std::lower_bound

From cppreference.com

Defined in header `<algorithm>`
	(1)
template< class ForwardIt, class T > ForwardIt lower_bound( ForwardIt first, ForwardIt last, const T& value );			(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 );			(since C++26)
		(2)
template< class ForwardIt, class T, class Compare > ForwardIt lower_bound( ForwardIt first, ForwardIt last, const T& value, Compare comp );				(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 );				(since C++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 C++20)

Equivalent to std::lower_bound(first, last, value, std::less{}).

(since C++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.

[edit] Parameters

first, last	-	the pair of iterators defining 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 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.

[edit] Return value

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

[edit] 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.

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.

[edit] 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;
}

[edit] 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`	(C++26)	List-initialization for algorithms (1,2)

[edit] 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

[edit] 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 $\scriptsize \log_{2}(N)+O(1)$ $log 2 (N)+1$
LWG 2150	C++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

[edit] See also

equal_range	returns range of elements matching a specific key (function template) [edit]
partition	divides a range of elements into two groups (function template) [edit]
partition_point (C++11)	locates the partition point of a partitioned range (function template) [edit]
upper_bound	returns an iterator to the first element greater than a certain value (function template) [edit]
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]
ranges::lower_bound (C++20)	returns an iterator to the first element not less than the given value (algorithm function object)[edit]

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