std::binary_search(3)

NAME
std::binary_search - std::binary_search

Synopsis
   Defined in header <algorithm>
   template< class ForwardIt, class T >
                        (constexpr since
   bool binary_search( ForwardIt first, C++20)
   ForwardIt last, (until C++26)
                       const T& value );
   template< class ForwardIt, class T =
   typename std::iterator_traits
    <ForwardIt>::value_type > (since C++26)
   constexpr bool binary_search( ForwardIt
   first, ForwardIt last,
                        const T&
   value );
   template< class ForwardIt, class T, class
   Compare > (1)
                        (constexpr since
   bool binary_search( ForwardIt first, C++20)
   ForwardIt last, (until C++26)
                       const T& value,
   Compare comp );
   template< class ForwardIt, class T =
   typename std::iterator_traits (2)
    <ForwardIt>::value_type,
             class Compare > (since C++26)
   constexpr bool binary_search( ForwardIt
   first, ForwardIt last,
                        const T&
   value, Compare comp );
   Checks if an element equivalent to value appears within the partitioned range
   [first, last).
   1) The equivalence is checked using operator<:
   If !bool(*iter < value) && !bool(value < *iter) is true for some
   iterator iter in [first, last), returns true. Otherwise returns false.
   If any of the following conditions is satisfied, the behavior is
   undefined: (until C++20)
     * For any element elem of [first, last), bool(elem < value) does not
       imply !bool(value < elem).
     * The elements elem of [first, last) are not partitioned with
       respect to expressions bool(elem < value) and !bool(value < elem).
   Equivalent to std::binary_search(first, last, value, std::less{}). (since C++20)
   2) The equivalence is checked using comp:
   If !bool(comp(*iter, value)) && !bool(comp(value, *iter)) is true for some iterator
   iter in [first, last), returns true. Otherwise returns false.
   If any of the following conditions is satisfied, the behavior is undefined:
     * For any element elem of [first, last), bool(comp(elem, value)) does not imply
       !bool(comp(value, elem)).
     * The elements elem of [first, last) are not partitioned with respect to
       expressions bool(comp(elem, value)) and !bool(comp(value, elem)).

Parameters
   first, last - the partitioned range of elements to examine
   value - value to compare the elements to
                 binary predicate which returns true if the first argument is ordered
                 before the second.
                 The signature of the predicate function should be equivalent to the
                 following:
                  bool pred(const Type1 &a, const Type2 &b);
   comp - While the signature does not need to have const &, the function must
                 not modify the objects passed to it and must be able to accept all
                 values of type (possibly const) Type1 and Type2 regardless of value
                 category (thus, Type1 & is not allowed
                 , nor is Type1 unless for Type1 a move is equivalent to a copy
                 (since C++11)).
                 The types Type1 and Type2 must be such that an object of type T can be
                 implicitly converted to both Type1 and Type2, and an object of type
                 ForwardIt can be dereferenced and then implicitly converted to both
                 Type1 and Type2.

Type requirements
   -
   ForwardIt must meet the requirements of LegacyForwardIterator.
   -
   Compare must meet the requirements of BinaryPredicate. It is not required to satisfy
   Compare.

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

Complexity
   Given \(\scriptsize N\)N as std::distance(first, last):
   1) At most \(\scriptsize \log_{2}(N)+O(1)\)log
   2(N)+O(1) comparisons with value using
   operator<
   (until C++20)
   std::less{}
   (since C++20).
   2) At most \(\scriptsize \log_{2}(N)+O(1)\)log
   2(N)+O(1) applications of the comparator comp.
   However, if ForwardIt is not a LegacyRandomAccessIterator, the number of iterator
   increments is linear in \(\scriptsize N\)N.

Notes
   Although std::binary_search only requires [first, last) to be partitioned, this
   algorithm is usually used in the case where [first, last) is sorted, so that the
   binary search is valid for any value.
   std::binary_search only checks whether an equivalent element exists. To obtain an
   iterator to that element (if exists), std::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
   See also the implementations in libstdc++ and libc++.
                        binary_search (1)
 template<class ForwardIt, class T = typename std::iterator_traits<ForwardIt>::value_type>
 bool binary_search(ForwardIt first, ForwardIt last, const T& value)
 {
     return std::binary_search(first, last, value, std::less{});
 }
                        binary_search (2)
 template<class ForwardIt, class T = typename std::iterator_traits<ForwardIt>::value_type,
          class Compare>
 bool binary_search(ForwardIt first, ForwardIt last, const T& value, Compare comp)
 {
     first = std::lower_bound(first, last, value, comp);
     return (!(first == last) and !(comp(value, *first)));
 }

Example
// Run this code
 #include <algorithm>
 #include <cassert>
 #include <complex>
 #include <iostream>
 #include <vector>
 int main()
 {
     const auto haystack = {1, 3, 4, 5, 9};
     for (const auto needle : {1, 2, 3})
     {
         std::cout << "Searching for " << needle << '\n';
         if (std::binary_search(haystack.begin(), haystack.end(), needle))
             std::cout << "Found " << needle << '\n';
         else
             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::binary_search(nums.cbegin(), nums.cend(), {4, 2}, cmpz));
     #else
         assert(std::binary_search(nums.cbegin(), nums.cend(), CD{4, 2}, cmpz));
     #endif
 }

Output:
 Searching for 1
 Found 1
 Searching for 2
 no dice!
 Searching for 3
 Found 3
   Defect reports
   The following behavior-changing defect reports were applied retroactively to
   previously published C++ standards.
     DR Applied to Behavior as published Correct behavior
                      Compare was required to satisfy only a partitioning is required;
   LWG 270 C++98 Compare and T was required heterogeneous comparisons
                      to be LessThanComparable (strict permitted
                      weak ordering required)
                      at most \(\scriptsize corrected to \(\scriptsize
   LWG 787 C++98 \log_{2}(N)+2\)log \log_{2}(N)+O(1)\)log
                      2(N)+2 comparisons were allowed 2(N)+O(1)

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