std::binary_search

 

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Defined in header <algorithm>
	(1)
template< class ForwardIt, class T > bool binary_search( ForwardIt first, ForwardIt last,                     const T& value );			(constexpr since C++20) (until C++26)
template< class ForwardIt, class T = typename std::iterator_traits                                          <ForwardIt>::value_type > constexpr bool binary_search( ForwardIt first, ForwardIt last,                               const T& value );			(since C++26)
		(2)
template< class ForwardIt, class T, class Compare > bool binary_search( ForwardIt first, ForwardIt last,                     const T& value, Compare comp );				(constexpr since C++20) (until C++26)
template< class ForwardIt, class T = typename std::iterator_traits                                          <ForwardIt>::value_type,           class Compare > constexpr bool binary_search( ForwardIt first, ForwardIt last,                               const T& value, Compare comp );				(since C++26)

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: 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).

(until C++20)

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
comp	-	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); 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 \(\scriptsize \log_{2}(N)+O(1)\)log2(N)+O(1) comparisons with value using operator<(until C++20)std::less{}(since C++20).

2) At most \(\scriptsize \log_{2}(N)+O(1)\)log2(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
LWG 270	C++98	Compare was required to satisfy Compare and T was required to be LessThanComparable (strict weak ordering required)	only a partitioning is required; heterogeneous comparisons permitted
LWG 787	C++98	at most \(\scriptsize \log_{2}(N)+2\)log2(N)+2 comparisons were allowed	corrected to \(\scriptsize \log_{2}(N)+O(1)\)log2(N)+O(1)

See also

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