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>
__lower_bound_bisecting(_Iter __first,const _Type & __value,typename iterator_traits<_Iter>::difference_type __len,_Comp & __comp,_Proj & __proj)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
__lower_bound_onesided(_ForwardIterator __first,_Sent __last,const _Type & __value,_Comp & __comp,_Proj & __proj)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
__lower_bound(_ForwardIterator __first,_Sent __last,const _Type & __value,_Comp & __comp,_Proj & __proj)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
lower_bound(_ForwardIterator __first,_ForwardIterator __last,const _Tp & __value,_Compare __comp)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
lower_bound(_ForwardIterator __first,_ForwardIterator __last,const _Tp & __value)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