NAME¶

std::ranges::lower_bound - std::ranges::lower_bound

Synopsis¶

Defined in header <algorithm>
Call signature
template< std::forward_iterator I, std::sentinel_for<I> S,

class T, class Proj = std::identity, (since
std::indirect_strict_weak_order C++20)
<const T*, std::projected<I, Proj>> Comp = (until
ranges::less > C++26)
constexpr I lower_bound( I first, S last, const T& value,

Comp comp = {}, Proj proj = {} );
template< std::forward_iterator I, std::sentinel_for<I> S,

class Proj = std::identity,
class T = std::projected_value_t<I, Proj>,
std::indirect_strict_weak_order (since
<const T*, std::projected<I, Proj>> Comp = C++26)
ranges::less >
constexpr I lower_bound( I first, S last, const T& value,

Comp comp = {}, Proj proj = {} );
template< ranges::forward_range R,

class T, class Proj = std::identity,
std::indirect_strict_weak_order (1)
<const T*, (since
std::projected<ranges::iterator_t<R>, C++20)
Proj>> Comp = (until
ranges::less > C++26)
constexpr ranges::borrowed_iterator_t<R>

lower_bound( R&& r, const T& value, Comp comp = {}, Proj
proj = {} );
template< ranges::forward_range R, (2)

class Proj = std::identity,
class T =
std::projected_value_t<ranges::iterator_t<R>, Proj>
std::indirect_strict_weak_order
<const T*, (since
std::projected<ranges::iterator_t<R>, C++26)
Proj>> Comp =
ranges::less >
constexpr ranges::borrowed_iterator_t<R>

lower_bound( R&& r, const T& value, Comp comp = {}, Proj
proj = {} );

1) 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
std::invoke(comp, std::invoke(proj, 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.
2) Same as (1), but uses r as the source range, as if using ranges::begin(r) as
first and ranges::end(r) as last.

The function-like entities described on this page are niebloids, that is:

* Explicit template argument lists cannot be specified when calling any of them.
* None of them are visible to argument-dependent lookup.
* When any of them are found by normal unqualified lookup as the name to the left
of the function-call operator, argument-dependent lookup is inhibited.

In practice, they may be implemented as function objects, or with special compiler
extensions.

Parameters¶

first, last - iterator-sentinel pair defining the partially-ordered range to examine
r - the partially-ordered range to examine
value - value to compare the projected elements to
comp - comparison predicate to apply to the projected elements
proj - projection to apply to the elements

Return value¶

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

Complexity¶

The number of comparisons and applications of the projection performed are
logarithmic in the distance between first and last (at most log
2(last - first) + O(1) comparisons and applications of the projection). However, for
an iterator that does not model random_access_iterator, the number of iterator
increments is linear.

Notes¶

On a range that's fully sorted (or more generally, partially ordered with respect to
value) after projection, std::ranges::lower_bound implements the binary search
algorithm. Therefore, std::ranges::binary_search can be implemented in terms of it.

Feature-test macro Value Std Feature
__cpp_lib_algorithm_default_value_type 202403 (C++26) List-initialization for
algorithms (1,2)

Possible implementation¶

struct lower_bound_fn
{
template<std::forward_iterator I, std::sentinel_for<I> S, class Proj = std::identity,
class T = std::projected_value_t<I, Proj>,
std::indirect_strict_weak_order
<const T*, std::projected<I, Proj>> Comp = ranges::less>
constexpr I operator()(I first, S last, const T& value,
Comp comp = {}, Proj proj = {}) const
{
I it;
std::iter_difference_t<I> count, step;
count = std::ranges::distance(first, last);

while (count > 0)
{
it = first;
step = count / 2;
ranges::advance(it, step, last);
if (comp(std::invoke(proj, *it), value))
{
first = ++it;
count -= step + 1;
}
else
count = step;
}
return first;
}

template<ranges::forward_range R, class Proj = std::identity,
class T = std::projected_value_t<ranges::iterator_t<R>, Proj>
std::indirect_strict_weak_order
<const T*, std::projected<ranges::iterator_t<R>,
Proj>> Comp = ranges::less>
constexpr ranges::borrowed_iterator_t<R>
operator()(R&& r, const T& value, Comp comp = {}, Proj proj = {}) const
{
return (*this)(ranges::begin(r), ranges::end(r), value,
std::ref(comp), std::ref(proj));
}
};

inline constexpr lower_bound_fn lower_bound;

Example¶

// Run this code

#include <algorithm>
#include <cassert>
#include <complex>
#include <iostream>
#include <iterator>
#include <vector>

namespace ranges = std::ranges;

template<std::forward_iterator I, std::sentinel_for<I> S, class T,
class Proj = std::identity,
std::indirect_strict_weak_order
<const T*, std::projected<I, Proj>> Comp = ranges::less>
constexpr I binary_find(I first, S last, const T& value, Comp comp = {}, Proj proj = {})
{
first = ranges::lower_bound(first, last, value, comp, proj);
return first != last && !comp(value, proj(*first)) ? first : last;
}

int main()
{
std::vector data{1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5};
// ^^^^^^^^^^
auto lower = ranges::lower_bound(data, 4);
auto upper = ranges::upper_bound(data, 4);

std::cout << "found a range [" << ranges::distance(data.cbegin(), lower)
<< ", " << ranges::distance(data.cbegin(), upper) << ") = { ";
ranges::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, 8, 16};
// ^
auto it = binary_find(data.cbegin(), data.cend(), 8); // '5' would return end()

if (it != data.cend())
std::cout << *it << " found at index "<< ranges::distance(data.cbegin(), it);

using CD = std::complex<double>;
std::vector<CD> nums{{1, 0}, {2, 2}, {2, 1}, {3, 0}};
auto cmpz = [](CD x, CD y) { return x.real() < y.real(); };
#ifdef __cpp_lib_algorithm_default_value_type
auto it2 = ranges::lower_bound(nums, {2, 0}, cmpz);
#else
auto it2 = ranges::lower_bound(nums, CD{2, 0}, cmpz);
#endif
assert((*it2 == CD{2, 2}));
}

Output:¶

found a range [6, 10) = { 4 4 4 4 }
8 found at index 3

See also¶

ranges::equal_range returns range of elements matching a specific key
(C++20) (niebloid)
ranges::partition divides a range of elements into two groups
(C++20) (niebloid)
ranges::partition_point locates the partition point of a partitioned range
(C++20) (niebloid)
ranges::upper_bound returns an iterator to the first element greater than a
(C++20) certain value
(niebloid)
returns an iterator to the first element not less than the
lower_bound given value
(function template)