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# std::lower_bound

From cppreference.com
< cpp‎ | algorithm

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

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`.

The range `[first, last)` must be at least partially ordered, i.e. partitioned with respect to the expression element < value or comp(element, value). A fully-sorted range meets this criterion, 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 | - | iterators defining the partially-ordered range 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 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 ForwardIt can be dereferenced and then implicitly converted to Type1. The type Type2 must be such that an object of type T can be implicitly converted to Type2. ​
Type requirements
- `ForwardIt` must meet the requirements of `ForwardIterator`.

### [edit] Return value

Iterator pointing to the first element that is not less than `value`, or `last` if no such element is found.

### [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). However, for non-`RandomAccessIterator`s, the number of iterator increments is linear.

### [edit] Possible implementation

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;
    }

### [edit] Example

Run this code

    #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

### [edit] See also

equal_range | returns range of elements matching a specific key (function template) [edit]
partition | divides a range of elements into two groups (function template) [edit]
upper_bound | returns an iterator to the first element greater than a certain value (function template) [edit]

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