< cpp‎ | algorithm
Algorithm library
Execution policies (C++17)
Non-modifying sequence operations
Modifying sequence operations

Operations on uninitialized storage
Partitioning operations
Sorting operations
Binary search operations
Set operations (on sorted ranges)
Heap operations
Minimum/maximum operations

Numeric operations
C library
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.


[edit] Parameters

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.

[edit] Return value

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

[edit] 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)));

[edit] Example

#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

[edit] See also

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