std::ranges::lower_bound

Since C++26

Header: <algorithm>

  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.

# Declarations

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 = {} );

(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)

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)

# Parameters

# Return value

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

# 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.

# Example

#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}));
}

# See also