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

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; }

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

#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>
 
template<class ForwardIt, class T, class Compare=std::less<>>
ForwardIt binary_find(ForwardIt first, ForwardIt last, const T& value, Compare comp={})
{
    // Note: BOTH type T and the type after ForwardIt is dereferenced 
    // must be implicitly convertible to BOTH Type1 and Type2, used in Compare. 
    // This is stricter than lower_bound requirement (see above)
 
    first = std::lower_bound(first, last, value, comp);
    return first != last && !comp(value, *first) ? first : last;
}
 
int main()
{
    std::vector<int> data = { 1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6 };
 
    auto lower = std::lower_bound(data.begin(), data.end(), 4);
    auto upper = std::upper_bound(data.begin(), data.end(), 4);
 
    std::copy(lower, upper, std::ostream_iterator<int>(std::cout, " "));
 
    std::cout << '\n';
 
    // classic binary search, returning a value only if it is present
 
    data = { 1, 2, 4, 6, 9, 10 }; 
 
    auto it = binary_find(data.cbegin(), data.cend(), 4); //< choosing '5' will return end()
 
    if(it != data.cend())
      std::cout << *it << " found at index "<< std::distance(data.cbegin(), it);
 
    return 0;
}

Output:

4 4 4 
4 found at index 2

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

equal_range	returns range of elements matching a specific key (function template)
partition	divides a range of elements into two groups (function template)
upper_bound	returns an iterator to the first element greater than a certain value (function template)