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std::binary_search

From cppreference.com
< cpp‎ | algorithm
 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
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(C++17)
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(C++11)                (C++11)(C++11)

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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
Sorting operations
Binary search operations
(on partitioned ranges)
binary_search
Set operations (on sorted ranges)
Merge operations (on sorted ranges)
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(C++11)
(C++17)
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C library
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Defined in header <algorithm>
template< class ForwardIt, class T >
bool binary_search( ForwardIt first, ForwardIt last, const T& value );
(1) (constexpr since C++20)
template< class ForwardIt, class T, class Compare >

bool binary_search( ForwardIt first, ForwardIt last, const T& value,

                    Compare comp );
(2) (constexpr since C++20)

Checks if an element equivalent to value appears within the partitioned range [firstlast).

1) The equivalence is checked using operator<:

If bool(*iter < value) && !bool(value < *iter) is true for some iterator iter in [firstlast), returns true. Otherwise returns false.

If any of the following conditions is satisfied, the behavior is undefined:

  • For any element elem of [firstlast), bool(elem < value) does not imply !bool(value < elem).
  • The elements elem of [firstlast) 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 [firstlast), returns true. Otherwise returns false.
If any of the following conditions is satisfied, the behavior is undefined:
  • For any element elem of [firstlast), bool(comp(elem, value)) does not imply !bool(comp(value, elem)).
  • The elements elem of [firstlast) are not partitioned with respect to expressions bool(comp(elem, value)) and !bool(comp(value, elem)).

Contents

[edit] 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.

[edit] Return value

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

[edit] Complexity

The number of comparisons performed is logarithmic in the distance between first and last (at most log
2
(last - first) + O(1)
comparisons). However, for non-LegacyRandomAccessIterators, number of iterator increments is linear.

[edit] Notes

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

[edit] Possible implementation

See also the implementations in libstdc++ and libc++.

binary_search (1)
template<class ForwardIt, class T>
bool binary_search(ForwardIt first, ForwardIt last, const T& value)
{
    first = std::lower_bound(first, last, value);
    return (!(first == last) and !(value < *first));
}
binary_search (2)
template<class ForwardIt, class T, 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)));
}

[edit] Example

#include <algorithm>
#include <iostream>
 
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";
    }
}

Output:

Searching for 1
Found 1
Searching for 2
no dice!
Searching for 3
Found 3

[edit] 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 log(last - first) + 2 comparisons were allowed corrected to log
2
(last - first) + O(1)

[edit] See also

returns range of elements matching a specific key
(function template) [edit]
returns an iterator to the first element not less than the given value
(function template) [edit]
returns an iterator to the first element greater than a certain value
(function template) [edit]
determines if an element exists in a partially-ordered range
(niebloid)[edit]