std::ranges::is_heap(3)

✨ NAME ✨

okay so this page is std::ranges::is_heap(3) — yes, the std::ranges::is_heap one — straight outta the C++ Standard Libary manual, bestie. That spelling stays, I don’t make the rules 💅.

🌸 Synopsis 🌸

Defined in header <algorithm>. Call signature incoming, and it’s giving template realness:

overload (1) — since C++20

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
    is_heap( I first, S last, Comp comp = {}, Proj proj = {} );

overload (2) — since C++20

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

Checks if the elements in range [first, last) are a max heap. Iconic behavior, honestly.

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. Very main character energy, lowkey.

🎀 Parameters 🎀

• first, last — the range of elements to examine, bestie.
• 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. That’s it. Periodt.

🦋 Complexity 🦋

Linear in the distance between first and last. Efficient enough, no cap.

🌈 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 👑

the page literally gives u a possible implementation, so here it is, untouched code-wise:

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, bestie:

#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 order — (C++20) (niebloid)
• is_heap — checks if the given range is a max heap — (C++11) (function template)

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