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std::binary_search

Defined in header `<algorithm>`
	(1)
template< class ForwardIt, class T > bool binary_search( ForwardIt first, ForwardIt last, const T& value );		(until C++20)
template< class ForwardIt, class T > constexpr bool binary_search( ForwardIt first, ForwardIt last, const T& value );		(since C++20)
	(2)
template< class ForwardIt, class T, class Compare > bool binary_search( ForwardIt first, ForwardIt last, const T& value, Compare comp );		(until C++20)
template< class ForwardIt, class T, class Compare > constexpr bool binary_search( ForwardIt first, ForwardIt last, const T& value, Compare comp );		(since C++20)

Checks if an element equivalent to value appears within the range [first, last).

For std::binary_search to succeed, the range [first, last) must be at least partially ordered with respect to value, i.e. it must satisfy all of the following requirements:

partitioned with respect to element < value or comp(element, value) (that is, all elements for which the expression is true precede all elements for which the expression is false)
partitioned with respect to !(value < element) or !comp(value, element)
for all elements, if element < value or comp(element, value) is true then !(value < element) or !comp(value, element) is also true

A fully-sorted range meets these criteria.

The first version uses operator< to compare the elements, the second version uses the given comparison function comp.

Parameters

first, last	-	the range of elements to examine
value	-	value to compare the elements to
comp	-	binary predicate which returns `true` if the first argument is less than (i.e. 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 equal to value is found, false otherwise.

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.

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))); }

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)));
}

Example

#include <algorithm>
#include <iostream>
#include <vector>
 
int main()
{
    std::vector<int> haystack {1, 3, 4, 5, 9};
    std::vector<int> needles {1, 2, 3};
 
    for (auto needle : needles)
    {
        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

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)

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)