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-exception 6 // 7 //===----------------------------------------------------------------------===// 8 9 #ifndef _LIBCPP___ALGORITHM_LOWER_BOUND_H 10 #define _LIBCPP___ALGORITHM_LOWER_BOUND_H 11 12 #include <__algorithm/comp.h> 13 #include <__algorithm/half_positive.h> 14 #include <__algorithm/iterator_operations.h> 15 #include <__config> 16 #include <__functional/identity.h> 17 #include <__iterator/advance.h> 18 #include <__iterator/distance.h> 19 #include <__iterator/iterator_traits.h> 20 #include <__type_traits/invoke.h> 21 #include <__type_traits/is_callable.h> 22 23 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 24 # pragma GCC system_header 25 #endif 26 27 _LIBCPP_BEGIN_NAMESPACE_STD 28 29 template <class _AlgPolicy, class _Iter, class _Type, class _Proj, class _Comp> 30 [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Iter __lower_bound_bisecting( 31 _Iter __first, 32 const _Type& __value, 33 typename iterator_traits<_Iter>::difference_type __len, 34 _Comp& __comp, 35 _Proj& __proj) { 36 while (__len != 0) { 37 auto __l2 = std::__half_positive(__len); 38 _Iter __m = __first; 39 _IterOps<_AlgPolicy>::advance(__m, __l2); 40 if (std::__invoke(__comp, std::__invoke(__proj, *__m), __value)) { 41 __first = ++__m; 42 __len -= __l2 + 1; 43 } else { 44 __len = __l2; 45 } 46 } 47 return __first; 48 } 49 50 // One-sided binary search, aka meta binary search, has been in the public domain for decades, and has the general 51 // advantage of being \Omega(1) rather than the classic algorithm's \Omega(log(n)), with the downside of executing at 52 // most 2*log(n) comparisons vs the classic algorithm's exact log(n). There are two scenarios in which it really shines: 53 // the first one is when operating over non-random-access iterators, because the classic algorithm requires knowing the 54 // container's size upfront, which adds \Omega(n) iterator increments to the complexity. The second one is when you're 55 // traversing the container in order, trying to fast-forward to the next value: in that case, the classic algorithm 56 // would yield \Omega(n*log(n)) comparisons and, for non-random-access iterators, \Omega(n^2) iterator increments, 57 // whereas the one-sided version will yield O(n) operations on both counts, with a \Omega(log(n)) bound on the number of 58 // comparisons. 59 template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp> 60 [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 61 __lower_bound_onesided(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) { 62 // step = 0, ensuring we can always short-circuit when distance is 1 later on 63 if (__first == __last || !std::__invoke(__comp, std::__invoke(__proj, *__first), __value)) 64 return __first; 65 66 using _Distance = typename iterator_traits<_ForwardIterator>::difference_type; 67 for (_Distance __step = 1; __first != __last; __step <<= 1) { 68 auto __it = __first; 69 auto __dist = __step - _IterOps<_AlgPolicy>::__advance_to(__it, __step, __last); 70 // once we reach the last range where needle can be we must start 71 // looking inwards, bisecting that range 72 if (__it == __last || !std::__invoke(__comp, std::__invoke(__proj, *__it), __value)) { 73 // we've already checked the previous value and it was less, we can save 74 // one comparison by skipping bisection 75 if (__dist == 1) 76 return __it; 77 return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj); 78 } 79 // range not found, move forward! 80 __first = __it; 81 } 82 return __first; 83 } 84 85 template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp> 86 [[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 87 __lower_bound(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) { 88 const auto __dist = _IterOps<_AlgPolicy>::distance(__first, __last); 89 return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj); 90 } 91 92 template <class _ForwardIterator, class _Tp, class _Compare> 93 [[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 94 lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value, _Compare __comp) { 95 static_assert(__is_callable<_Compare&, decltype(*__first), const _Tp&>::value, "The comparator has to be callable"); 96 auto __proj = std::__identity(); 97 return std::__lower_bound<_ClassicAlgPolicy>(__first, __last, __value, __comp, __proj); 98 } 99 100 template <class _ForwardIterator, class _Tp> 101 [[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 102 lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value) { 103 return std::lower_bound(__first, __last, __value, __less<>()); 104 } 105 106 _LIBCPP_END_NAMESPACE_STD 107 108 #endif // _LIBCPP___ALGORITHM_LOWER_BOUND_H 109