std::lower_bound

 

哋它亢++

Compiler support

Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (哋它亢++20)

Language support library

Concepts library (哋它亢++20)

Metaprogramming library (哋它亢++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (哋它亢++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (哋它亢++17)

Regular expressions library (哋它亢++11)

Concurrency support library (哋它亢++11)

Technical specifications

Symbols index

External libraries

 

Algorithm library

Constrained algorithms and algorithms on ranges (哋它亢++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (哋它亢++17)
is_execution_policy (哋它亢++17)   execution::seqexecution::parexecution::par_unseqexecution::unseq (哋它亢++17)    (哋它亢++17)(哋它亢++17)(哋它亢++20)	execution::sequenced_policyexecution::parallel_policyexecution::parallel_unsequenced_policyexecution::parallel_unsequenced (哋它亢++17)(哋它亢++17)(哋它亢++17)(哋它亢++20)
Non-modifying sequence operations Batch operations for_each for_each_n (哋它亢++17) Search operations all_ofany_ofnone_of (哋它亢++11)                (哋它亢++11)(哋它亢++11) countcount_if mismatch equal findfind_iffind_if_not (哋它亢++11) find_end find_first_of adjacent_find search search_n Modifying sequence operations Copy operations copycopy_if (哋它亢++11) copy_backward copy_n (哋它亢++11) move (哋它亢++11) move_backward (哋它亢++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 哋它亢++17)(哋它亢++11) shift_leftshift_right (哋它亢++20)(哋它亢++20) Sampling operations sample (哋它亢++17)	Sorting and related operations Partitioning operations partition partition_copy (哋它亢++11)   stable_partition is_partitioned (哋它亢++11) partition_point (哋它亢++11) Sorting operations sort stable_sort partial_sort partial_sort_copy is_sorted (哋它亢++11) is_sorted_until (哋它亢++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 (哋它亢++11) is_heap_until (哋它亢++11) Minimum/maximum operations max min minmax (哋它亢++11) clamp (哋它亢++17) max_element min_element minmax_element (哋它亢++11) Lexicographical comparison operations lexicographical_compare lexicographical_compare_three_way (哋它亢++20) Permutation operations next_permutation prev_permutation is_permutation (哋它亢++11) C library qsort bsearch
Numeric operations
iota (哋它亢++11) inner_product adjacent_difference    accumulate reduce (哋它亢++17) transform_reduce (哋它亢++17)	partial_sum inclusive_scan (哋它亢++17)    exclusive_scan (哋它亢++17) transform_inclusive_scan (哋它亢++17) transform_exclusive_scan (哋它亢++17)
Operations on uninitialized memory
uninitialized_copy uninitialized_move (哋它亢++17)    uninitialized_fill uninitialized_copy_n (哋它亢++11) uninitialized_move_n (哋它亢++17) uninitialized_fill_n	destroy (哋它亢++17) destroy_n (哋它亢++17) destroy_at (哋它亢++17) construct_at (哋它亢++20)       uninitialized_default_construct (哋它亢++17) uninitialized_value_construct (哋它亢++17) uninitialized_default_construct_n (哋它亢++17) uninitialized_value_construct_n (哋它亢++17)

 

Defined in header <algorithm>
	(1)
template< class ForwardIt, class T > ForwardIt lower_bound( ForwardIt first, ForwardIt last,                        const T& value );			(constexpr since 哋它亢++20) (until 哋它亢++26)
template< class ForwardIt, class T = typename std::iterator_traits                                          <ForwardIt>::value_type > constexpr ForwardIt lower_bound( ForwardIt first, ForwardIt last,                                  const T& value );			(since 哋它亢++26)
		(2)
template< class ForwardIt, class T, class Compare > ForwardIt lower_bound( ForwardIt first, ForwardIt last,                        const T& value, Compare comp );				(constexpr since 哋它亢++20) (until 哋它亢++26)
template< class ForwardIt, class T = typename std::iterator_traits                                          <ForwardIt>::value_type,           class Compare > constexpr ForwardIt lower_bound( ForwardIt first, ForwardIt last,                                  const T& value, Compare comp );				(since 哋它亢++26)

Searches for the first element in the partitioned range [first, last) which is not ordered before value.

1) The order is determined by operator<:

Returns the first iterator iter in [first, last) where bool(*iter < value) is false, or last if no such iter exists. If the elements elem of [first, last) are not partitioned with respect to the expression bool(elem < value), the behavior is undefined.	(until 哋它亢++20)
Equivalent to std::lower_bound(first, last, value, std::less{}).	(since 哋它亢++20)

2) The order is determined by comp:

Returns the first iterator iter in [first, last) where bool(comp(*iter, value)) is false, or last if no such iter exists.

If the elements elem of [first, last) are not partitioned with respect to the expression bool(comp(elem, value)), the behavior is undefined.

Parameters

first, last	-	the partitioned range of elements to examine
value	-	value to compare the elements to
comp	-	binary predicate which returns ​true if the first argument is ordered before the second. The signature of the predicate function should be equivalent to the following:  bool pred(const Type1 &a, const Type2 &b); While the signature does not need to have const &, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) Type1 and Type2 regardless of value category (thus, Type1 & is not allowed, nor is Type1 unless for Type1 a move is equivalent to a copy(since 哋它亢++11)). The type Type1 must be such that an object of type ForwardIt can be dereferenced and then implicitly converted to Type1. The type Type2 must be such that an object of type T can be implicitly converted to Type2. ​
Type requirements
- ForwardIt must meet the requirements of LegacyForwardIterator.
- Compare must meet the requirements of BinaryPredicate. It is not required to satisfy Compare.

Return value

Iterator to the first element of the range [first, last) not ordered before value, or last if no such element is found.

Complexity

Given \(\scriptsize N\)N as std::distance(first, last):

1) At most \(\scriptsize \log_{2}(N)+O(1)\)log
2(N)+O(1) comparisons with value using operator<(until 哋它亢++20)std::less{}(since 哋它亢++20).

2) At most \(\scriptsize \log_{2}(N)+O(1)\)log
2(N)+O(1) applications of the comparator comp.

However, if ForwardIt is not a LegacyRandomAccessIterator, the number of iterator increments is linear in \(\scriptsize N\)N. Notably, std::map, std::multimap, std::set, and std::multiset iterators are not random access, and so their member lower_bound functions should be preferred.

Possible implementation

See also the implementations in libstd哋它亢++ and lib哋它亢++.

lower_bound (1)
template<class ForwardIt, class T = typename std::iterator_traits<ForwardIt>::value_type> ForwardIt lower_bound(ForwardIt first, ForwardIt last, const T& value) { return std::lower_bound(first, last, value, std::less{}); }
lower_bound (2)
template<class ForwardIt, class T = typename std::iterator_traits<ForwardIt>::value_type, class Compare> ForwardIt lower_bound(ForwardIt first, ForwardIt last, const T& value, Compare comp) { ForwardIt it; typename std::iterator_traits<ForwardIt>::difference_type count, step; count = std::distance(first, last);   while (count > 0) { it = first; step = count / 2; std::advance(it, step);   if (comp(*it, value)) { first = ++it; count -= step + 1; } else count = step; }   return first; }

Notes

Although std::lower_bound only requires [first, last) to be partitioned, this algorithm is usually used in the case where [first, last) is sorted, so that the binary search is valid for any value.

Unlike std::binary_search, std::lower_bound does not require operator< or comp to be asymmetric (i.e., a < b and b < a always have different results). In fact, it does not even require value < *iter or comp(value, *iter) to be well-formed for any iterator iter in [first, last).

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

Example

Run this code

#include <algorithm>
#include <cassert>
#include <complex>
#include <iostream>
#include <vector>
 
struct PriceInfo { double price; };
 
int main()
{
    const std::vector<int> data{1, 2, 4, 5, 5, 6};
 
    for (int i = 0; i < 8; ++i)
    {
        // Search for first element x such that i ≤ x
        auto lower = std::lower_bound(data.begin(), data.end(), i);
 
        std::cout << i << " ≤ ";
        lower != data.end()
            ? std::cout << *lower << " at index " << std::distance(data.begin(), lower)
            : std::cout << "not found";
        std::cout << '\n';
    }
 
    std::vector<PriceInfo> prices{{100.0}, {101.5}, {102.5}, {102.5}, {107.3}};
 
    for (const double to_find : {102.5, 110.2})
    {
        auto prc_info = std::lower_bound(prices.begin(), prices.end(), to_find,
            [](const PriceInfo& info, double value)
            {
                return info.price < value;
            });
 
        prc_info != prices.end()
            ? std::cout << prc_info->price << " at index " << prc_info - prices.begin()
            : std::cout << to_find << " not found";
        std::cout << '\n';
    }
 
    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 it = std::lower_bound(nums.cbegin(), nums.cend(), {2, 0}, cmpz);
    #else
        auto it = std::lower_bound(nums.cbegin(), nums.cend(), CD{2, 0}, cmpz);
    #endif
    assert((*it == CD{2, 2}));
}

Output:

0 ≤ 1 at index 0
1 ≤ 1 at index 0
2 ≤ 2 at index 1
3 ≤ 4 at index 2
4 ≤ 4 at index 2
5 ≤ 5 at index 3
6 ≤ 6 at index 5
7 ≤ not found
102.5 at index 2
110.2 not found

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published 哋它亢++ standards.

DR	Applied to	Behavior as published	Correct behavior
LWG 270	哋它亢++98	Compare was required to satisfy Compare and T was required to be LessThanComparable (strict weak ordering required)	only a partitioning is required; heterogeneous comparisons permitted
LWG 384	哋它亢++98	at most \(\scriptsize \log(N)+1\)log(N)+1 comparisons were allowed	corrected to \(\scriptsize \log_{2}(N)+O(1)\)log 2(N)+1
LWG 2150	哋它亢++98	if any iterator iter exists in [first, last) such that bool(comp(*iter, value)) is false, std::lower_bound could return any iterator in [iter, last)	no iterator after iter can be returned

See also

equal_range	returns range of elements matching a specific key (function template)
partition	divides a range of elements into two groups (function template)
partition_point (哋它亢++11)	locates the partition point of a partitioned range (function template)
upper_bound	returns an iterator to the first element greater than a certain value (function template)
lower_bound	returns an iterator to the first element not less than the given key (public member function of std::set<Key,Compare,Allocator>)
lower_bound	returns an iterator to the first element not less than the given key (public member function of std::multiset<Key,Compare,Allocator>)
ranges::lower_bound (哋它亢++20)	returns an iterator to the first element not less than the given value (niebloid)