NAME¶

std::ranges::is_heap_until - std::ranges::is_heap_until

Synopsis¶

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

class Proj = std::identity, std::indirect_strict_weak_order< (since
std::projected<I, Proj>> Comp = ranges::less > (1) C++20)
constexpr I

is_heap_until( I first, S last, Comp comp = {}, Proj proj = {} );
template< ranges::random_access_range R, class Proj = std::identity,

std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>, (since
Proj>> (2) C++20)
Comp = ranges::less >
constexpr ranges::borrowed_iterator_t<R>

is_heap_until( R&& r, Comp comp = {}, Proj proj = {} );

Examines the range [first, last) and finds the largest range beginning at first
which is a max heap.

1) Elements are compared using the given binary comparison function comp and
projection object proj.
2) Same as (1), but uses r as the 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 - the range of elements to examine
r - the range of elements to examine
pred - predicate to apply to the projected elements
proj - projection to apply to the elements

Return value¶

The upper bound of the largest range beginning at first which is a max heap. That
is, the last iterator it for which range [first, it) is a max heap with respect to
comp and proj.

Complexity¶

Linear in the distance between first and last.

Notes¶

A max heap is a range of elements [f, l), arranged with respect to comparator comp
and projection proj, that has the following properties:

* With N = l - f, p = f[(i - 1) / 2], and q = f[i], for all 0 < i < N, the
expression std::invoke(comp, std::invoke(proj, p), std::invoke(proj, q))
evaluates to false.
* A new element can be added using ranges::push_heap, in \(\scriptsize
\mathcal{O}(\log N)\)𝓞(log N) time.
* The first element can be removed using ranges::pop_heap, in \(\scriptsize
\mathcal{O}(\log N)\)𝓞(log N) time.

Possible implementation¶

struct is_heap_until_fn {
template<std::random_access_iterator I, std::sentinel_for<I> S,
class Proj = std::identity, std::indirect_strict_weak_order<
std::projected<I, Proj>> Comp = ranges::less>
constexpr I
operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
{
std::iter_difference_t<I> n{ranges::distance(first, last)}, dad{0}, son{1};
for (; son != n; ++son)
{
if (std::invoke(comp, std::invoke(proj, *(first + dad)),
std::invoke(proj, *(first + son))))
return first + son;
else if ((son % 2) == 0)
++dad;
}
return first + n;
}

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

inline constexpr is_heap_until_fn is_heap_until {};

Example¶

The example renders a given vector as a (balanced) Binary tree.

// Run this code

#include <algorithm>
#include <cmath>
#include <iostream>
#include <iterator>
#include <vector>

void out(const auto& what, int n = 1)
{
while (n-- > 0)
std::cout << what;
}

void draw_bin_tree(auto first, auto last)
{
auto bails = [](int n, int w)
{
auto b = [](int w) { out("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
n /= 2;
if (!n)
return;
for (out(' ', w); n-- > 0;)
b(w), out(' ', w + w + 1);
out('\n');
};
auto data = [](int n, int w, auto& first, auto last)
{
for (out(' ', w); n-- > 0 && first != last; ++first)
out(*first), out(' ', w + w + 1);
out('\n');
};
auto tier = [&](int t, int m, auto& first, auto last)
{
const int n{1 << t};
const int w{(1 << (m - t - 1)) - 1};
bails(n, w), data(n, w, first, last);
};
const auto size{std::ranges::distance(first, last)};
const int m{static_cast<int>(std::ceil(std::log2(1 + size)))};
for (int i{}; i != m; ++i)
tier(i, m, first, last);
}

int main()
{
std::vector<int> v{3, 1, 4, 1, 5, 9};
std::ranges::make_heap(v);

// probably mess up the heap
v.push_back(2);
v.push_back(6);

out("v after make_heap and push_back:\n");
draw_bin_tree(v.begin(), v.end());

out("the max-heap prefix of v:\n");
const auto heap_end = std::ranges::is_heap_until(v);
draw_bin_tree(v.begin(), heap_end);
}

Output:¶

v after make_heap and push_back:
9
┌───┴───┐
5 4
┌─┴─┐ ┌─┴─┐
1 1 3 2
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
6
the max-heap prefix of v:
9
┌─┴─┐
5 4
┌┴┐ ┌┴┐
1 1 3 2

See also¶

ranges::is_heap checks if the given range is a max heap
(C++20) (niebloid)
ranges::make_heap creates a max heap out of a range of elements
(C++20) (niebloid)
ranges::push_heap adds an element to a max heap
(C++20) (niebloid)
ranges::pop_heap removes the largest element from a max heap
(C++20) (niebloid)
ranges::sort_heap turns a max heap into a range of elements sorted in ascending
(C++20) order
(niebloid)
is_heap_until finds the largest subrange that is a max heap
(C++11) (function template)