std::binary_search() algorithm

since C++20

// (1)
template< class ForwardIt, class T >
constexpr bool binary_search( ForwardIt first, ForwardIt last, const T& value );

// (2)
template< class ForwardIt, class T, class Compare >
constexpr bool binary_search( ForwardIt first, ForwardIt last, const T& value, Compare comp );

until C++20

// (1)
template< class ForwardIt, class T >
bool binary_search( ForwardIt first, ForwardIt last, const T& value );

// (2)
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 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 precede 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.

• (1) Uses operator< to compare elements.

• (2) Uses the given comparison function comp to compare elements.

Parameters

first last	The partially-ordered range to search in.
value	The value to compare the elements to.
comp	Comparison function object (i.e. an object that satisfies the requirements of Compare). 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 must not modify arguments. Must accept all values of type (possibly const) Type and Type2, regardless of value category (so 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 RandomIt can be implicitly converted to both of them.

Type requirements

ForwardIt	LegacyForwardIterator
Compare	BinaryPredicate

Compare is not required to satisfy Compare.

Return value

If an element equal to value is found, true.

Otherwise, false.

Complexity

The number of comparisons performed is logarithmic in the distance between first and last (at most log2(last - first) + O(1) comparisons).

However, for non-LegacyRandomAccessIterators, the number of iterator increments is linear.

Exceptions

(none)

Possible implementation

binary_search (1)

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) and !(value < *first));
}

binary_search (2)

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) and !(comp(value, *first)));
}

Examples

Main.cpp

#include <algorithm>
#include <iostream>
#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