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)

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