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std::binary_search

From cppreference.com
 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Non-modifying sequence operations    
Batch operations
(C++17)
Search operations
Modifying sequence operations
Copy operations
(C++11)
(C++11)
Swap operations
Transformation operations
Generation operations
Removing operations
Order-changing operations
(until C++17)(C++11)
(C++20)(C++20)
Sampling operations
(C++17)

Sorting and related operations
Partitioning operations
(C++11)    

Sorting operations
Binary search operations
(on partitioned ranges)
Set operations (on sorted ranges)
Merge operations (on sorted ranges)
Heap operations
Minimum/maximum operations
(C++11)
(C++17)
Lexicographical comparison operations
Permutation operations


 
Defined in header <algorithm>
template< class ForwardIt, class T >
bool binary_search( ForwardIt first, ForwardIt last,
                    const T& value );
(1) (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)
template< class ForwardIt, class T, class Compare >
bool binary_search( ForwardIt first, ForwardIt last,
                    const T& value, Compare comp );
(2) (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 exists in the partitioned source range [first, last). An element is considered equivalent to value if it neither orders before nor orders after value.

1) The order is determined by operator<(until C++20)std::less{}(since C++20).
Given two expressions bool(e < value) and !bool(value < e)(until C++20)bool(std::less{}(e, value)) and !bool(std::less{}(value, e))(since C++20). If any of the following conditions is satisfied, the behavior is undefined:
  • The elements e of the source range are not partitioned with respect to these two expressions at the same time.
  • There exists an element e in the source range such that these two expressions yield different values.
2) The order is determined by comp.
Given two expressions bool(comp(e, value)) and !bool(comp(value, e)). If any of the following conditions is satisfied, the behavior is undefined:
  • The elements e of the source range are not partitioned with respect to these two expressions at the same time.
  • There exists an element e in the source range such that these two expressions yield different values.

Parameters

first, last - the pair of iterators defining the source range
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 type Type1 must be such that an object of type ForwardIt can be dereferenced and then implicitly converted to Type1. The type Type2 must be such that an object of type T can be implicitly converted to 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 exists, false otherwise.

Complexity

Given N as std::distance(first, last):

1) At most log2(N)+𝓞(1) comparisons with value using operator<(until C++20)std::less{}(since C++20).
2) At most log2(N)+𝓞(1) applications of the comparator comp.

Notes

Although std::binary_search only requires the source range to be partitioned, this algorithm is usually used in the case where the source range 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.

If ForwardIt is not a LegacyRandomAccessIterator, the number of iterator increments is linear in std::distance(first, last).

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

#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 << "Not found!\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
Not found!
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 log2(N)+2 comparisons were allowed corrected to 2log2(N)+𝓞(1)

See also

determines if an element exists in a range using binary search
(algorithm function object)[edit]
finds the range of elements matching the given value using binary search
(function template & algorithm function object)[edit]
finds the first element not less than the given value using binary search
(function template & algorithm function object)[edit]
finds the first element greater than the given value using binary search
(function template & algorithm function object)[edit]