std::ranges::binary_search(3)

NAME
std::ranges::binary_search - std::ranges::binary_search

Synopsis
   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 (since
                 <const T*, std::projected<I, Proj>> Comp = C++20)
   ranges::less > (until
   constexpr bool binary_search( I first, S last, const T& C++26)
   value,
                        Comp comp = {}, Proj proj = {}
   );
   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 = (since
   ranges::less > C++26)
   constexpr bool binary_search( I first, S last, const T&
   value,
                        Comp comp = {}, Proj proj = {}
   );
   template< ranges::forward_range R,
                        (1)
             class T, class Proj = std::identity,
             std::indirect_strict_weak_order
                 <const T*, (since
   std::projected<ranges::iterator_t<R>, C++20)
                        Proj>> Comp = (until
   ranges::less > C++26)
   constexpr bool binary_search( R&& r, const T& value,
                        Comp comp = {}, Proj proj = {}
   );
   template< ranges::forward_range R, (2)
             class Proj = std::identity,
             class T =
   std::projected_value_t<ranges::iterator_t<R>, Proj>,
             std::indirect_strict_weak_order
                 <const T*, (since
   std::projected<ranges::iterator_t<R>, C++26)
                        Proj>> Comp =
   ranges::less >
   constexpr bool binary_search( R&& r, const T& value,
                        Comp comp = {}, Proj proj = {}
   );
   1) Checks if a projected element equivalent to value appears within the range
   [first, last).
   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.
   For ranges::binary_search to succeed, the range [first, last) must be at least
   partially ordered with respect to value, i.e. it must satisfy all of the following
   requirements:
     * partitioned with respect to std::invoke(comp, std::invoke(proj, element), value)
       (that is, all projected elements for which the expression is true precedes all
       elements for which the expression is false).
     * partitioned with respect to !std::invoke(comp, value, std::invoke(proj,
       element)).
     * for all elements, if std::invoke(comp, std::invoke(proj, element), value) is
       true then !std::invoke(comp, value, std::invoke(proj, element)) is also true.
   A fully-sorted range meets these criteria.
   The function-like entities described on this page are 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.
   In practice, they may be implemented as function objects, or with special compiler
   extensions.

Parameters
   first, last - the range of elements to examine
   r - the range of elements to examine
   value - value to compare the elements to
   comp - comparison function to apply to the projected elements
   proj - projection to apply to the elements

Return value
   true if an element equal to value is found, false otherwise.

Complexity
   The number of comparisons and projections performed is logarithmic in the distance
   between first and last (at most log
   2(last - first) + O(1) comparisons and projections). However, for iterator-sentinel
   pair that does not model std::random_access_iterator, number of iterator increments
   is linear.

Notes
   std::ranges::binary_search doesn't return an iterator to the found element when an
   element whose projection equals value is found. If an iterator is desired,
   std::ranges::lower_bound should be used instead.
             Feature-test macro Value Std Feature
   __cpp_lib_algorithm_default_value_type 202403 (C++26) List-initialization for
                        algorithms (1,2)

Possible implementation
struct binary_search_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 bool operator()(I first, S last, const T& value,
                        Comp comp = {}, Proj proj = {}) const
    {
        auto x = ranges::lower_bound(first, last, value, comp, proj);
        return (!(x == last) && !(std::invoke(comp, value, std::invoke(proj, *x))));
    }
    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 bool operator()(R&& r, const T& value, Comp comp = {}, Proj proj = {}) const
    {
        return (*this)(ranges::begin(r), ranges::end(r), value,
                       std::move(comp), std::move(proj));
    } }; inline constexpr binary_search_fn binary_search;

Example
// Run this code
 #include <algorithm>
 #include <cassert>
 #include <complex>
 #include <iostream>
 #include <ranges>
 #include <vector>
 int main()
 {
     constexpr static auto haystack = {1, 3, 4, 5, 9};
     static_assert(std::ranges::is_sorted(haystack));
     for (const int needle : std::views::iota(1)
                        | std::views::take(3))
     {
         std::cout << "Searching for " << needle << ": ";
         std::ranges::binary_search(haystack, needle)
             ? std::cout << "found " << needle << '\n'
             : std::cout << "no dice!\n";
     }
     using CD = std::complex<double>;
     std::vector<CD> nums{{1, 1}, {2, 3}, {4, 2}, {4, 3}};
     auto cmpz = [](CD x, CD y){ return abs(x) < abs(y); };
     #ifdef __cpp_lib_algorithm_default_value_type
         assert(std::ranges::binary_search(nums, {4, 2}, cmpz));
     #else
         assert(std::ranges::binary_search(nums, CD{4, 2}, cmpz));
     #endif
 }

Output:
 Searching for 1: found 1
 Searching for 2: no dice!
 Searching for 3: found 3

See also
   ranges::equal_range returns range of elements matching a specific key
   (C++20) (niebloid)
   ranges::lower_bound returns an iterator to the first element not less than the
   (C++20) given value
                        (niebloid)
   ranges::upper_bound returns an iterator to the first element greater than a
   (C++20) certain value
                        (niebloid)
   ranges::contains
   ranges::contains_subrange checks if the range contains the given element or subrange
   (C++23) (niebloid)
   (C++23)
                        determines if an element exists in a partially-ordered
   binary_search range
                        (function template)