# std::ranges::lower_bound

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< cpp‎ | algorithm‎ | ranges

Defined in header `<algorithm>` |  |
Call signature |  |
| (1) |
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 = {} ); |  | (since C++20) (until C++26)
template< std::forward_iterator I, std::sentinel_for <I> S, class Proj = std::identity, class T = std::projected_value_t<I, Proj>, 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 = {} ); |  | (since C++26)
| (2) |
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 = {} ); |  | (since C++20) (until C++26)
template< ranges::forward_range R, class Proj = std::identity, class T = std::projected_value_t< ranges::iterator_t <R>, Proj> 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 = {} ); |  | (since C++26)

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 algorithm function objects (informally known as niebloids), that is:

- Explicit template argument lists cannot be specified when calling any of them.
- None of them are visible to argument-dependent lookup.
- When any of them are found by normal unqualified lookup as the name to the left of the function-call operator, argument-dependent lookup is inhibited.

### 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.

### Notes

On a range that's fully sorted (or more generally, partially ordered with respect to value) after projection, `std::ranges::lower_bound` implements the binary search algorithm. Therefore, std::ranges::binary_search can be implemented in terms of it.

Feature-test macro | Value | Std | Feature
--- | --- | --- | ---
`__cpp_lib_algorithm_default_value_type` | `202403` | (C++26) | List-initialization for algorithms (1,2)

### Possible implementation

    struct lower_bound_fn
    {
        template<std::forward_iterator I, std::sentinel_for<I> S, class Proj = std::identity,
                 class T = std::projected_value_t<I, Proj>,
                 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 Proj = std::identity,
              class T = std::projected_value_t<ranges::iterator_t<R>, Proj>
              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

Run this code

    #include <algorithm>
    #include <cassert>
    #include <complex>
    #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);

        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 it2 = ranges::lower_bound(nums, {2, 0}, cmpz);
        #else
            auto it2 = ranges::lower_bound(nums, CD{2, 0}, cmpz);
        #endif
        assert((*it2 == CD{2, 2}));
    }

Output:

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

### See also

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

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