std::ranges::is_heap_until(3)

💅 std::ranges::is_heap_until 💅

okay bestie, you’re in the C++ Standard Libary manual and today’s main character is std::ranges::is_heap_until. like, the whole page. no cap.

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🎀 NAME 🎀

• std::ranges::is_heap_until — literally std::ranges::is_heap_until. that’s the name, bestie 💖

✨ Synopsis ✨

Defined in header <algorithm>.

✨ Call signature ✨

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

(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 ranges::borrowed_iterator_t<R>
    is_heap_until( R&& r, Comp comp = {}, Proj proj = {} );

okay so what it does: it examines the range [first, last) and finds the largest range beginning at first which is 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, which means:

• 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. slay 💅

🌸 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. lowkey efficient, highkey useful.

💜 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 🧚

here’s the possible implementation, bestie — all the little details kept exactly where they belong:

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. cute, right?

// 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 order (C++20) (niebloid)
• is_heap_until — finds the largest subrange that is a max heap (C++11) (function template)

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that’s the whole vibe check, bestie. source: cppreference.com; version/date: 2024.06.10. mwah 💋