# std::binary_search

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< cpp‎ | algorithm

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:

- partitioned with respect to element < value or comp(element, value) (that is, all elements for which the expression is true precedes all elements for which the expression is false)
- 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.

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

-

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:

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

While the signature does not need to have const &, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) `Type1` and `Type2` regardless of value category (thus, Type1 & is not allowed, nor is Type1 unless for `Type1` a move is equivalent to a copy (since C++11)).
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 LegacyForwardIterator.
- `Compare` must meet the requirements of BinaryPredicate. it is not required to satisfy Compare

### 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-LegacyRandomAccessIterators, 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

### Defect reports

The following behavior-changing 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 be a strict weak ordering | only a partitioning is needed; heterogeneous comparisons permitted

### See also

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

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