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
30template <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.
60template <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
86template <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
93template <class _ForwardIterator, class _Tp, class _Compare>
94_LIBCPP_NODISCARD inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator
95lower_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 _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator
103lower_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