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# std::binary_search

From cppreference.com
< 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`.

### [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 type Type1 must be such that an object of type T can be implicitly converted to Type1. The type Type2 must be such that an object of type ForwardIt can be dereferenced and then implicitly converted to Type2. ​
| This section is incomplete Reason: Update type requirements? The types Type1 and Type2 must be such that an object of type T can be implicitly converted to either type, and such that an object of type ForwardIt can be dereferenced and then implicitly converted to either type. Generally Type1 and Type2 will be the same type, although this is not required.
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
2(last - first) + O(1) comparisons)

### [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

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

### [edit] See also

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

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