NAME¶

std::ranges::is_heap - std::ranges::is_heap

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 bool

is_heap( 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 bool

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

Checks if the elements in range [first, last) are 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¶

true if the range is max heap, false otherwise.

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_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 bool operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
{
return (last == ranges::is_heap_until(first, last,
std::move(comp), std::move(proj)));
}

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 bool 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_fn is_heap {};

Example¶

// Run this code

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

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

void draw_heap(auto const& v)
{
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 int m{static_cast<int>(std::ceil(std::log2(1 + v.size())))};
auto first{v.cbegin()};
for (int i{}; i != m; ++i)
tier(i, m, first, v.cend());
}

int main()
{
std::vector<int> v{3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8};

out("initially, v:\n");
for (auto i : v)
std::cout << i << ' ';
out('\n');

if (!std::ranges::is_heap(v))
{
out("making heap...\n");
std::ranges::make_heap(v);
}

out("after make_heap, v:\n");
for (auto t{1U}; auto i : v)
std::cout << i << (std::has_single_bit(++t) ? " │ " : " ");

out("\n" "corresponding binary tree is:\n");
draw_heap(v);
}

Output:¶

initially, v:
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8
making heap...
after make_heap, v:
9 │ 8 9 │ 6 5 8 9 │ 3 5 3 5 3 4 7 2 │ 1 2 3 1
corresponding binary tree is:
9
┌───────┴───────┐
8 9
┌───┴───┐ ┌───┴───┐
6 5 8 9
┌─┴─┐ ┌─┴─┐ ┌─┴─┐ ┌─┴─┐
3 5 3 5 3 4 7 2
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
1 2 3 1

See also¶

ranges::is_heap_until finds the largest subrange that 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 checks if the given range is a max heap
(C++11) (function template)