std::lower_bound

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

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

1) The order is determined by operator<(until C++20)std::less{}(since C++20).

If the elements e of the source range are not partitioned with respect to the expression bool(e < value)(until C++20)bool(std::less{}(e, value))(since C++20), the behavior is undefined.

2) The order is determined by comp.

If the elements e of the source range are not partitioned with respect to the expression bool(comp(e, value)), the behavior is undefined.

Parameters

first, last	-	the pair of iterators defining the source range
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 C++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 which is 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

log 2 (N)+𝓞(1)

comparisons with value using operator<(until C++20)std::less{}(since C++20).

2) At most

log 2 (N)+𝓞(1)

applications of the comparator comp.

Notes

Although std::lower_bound only requires the source range to be partitioned, this algorithm is usually used in the case where the source range 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 every iterator iter in the source range.

If ForwardIt is not a LegacyRandomAccessIterator, the number of iterator increments is linear in std::distance(first, last). 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.

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

Possible implementation

See also the implementations in libstdc++ and libc++.

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;
}

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 C++ standards.

DR	Applied to	Behavior as published	Correct behavior
LWG 270	C++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	C++98	at most $\scriptsize \log(N)+1$ $log(N)+1$ comparisons were allowed	corrected to $log 2 (N)+𝓞(1)$
LWG 2150	C++98	if any iterator `iter` exists in the source range 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

Compiler support
Freestanding and hosted
Language
Standard library
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Diagnostics library
Memory management library
Metaprogramming library (C++11)
General utilities library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Strings library
Text processing library
Numerics library
Date and time library
Input/output library
Filesystem library (C++17)
Concurrency support library (C++11)
Execution control library (C++26)
Technical specifications
Symbols index
External libraries

ranges::lower_bound (C++20)	finds the first element not less than the given value using binary search (algorithm function object)[edit]
equal_range	finds the range of elements matching the given value using binary search (function template & algorithm function object)[edit]
ranges::equal_range (C++20)
partition	divides a range of elements into two groups (function template & algorithm function object)[edit]
ranges::partition (C++20)
partition_point (C++11)	locates the partition point of a partitioned range (function template & algorithm function object)[edit]
ranges::partition_point (C++20)
upper_bound	finds the first element greater than the given value using binary search (function template & algorithm function object)[edit]
ranges::upper_bound (C++20)
lower_bound	returns an iterator to the first element not less than the given key (public member function of `std::set<Key,Compare,Allocator>`) [edit]
lower_bound	returns an iterator to the first element not less than the given key (public member function of `std::multiset<Key,Compare,Allocator>`) [edit]

cppreference.com

Search

Namespaces

Variants

Views

Actions

std::lower_bound

Contents