std::lower_bound

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< cpp‎ | algorithm
 
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
(C++11)(C++11)(C++11)
(C++17)
Modifying sequence operations
Partitioning operations
Sorting operations
(C++11)
Binary search operations
lower_bound
Set operations (on sorted ranges)
Heap operations
(C++11)
Minimum/maximum operations
(C++11)
(C++17)

Permutations
Numeric operations
Operations on uninitialized storage
(C++17)
(C++17)
(C++17)
C library
 
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 [firstlast) such that element < value (or comp(element, value)) is false, (i.e. that is greater than or equal to value), or last if no such element is found.

The range [firstlast) 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 fully-sorted range meets this criterion.

The first version uses operator< to compare the elements, the second version uses the given comparison function comp.

Parameters

first, last - iterators defining the partially-ordered 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:

 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 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 LegacyForwardIterator.
-
Compare must meet the requirements of BinaryPredicate. It is not required to satisfy Compare.

Return value

Iterator pointing to the first element in the range [firstlast) such that element < value (or comp(element, value)) is false, or last if no such element is found.

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, the number of iterator increments is linear. Notably, std::map, std::multimap, std::set, and std::multiset iterators are not random access, and so their member lower_bound functions should be preferred.

Possible implementation

See also the implementations in libstdc++ and libc++.

lower_bound (1)
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;
}
lower_bound (2)
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;
}

Example

#include <algorithm>
#include <iostream>
#include <vector>
 
struct PriceInfo { double price; };
 
int main()
{
    const std::vector<int> data{1, 2, 4, 5, 5, 6};
 
    for (int i = 0; i < 8; ++i)
    {
        // Search for first element x such that i ≤ x
        auto lower = std::lower_bound(data.begin(), data.end(), i);
 
        std::cout << i << " ≤ ";
        lower != data.end()
            ? std::cout << *lower << " at index " << std::distance(data.begin(), lower)
            : std::cout << "not found";
        std::cout << '\n';
    }
 
    std::vector<PriceInfo> prices{{100.0}, {101.5}, {102.5}, {102.5}, {107.3}};
 
    for (double to_find : {102.5, 110.2})
    {
        auto prc_info = std::lower_bound(prices.begin(), prices.end(), to_find,
            [](const PriceInfo& info, double value)
            {
                return info.price < value;
            });
 
        prc_info != prices.end()
            ? std::cout << prc_info->price << " at index " << prc_info - prices.begin()
            : std::cout << to_find << " not found";
        std::cout << '\n';
    }
}

Output:

0 ≤ 1 at index 0
1 ≤ 1 at index 0
2 ≤ 2 at index 1
3 ≤ 4 at index 2
4 ≤ 4 at index 2
5 ≤ 5 at index 3
6 ≤ 6 at index 5
7 ≤ not found
102.5 at index 2
110.2 not found

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 satisfy Compare and T was required
to be LessThanComparable (strict weak ordering required)
only a partitioning is required;
heterogeneous comparisons permitted
LWG 384 C++98 at most log(last - first) + 1 comparisons were allowed corrected to log
2
(last - first) + O(1)

See also

returns range of elements matching a specific key
(function template)
divides a range of elements into two groups
(function template)
locates the partition point of a partitioned range
(function template)
returns an iterator to the first element greater than a certain value
(function template)
returns an iterator to the first element not less than the given key
(public member function of std::set<Key,Compare,Allocator>)
returns an iterator to the first element not less than the given key
(public member function of std::multiset<Key,Compare,Allocator>)
returns an iterator to the first element not less than the given value
(niebloid)