM_ABI _ForwardIterator62__lower_bound_onesided(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) {63 // step = 0, ensuring we can always short-circuit when distance is 1 later on64 if (__first == __last || !std::__invoke(__comp, std::__invoke(__proj, *__first), __value))65 return __first;66 67 using _Distance = typename iterator_traits<_ForwardIterator>::difference_type;68 for (_Distance __step = 1; __first != __last; __step <<= 1) {69 auto __it = __first;70 auto __dist = __step - _IterOps<_AlgPolicy>::__advance_to(__it, __step, __last);71 // once we reach the last range where needle can be we must start72 // looking inwards, bisecting that range73 if (__it == __last || !std::__invoke(__comp, std::__invoke(__proj, *__it), __value)) {74 // we've already checked the previous value and it was less, we can save75 // one comparison by skipping bisection76 if (__dist == 1)77 return __it;78 return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj);79 }80 // range not found, move forward!81 __first = __it;82 }83 return __first;84}85 86template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp>87_LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _ForwardIterator88__lower_bound(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) {89 const auto __dist = _IterOps<_AlgPolicy>::distance(__first, __last);90 return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj);91}92 93template <class _ForwardIterator, class _Tp, class _Compare>94_LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _ForwardIterator95lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value, _Compare __comp) {96 static_assert(__is_callable<_Compare, decltype(*__first), const _Tp&>::value, "The comparator has to be callable");97 auto __proj = std::__identity();98 return std::__lower_bound<_ClassicAlgPolicy>(__first, __last, __value, __comp, __proj);99}100 101template <class _ForwardIterator, class _Tp>102_LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _ForwardIterator103lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value) {104 return std::lower_bound(__first, __last, __value, __less<>());105}106 107_LIBCPP_END_NAMESPACE_STD108 109#endif // _LIBCPP___CXX03___ALGORITHM_LOWER_BOUND_H110