# std::binary_search

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< cpp‎ | algorithm

Defined in header `<algorithm>` |  |
template< class ForwardIt, class T > bool binary_search( ForwardIt first, ForwardIt last, const T& value ); | (1) |
template< class ForwardIt, class T, class Compare > bool binary_search( ForwardIt first, ForwardIt last, const T& value, Compare comp ); | (2) |

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`.

### 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`.

### 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-`RandomAccessIterator`s, 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)));
    }

### Example

Run this code

    #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";
            }
        }
    }

Output:

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

### See also

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

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