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std::ranges::lower_bound - cppreference.com

Call signature

Returns an iterator pointing to the first element in the range

that is

than (i.e. greater or equal to)

, or

if no such element is found. The range

must be partitioned with respect to the expression

, i.e., all elements for which the expression is

must precede all elements for which the expression is

. A fully-sorted range meets this criterion.

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.

Iterator pointing to the first element that is not less than value, or last if no such element is found.

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.

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.

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;

#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

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