std::lower_bound

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 \(\scriptsize \log_{2}(N)+O(1)\)log2(N)+O(1) comparisons with value using operator<(until C++20)std::less {}(since C++20).

2) At most \(\scriptsize \log_{2}(N)+O(1)\)log2(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 \(\scriptsize \log_{2}(N)+O(1)\)log2(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