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:
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
) !(value < element)
or !comp(value, element)
element < value
or comp(element, value)
is true
then !(value < element)
or !comp(value, element)
is also true
A fullysorted range meets these criteria.
The first version uses operator< to compare the elements, the second version uses the given comparison function comp
.
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:
While the signature does not need to have 
Type requirements  
ForwardIt must meet the requirements of LegacyForwardIterator. 

Compare must meet the requirements of BinaryPredicate. It is not required to satisfy Compare. 
true
if an element equal to value
is found, false
otherwise.
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 nonLegacyRandomAccessIterators, number of iterator increments is linear.
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))); } 
#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
The following behaviorchanging 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 requiredto 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) 
returns range of elements matching a specific key (function template) 

returns an iterator to the first element not less than the given value (function template) 

returns an iterator to the first element greater than a certain value (function template) 

(C++20)  determines if an element exists in a partiallyordered range (niebloid) 
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