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std::ranges::lower_bound

Defined in header <algorithm>
Call signature 
template< std::forward_iterator I, std::sentinel_for<I> S,
          class T, class Proj = std::identity,
          std::indirect_strict_weak_order<
              const T*,
              std::projected<I, Proj>> Comp = ranges::less >
constexpr I
    lower_bound( I first, S last, const T& value, Comp comp = {}, Proj proj = {} );
 (1) (since C++20) 
template< ranges::forward_range R, class T, class Proj = std::identity,
          std::indirect_strict_weak_order<
              const T*,
              std::projected<ranges::iterator_t<R>, Proj>> Comp = ranges::less >
constexpr ranges::borrowed_iterator_t<R>
    lower_bound( R&& r, const T& value, Comp comp = {}, Proj proj = {} );
 (2) (since C++20)
1) 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 std::invoke(comp, std::invoke(proj, 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.
2) Same as (1), but uses r as the source range, as if using ranges::begin(r) as first and ranges::end(r) as last.

The function-like entities described on this page are niebloids, that is:

In practice, they may be implemented as function objects, or with special compiler extensions.

Parameters

first, last - iterator-sentinel pair defining the partially-ordered range to examine
r - the partially-ordered range to examine
value - value to compare the projected elements to
comp - comparison predicate to apply to the projected elements
proj - projection to apply to the elements

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 and applications of the projection performed are logarithmic in the distance between first and last (at most log2(last - first) + O(1) comparisons and applications of the projection). However, for an iterator that does not model random_access_iterator, the number of iterator increments is linear.

Possible implementation

struct lower_bound_fn
{
    template<std::forward_iterator I, std::sentinel_for<I> S,
             class T, class Proj = std::identity,
             std::indirect_strict_weak_order<
                 const T*,
                 std::projected<I, Proj>> Comp = ranges::less>
    constexpr I operator()(I first, S last, const T& value,
                           Comp comp = {}, Proj proj = {}) const
    {
        I it;
        std::iter_difference_t<I> count, step;
        count = std::ranges::distance(first, last);
 
        while (count > 0)
        {
            it = first;
            step = count / 2;
            ranges::advance(it, step, last);
            if (comp(std::invoke(proj, *it), value))
            {
                first = ++it;
                count -= step + 1;
            }
            else
                count = step;
        }
        return first;
    }
 
    template<ranges::forward_range R, class T, class Proj = std::identity,
             std::indirect_strict_weak_order<
                 const T*,
                 std::projected<ranges::iterator_t<R>, Proj>> Comp = ranges::less>
    constexpr ranges::borrowed_iterator_t<R>
        operator()(R&& r, const T& value, Comp comp = {}, Proj proj = {}) const
    {
        return (*this)(ranges::begin(r), ranges::end(r), value,
                       std::ref(comp), std::ref(proj));
    }
};
 
inline constexpr lower_bound_fn lower_bound;

Example

#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>
 
namespace ranges = std::ranges;
 
template<std::forward_iterator I, std::sentinel_for<I> S, class T,
         class Proj = std::identity,
         std::indirect_strict_weak_order<
             const T*,
             std::projected<I, Proj>> Comp = ranges::less>
constexpr
    I binary_find(I first, S last, const T& value, Comp comp = {}, Proj proj = {})
{
    first = ranges::lower_bound(first, last, value, comp, proj);
    return first != last && !comp(value, proj(*first)) ? first : last;
}
 
int main()
{
    std::vector data{1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5};
    //                                 ^^^^^^^^^^
    auto lower = ranges::lower_bound(data, 4);
    auto upper = ranges::upper_bound(data, 4);
 
    std::cout << "found a range [" << ranges::distance(data.cbegin(), lower)
              << ", " << ranges::distance(data.cbegin(), upper) << ") = { ";
    ranges::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, 8, 16};
    //               ^
    auto it = binary_find(data.cbegin(), data.cend(), 8); // '5' would return end()
 
    if (it != data.cend())
        std::cout << *it << " found at index "<< ranges::distance(data.cbegin(), it);
}

Output:

found a range [6, 10) = { 4 4 4 4 }
8 found at index 3

See also

(C++20)
returns range of elements matching a specific key
(niebloid)
(C++20)
divides a range of elements into two groups
(niebloid)
(C++20)
locates the partition point of a partitioned range
(niebloid)
(C++20)
returns an iterator to the first element greater than a certain value
(niebloid)
returns an iterator to the first element not less than the given value
(function template)

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