std::ranges::lower_bound

 

C++

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Feature test macros (C++20)

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Containers library

Iterators library

Ranges library (C++20)

Algorithms library

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Filesystem library (C++17)

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Concurrency support library (C++11)

Execution support library (C++26)

Technical specifications

Symbols index

External libraries

 

Algorithm library

Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
is_execution_policy (C++17)   execution::seqexecution::parexecution::par_unseqexecution::unseq (C++17)    (C++17)(C++17)(C++20)	execution::sequenced_policyexecution::parallel_policyexecution::parallel_unsequenced_policyexecution::parallel_unsequenced (C++17)(C++17)(C++17)(C++20)
Non-modifying sequence operations Batch operations for_each for_each_n (C++17) Search operations all_ofany_ofnone_of (C++11)                (C++11)(C++11) countcount_if mismatch equal findfind_iffind_if_not (C++11) find_end find_first_of adjacent_find search search_n Modifying sequence operations Copy operations copycopy_if (C++11) copy_backward copy_n (C++11) move (C++11) move_backward (C++11) Swap operations swap iter_swap swap_ranges Transformation operations replacereplace_if transform replace_copyreplace_copy_if Generation operations fill fill_n generate generate_n Removing operations removeremove_if unique remove_copyremove_copy_if unique_copy Order-changing operations reverse reverse_copy rotate rotate_copy random_shuffleshuffle (until C++17)(C++11) shift_leftshift_right (C++20)(C++20) Sampling operations sample (C++17)	Sorting and related operations Partitioning operations partition partition_copy (C++11)   stable_partition is_partitioned (C++11) partition_point (C++11) Sorting operations sort stable_sort partial_sort partial_sort_copy is_sorted (C++11) is_sorted_until (C++11) nth_element Binary search operations (on partitioned ranges) lower_bound upper_bound equal_range binary_search Set operations (on sorted ranges) includes set_union set_intersection set_difference set_symmetric_difference Merge operations (on sorted ranges) merge inplace_merge Heap operations push_heap pop_heap make_heap sort_heap is_heap (C++11) is_heap_until (C++11) Minimum/maximum operations max min minmax (C++11) clamp (C++17) max_element min_element minmax_element (C++11) Lexicographical comparison operations lexicographical_compare lexicographical_compare_three_way (C++20) Permutation operations next_permutation prev_permutation is_permutation (C++11) C library qsort bsearch
Numeric operations
iota (C++11) inner_product adjacent_difference    accumulate reduce (C++17) transform_reduce (C++17)	partial_sum inclusive_scan (C++17)    exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
Operations on uninitialized memory
uninitialized_copy uninitialized_move (C++17)    uninitialized_fill uninitialized_copy_n (C++11) uninitialized_move_n (C++17) uninitialized_fill_n	destroy (C++17) destroy_n (C++17) destroy_at (C++17) construct_at (C++20)       uninitialized_default_construct (C++17) uninitialized_value_construct (C++17) uninitialized_default_construct_n (C++17) uninitialized_value_construct_n (C++17)

 

Constrained algorithms

All names in this menu belong to namespace std::ranges

Non-modifying sequence operations

all_ofany_ofnone_of for_each for_each_n    countcount_if adjacent_find mismatch equal lexicographical_compare    containscontains_subrange (C++23)(C++23) findfind_iffind_if_not find_lastfind_last_iffind_last_if_not (C++23)(C++23)(C++23)   find_end find_first_of search search_n starts_with (C++23) ends_with (C++23)

Modifying sequence operations

copycopy_if copy_n copy_backward    move move_backward shift_leftshift_right (C++23)(C++23)   fill fill_n generate generate_n    transform swap_ranges    shuffle sample removeremove_if replacereplace_if reverse rotate remove_copyremove_copy_if    unique replace_copyreplace_copy_if reverse_copy rotate_copy unique_copy

Partitioning operations

is_partitioned    partition_point    partition    partition_copy    stable_partition

Sorting operations

is_sorted is_sorted_until     sort stable_sort         partial_sort       nth_element partial_sort_copy

Binary search operations (on sorted ranges)

lower_bound         upper_bound         binary_search      equal_range

Set operations (on sorted ranges)

merge inplace_merge       set_difference set_intersection    set_union          includes set_symmetric_difference

Heap operations

is_heap is_heap_until       make_heap           sort_heap push_heap pop_heap

Minimum/maximum operations

max max_element         min min_element         minmax minmax_element     clamp

Permutation operations

is_permutation      next_permutation    prev_permutation

Fold operations

fold_left (C++23) fold_left_first (C++23)   fold_right (C++23) fold_right_last (C++23)   fold_left_with_iter (C++23) fold_left_first_with_iter (C++23)

Numeric operations iota (C++23)             Random number generation generate_random (C++26)

Operations on uninitialized storage

construct_at    destroy destroy_n destroy_at uninitialized_copy    uninitialized_move uninitialized_fill uninitialized_copy_n    uninitialized_move_n uninitialized_fill_n uninitialized_default_construct uninitialized_default_construct_n uninitialized_value_construct uninitialized_value_construct_n

Return types

in_fun_result in_in_result in_found_result    in_out_result in_in_out_result    in_out_out_result    min_max_result out_value_result (C++23) in_value_result (C++23)

 

Defined in header <algorithm>
Call signature
	(1)
template< std::forward_iterator I, std::sentinel_for<I> S,           class T, class Proj = std::identity,           std::indirect_strict_weak_order               <const T*, std::projected<I, Proj>> Comp = ranges::less > constexpr I lower_bound( I first, S last, const T& value,                          Comp comp = {}, Proj proj = {} );			(since C++20) (until C++26)
template< std::forward_iterator I, std::sentinel_for<I> S,           class Proj = std::identity,           class T = std::projected_value_t<I, Proj>,           std::indirect_strict_weak_order               <const T*, std::projected<I, Proj>> Comp = ranges::less > constexpr I lower_bound( I first, S last, const T& value,                          Comp comp = {}, Proj proj = {} );			(since C++26)
		(2)
template< ranges::forward_range R,           class T, class Proj = std::identity,           std::indirect_strict_weak_order               <const T*, std::projected<ranges::iterator_t<R>,                                         Proj>> Comp = ranges::less > constexpr ranges::borrowed_iterator_t<R>     lower_bound( R&& r, const T& value, Comp comp = {}, Proj proj = {} );				(since C++20) (until C++26)
template< ranges::forward_range R,           class Proj = std::identity,           class T = std::projected_value_t<ranges::iterator_t<R>, Proj>           std::indirect_strict_weak_order               <const T*, std::projected<ranges::iterator_t<R>,                                         Proj>> Comp = ranges::less > constexpr ranges::borrowed_iterator_t<R>     lower_bound( R&& r, const T& value, Comp comp = {}, Proj proj = {} );				(since C++26)

1) Returns an iterator pointing to the first element in the range [first, last) that is not less than (i.e. greater or equal to) value, or last if no such element is found. The range [first, last) must be partitioned with respect to the expression std::invoke(comp, std::invoke(proj, element), value), i.e., all elements for which the expression is true must precede all elements for which the expression is false. A fully-sorted range meets this criterion.

2) Same as (1), but uses r as the source range, as if using ranges::begin(r) as first and ranges::end(r) as last.

The function-like entities described on this page are niebloids, that is:

• Explicit template argument lists cannot be specified when calling any of them.
• None of them are visible to argument-dependent lookup.
• When any of them are found by normal unqualified lookup as the name to the left of the function-call operator, argument-dependent lookup is inhibited.

In practice, they may be implemented as function objects, or with special compiler extensions.

Parameters

first, last	-	iterator-sentinel pair defining the partially-ordered range to examine
r	-	the partially-ordered range to examine
value	-	value to compare the projected elements to
comp	-	comparison predicate to apply to the projected elements
proj	-	projection to apply to the elements

Return value

Iterator pointing to the first element that is not less than value, or last if no such element is found.

Complexity

The number of comparisons and applications of the projection performed are logarithmic in the distance between first and last (at most log2(last - first) + O(1) comparisons and applications of the projection). However, for an iterator that does not model random_access_iterator, the number of iterator increments is linear.

Notes

On a range that's fully sorted (or more generally, partially ordered with respect to value) after projection, std::ranges::lower_bound implements the binary search algorithm. Therefore, std::ranges::binary_search can be implemented in terms of it.

Feature-test macro	Value	Std	Feature
__cpp_lib_algorithm_default_value_type	202403	(C++26)	List-initialization for algorithms (1,2)

Possible implementation

struct lower_bound_fn { template<std::forward_iterator I, std::sentinel_for<I> S, class Proj = std::identity, class T = std::projected_value_t<I, Proj>, std::indirect_strict_weak_order <const T*, std::projected<I, Proj>> Comp = ranges::less> constexpr I operator()(I first, S last, const T& value, Comp comp = {}, Proj proj = {}) const { I it; std::iter_difference_t<I> count, step; count = std::ranges::distance(first, last);   while (count > 0) { it = first; step = count / 2; ranges::advance(it, step, last); if (comp(std::invoke(proj, *it), value)) { first = ++it; count -= step + 1; } else count = step; } return first; }   template<ranges::forward_range R, class Proj = std::identity, class T = std::projected_value_t<ranges::iterator_t<R>, Proj> std::indirect_strict_weak_order <const T*, std::projected<ranges::iterator_t<R>, Proj>> Comp = ranges::less> constexpr ranges::borrowed_iterator_t<R> operator()(R&& r, const T& value, Comp comp = {}, Proj proj = {}) const { return (*this)(ranges::begin(r), ranges::end(r), value, std::ref(comp), std::ref(proj)); } };   inline constexpr lower_bound_fn lower_bound;

Example

Run this code

#include <algorithm>
#include <cassert>
#include <complex>
#include <iostream>
#include <iterator>
#include <vector>
 
namespace ranges = std::ranges;
 
template<std::forward_iterator I, std::sentinel_for<I> S, class T,
         class Proj = std::identity,
         std::indirect_strict_weak_order
             <const T*, std::projected<I, Proj>> Comp = ranges::less>
constexpr I binary_find(I first, S last, const T& value, Comp comp = {}, Proj proj = {})
{
    first = ranges::lower_bound(first, last, value, comp, proj);
    return first != last && !comp(value, proj(*first)) ? first : last;
}
 
int main()
{
    std::vector data{1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5};
    //                                 ^^^^^^^^^^
    auto lower = ranges::lower_bound(data, 4);
    auto upper = ranges::upper_bound(data, 4);
 
    std::cout << "found a range [" << ranges::distance(data.cbegin(), lower)
              << ", " << ranges::distance(data.cbegin(), upper) << ") = { ";
    ranges::copy(lower, upper, std::ostream_iterator<int>(std::cout, " "));
    std::cout << "}\n";
 
    // classic binary search, returning a value only if it is present
 
    data = {1, 2, 4, 8, 16};
    //               ^
    auto it = binary_find(data.cbegin(), data.cend(), 8); // '5' would return end()
 
    if (it != data.cend())
        std::cout << *it << " found at index "<< ranges::distance(data.cbegin(), it);
 
    using CD = std::complex<double>;
    std::vector<CD> nums{{1, 0}, {2, 2}, {2, 1}, {3, 0}};
    auto cmpz = [](CD x, CD y) { return x.real() < y.real(); };
    #ifdef __cpp_lib_algorithm_default_value_type
        auto it2 = ranges::lower_bound(nums, {2, 0}, cmpz);
    #else
        auto it2 = ranges::lower_bound(nums, CD{2, 0}, cmpz);
    #endif
    assert((*it2 == CD{2, 2}));
}

Output:

found a range [6, 10) = { 4 4 4 4 }
8 found at index 3

See also

ranges::equal_range (C++20)	returns range of elements matching a specific key (niebloid)
ranges::partition (C++20)	divides a range of elements into two groups (niebloid)
ranges::partition_point (C++20)	locates the partition point of a partitioned range (niebloid)
ranges::upper_bound (C++20)	returns an iterator to the first element greater than a certain value (niebloid)
lower_bound	returns an iterator to the first element not less than the given value (function template)