Defined in header <algorithm>  

(1)  
template< class ForwardIt, class T > ForwardIt lower_bound( ForwardIt first, ForwardIt last, const T& value );  (until C++20)  
template< class ForwardIt, class T > constexpr ForwardIt lower_bound( ForwardIt first, ForwardIt last, const T& value );  (since C++20)  
(2)  
template< class ForwardIt, class T, class Compare > ForwardIt lower_bound( ForwardIt first, ForwardIt last, const T& value, Compare comp );  (until C++20)  
template< class ForwardIt, class T, class Compare > constexpr ForwardIt lower_bound( ForwardIt first, ForwardIt last, const T& value, Compare comp );  (since C++20) 
Returns an iterator pointing to the first element in the range [first, last)
that is not less than (i.e. greater or equal to) value
, or last
if no such element is found.
The range [first, last)
must be partitioned with respect to the expression element < value
or comp(element, value)
, i.e., all elements for which the expression is true
must precede all elements for which the expression is false
. A fullysorted range meets this criterion.
The first version uses operator<
to compare the elements, the second version uses the given comparison function comp
.
first, last    iterators defining the partiallyordered range 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:
While the signature does not need to have 
Type requirements  
ForwardIt must meet the requirements of LegacyForwardIterator. 

Compare must meet the requirements of BinaryPredicate. it is not required to satisfy Compare 
Iterator pointing to the first element that is not less than value
, or last
if no such element is found.
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 nonLegacyRandomAccessIterators, the number of iterator increments is linear.
First version 

template<class ForwardIt, class T> ForwardIt lower_bound(ForwardIt first, ForwardIt last, const T& value) { ForwardIt it; typename std::iterator_traits<ForwardIt>::difference_type count, step; count = std::distance(first, last); while (count > 0) { it = first; step = count / 2; std::advance(it, step); if (*it < value) { first = ++it; count = step + 1; } else count = step; } return first; } 
Second version 
template<class ForwardIt, class T, class Compare> ForwardIt lower_bound(ForwardIt first, ForwardIt last, const T& value, Compare comp) { ForwardIt it; typename std::iterator_traits<ForwardIt>::difference_type count, step; count = std::distance(first, last); while (count > 0) { it = first; step = count / 2; std::advance(it, step); if (comp(*it, value)) { first = ++it; count = step + 1; } else count = step; } return first; } 
#include <algorithm> #include <iostream> #include <iterator> #include <vector> template<class ForwardIt, class T, class Compare=std::less<>> ForwardIt binary_find(ForwardIt first, ForwardIt last, const T& value, Compare comp={}) { // Note: BOTH type T and the type after ForwardIt is dereferenced // must be implicitly convertible to BOTH Type1 and Type2, used in Compare. // This is stricter than lower_bound requirement (see above) first = std::lower_bound(first, last, value, comp); return first != last && !comp(value, *first) ? first : last; } int main() { std::vector<int> data = { 1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6 }; auto lower = std::lower_bound(data.begin(), data.end(), 4); auto upper = std::upper_bound(data.begin(), data.end(), 4); std::copy(lower, upper, std::ostream_iterator<int>(std::cout, " ")); std::cout << '\n'; // classic binary search, returning a value only if it is present data = { 1, 2, 4, 6, 9, 10 }; auto it = binary_find(data.cbegin(), data.cend(), 4); //< choosing '5' will return end() if(it != data.cend()) std::cout << *it << " found at index "<< std::distance(data.cbegin(), it); return 0; }
Output:
4 4 4 4 found at index 2
The following behaviorchanging 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 
returns range of elements matching a specific key (function template) 

divides a range of elements into two groups (function template) 

returns an iterator to the first element greater than a certain value (function template) 
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