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 <__functional/invoke.h> 18 #include <__iterator/advance.h> 19 #include <__iterator/distance.h> 20 #include <__iterator/iterator_traits.h> 21 #include <__type_traits/is_callable.h> 22 #include <__type_traits/remove_reference.h> 23 24 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 25 # pragma GCC system_header 26 #endif 27 28 _LIBCPP_BEGIN_NAMESPACE_STD 29 30 template <class _AlgPolicy, class _Iter, class _Type, class _Proj, class _Comp> 31 _LIBCPP_NODISCARD _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _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 general 52 // advantage of being \Omega(1) rather than the classic algorithm's \Omega(log(n)), with the downside of executing at 53 // 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 the 55 // container's size upfront, which adds \Omega(n) iterator increments to the complexity. The second one is when you're 56 // traversing the container in order, trying to fast-forward to the next value: in that case, the classic algorithm 57 // 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 of 59 // comparisons. 60 template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp> 61 _LIBCPP_NODISCARD _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 62 __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 on 64 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 start 72 // looking inwards, bisecting that range 73 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 save 75 // one comparison by skipping bisection 76 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 86 template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp> 87 _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 88 __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 93 template <class _ForwardIterator, class _Tp, class _Compare> 94 _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 95 lower_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 } 100 101 template <class _ForwardIterator, class _Tp> 102 _LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator 103 lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value) { 104 return std::lower_bound(__first, __last, __value, __less<>()); 105 } 106 107 _LIBCPP_END_NAMESPACE_STD 108 109 #endif // _LIBCPP___ALGORITHM_LOWER_BOUND_H 110