std::lower_bound

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

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 element < value or comp(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.

The first version uses operator< to compare the elements, the second version uses the given comparison function comp.

Parameters

first, last	-	iterators defining the partially-ordered range to examine
value	-	value to compare the elements to
comp	-	binary predicate which returns true if the first argument is less than (i.e. 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 pointing to the first element that is not less than value, or last if no such element is found.

Complexity

The number of comparisons performed is logarithmic in the distance between first and last (At most $log 2 (last - first) + O(1)$ comparisons). However, for non-LegacyRandomAccessIterators, the number of iterator increments is linear.

Possible implementation

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

First version

template<class ForwardIt, class T>
ForwardIt lower_bound(ForwardIt first, ForwardIt last, const T& value)
{
    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 (*it < value) {
            first = ++it; 
            count -= step + 1; 
        }
        else
            count = step;
    }
    return first;
}

Second version

template<class ForwardIt, class T, 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 <iostream>
#include <vector>
 
int main()
{
    std::vector<int> data = { 1, 2, 4, 5, 5, 6 };
 
    for (int i = 0; i < 8; ++i) {
        // Search for first element that is not less than i
        auto lower = std::lower_bound(data.begin(), data.end(), i);
 
        std::cout << i << " <= ";
        if (lower != data.end())
            std::cout << *lower << " at index " << std::distance(data.begin(), lower);
        else
            std::cout << "not found";
        std::cout << '\n';
    }
}

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

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 be a strict weak ordering	only a partitioning is needed; heterogeneous comparisons permitted

Language
Standard Library Headers
Freestanding and hosted implementations
Named requirements
Language support library
Concepts library (C++20)
Diagnostics library
Utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (C++17)
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Technical Specifications

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 (C++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)