Defined in header <algorithm>
template< class ForwardIt, class T >
bool binary_search( ForwardIt first, ForwardIt last, const T& value );
template< class ForwardIt, class T, class Compare >
bool binary_search( ForwardIt first, ForwardIt last, const T& value, Compare comp );

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, i.e. it must satisfy all of the following requirements:

  • partitioned with respect to element < value or comp(element, value)
  • 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, as does a range resulting from a call to std::partition.

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 - comparison function object (i.e. an object that satisfies the requirements of Compare) which returns ​true if the first argument is less than (i.e. is ordered before) the second.

The signature of the comparison function should be equivalent to the following:

bool cmp(const Type1 &a, const Type2 &b);

The signature does not need to have const &, but the function object must not modify the objects passed to it.
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 ForwardIterator.

Return value

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
(last - first) + O(1) comparisons). However, for non-RandomAccessIterators, number of iterator increments is linear.

Possible implementation

First version
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) && !(value < *first));
Second version
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) && !(comp(value, *first)));


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


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

See also

returns range of elements matching a specific key
(function template)

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