v1/__algorithm/lower_bound.h

0001 //===----------------------------------------------------------------------===//
0002 //
0003 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
0004 // See https://llvm.org/LICENSE.txt for license information.
0005 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
0006 //
0007 //===----------------------------------------------------------------------===//
0008
0009 #ifndef _LIBCPP___ALGORITHM_LOWER_BOUND_H
0010 #define _LIBCPP___ALGORITHM_LOWER_BOUND_H
0011
0012 #include <__algorithm/comp.h>
0013 #include <__algorithm/half_positive.h>
0014 #include <__algorithm/iterator_operations.h>
0015 #include <__config>
0016 #include <__functional/identity.h>
0017 #include <__iterator/advance.h>
0018 #include <__iterator/distance.h>
0019 #include <__iterator/iterator_traits.h>
0020 #include <__type_traits/invoke.h>
0021 #include <__type_traits/is_callable.h>
0022
0023 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
0024 #  pragma GCC system_header
0025 #endif
0026
0027 _LIBCPP_BEGIN_NAMESPACE_STD
0028
0029 template <class _AlgPolicy, class _Iter, class _Type, class _Proj, class _Comp>
0030 [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Iter __lower_bound_bisecting(
0031     _Iter __first,
0032     const _Type& __value,
0033     typename iterator_traits<_Iter>::difference_type __len,
0034     _Comp& __comp,
0035     _Proj& __proj) {
0036   while (__len != 0) {
0037     auto __l2 = std::__half_positive(__len);
0038     _Iter __m = __first;
0039     _IterOps<_AlgPolicy>::advance(__m, __l2);
0040     if (std::__invoke(__comp, std::__invoke(__proj, *__m), __value)) {
0041       __first = ++__m;
0042       __len -= __l2 + 1;
0043     } else {
0044       __len = __l2;
0045     }
0046   }
0047   return __first;
0048 }
0049
0050 // One-sided binary search, aka meta binary search, has been in the public domain for decades, and has the general
0051 // advantage of being \Omega(1) rather than the classic algorithm's \Omega(log(n)), with the downside of executing at
0052 // most 2*log(n) comparisons vs the classic algorithm's exact log(n). There are two scenarios in which it really shines:
0053 // the first one is when operating over non-random-access iterators, because the classic algorithm requires knowing the
0054 // container's size upfront, which adds \Omega(n) iterator increments to the complexity. The second one is when you're
0055 // traversing the container in order, trying to fast-forward to the next value: in that case, the classic algorithm
0056 // would yield \Omega(n*log(n)) comparisons and, for non-random-access iterators, \Omega(n^2) iterator increments,
0057 // whereas the one-sided version will yield O(n) operations on both counts, with a \Omega(log(n)) bound on the number of
0058 // comparisons.
0059 template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp>
0060 [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator
0061 __lower_bound_onesided(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) {
0062   // step = 0, ensuring we can always short-circuit when distance is 1 later on
0063   if (__first == __last || !std::__invoke(__comp, std::__invoke(__proj, *__first), __value))
0064     return __first;
0065
0066   using _Distance = typename iterator_traits<_ForwardIterator>::difference_type;
0067   for (_Distance __step = 1; __first != __last; __step <<= 1) {
0068     auto __it   = __first;
0069     auto __dist = __step - _IterOps<_AlgPolicy>::__advance_to(__it, __step, __last);
0070     // once we reach the last range where needle can be we must start
0071     // looking inwards, bisecting that range
0072     if (__it == __last || !std::__invoke(__comp, std::__invoke(__proj, *__it), __value)) {
0073       // we've already checked the previous value and it was less, we can save
0074       // one comparison by skipping bisection
0075       if (__dist == 1)
0076         return __it;
0077       return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj);
0078     }
0079     // range not found, move forward!
0080     __first = __it;
0081   }
0082   return __first;
0083 }
0084
0085 template <class _AlgPolicy, class _ForwardIterator, class _Sent, class _Type, class _Proj, class _Comp>
0086 [[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator
0087 __lower_bound(_ForwardIterator __first, _Sent __last, const _Type& __value, _Comp& __comp, _Proj& __proj) {
0088   const auto __dist = _IterOps<_AlgPolicy>::distance(__first, __last);
0089   return std::__lower_bound_bisecting<_AlgPolicy>(__first, __value, __dist, __comp, __proj);
0090 }
0091
0092 template <class _ForwardIterator, class _Tp, class _Compare>
0093 [[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator
0094 lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value, _Compare __comp) {
0095   static_assert(__is_callable<_Compare&, decltype(*__first), const _Tp&>::value, "The comparator has to be callable");
0096   auto __proj = std::__identity();
0097   return std::__lower_bound<_ClassicAlgPolicy>(__first, __last, __value, __comp, __proj);
0098 }
0099
0100 template <class _ForwardIterator, class _Tp>
0101 [[__nodiscard__]] inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _ForwardIterator
0102 lower_bound(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value) {
0103   return std::lower_bound(__first, __last, __value, __less<>());
0104 }
0105
0106 _LIBCPP_END_NAMESPACE_STD
0107
0108 #endif // _LIBCPP___ALGORITHM_LOWER_BOUND_H