std::ranges::make_heap() algorithm

od C++20

Simplified

// (1)
constexpr I
    make_heap( I first, S last, Comp comp = {}, Proj proj = {} );

// (2)
constexpr ranges::borrowed_iterator_t<R>
    make_heap( R&& r, Comp comp = {}, Proj proj = {} );

The type of arguments are generic and have the following constraints:

• I - std::random_access_iterator
• S - std::sentinel_for<I>
• R - std::ranges::random_access_range
• Comp - (none)
• Proj - (none)

The Proj and Comp template arguments have the following default types: std::identity, ranges::less for all overloads.

Additionally, each overload has the following constraints:

• (1) - std::sortable<I, Comp, Proj>
• (2) - std::sortable<ranges::iterator_t<R>, Comp, Proj>

Detailed

// (1)
template<
  std::random_access_iterator I,
  std::sentinel_for<I> S,
  class Comp = ranges::less,
  class Proj = std::identity
>
  requires std::sortable<I, Comp, Proj>
constexpr I
    make_heap( I first, S last, Comp comp = {}, Proj proj = {} );

// (2)
template<
  ranges::random_access_range R,
  class Comp = ranges::less,
  class Proj = std::identity
>
  requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
constexpr ranges::borrowed_iterator_t<R>
    make_heap( R&& r, Comp comp = {}, Proj proj = {} );

Constructs a max heap in the range [first; last).

• (1) Elements are compared using the given binary comparison function comp and projection object proj.

• (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.

Parameters

first last	The range of elements to make a heap from.
r	The range of elements to make a heap from.
pred	Predicate to apply to the projected elements.
proj	The projection to apply to the elements.

Return value

An iterator equal to last.

Complexity

Given N as ranges::distance(first, last):

At most 3 * N comparisons and 6 * N projections.

Exceptions

(none)

Possible implementation

make_heap(1) and make_heap(2)

struct make_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::make_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 make_heap_fn make_heap {};

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:

• Given N as 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 O(log(N)) time.
• The first element can be removed using ranges::pop_heap, in O(log(N)) time.

Examples

Main.cpp

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

void draw_heap(auto const& v);

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

void print(auto rem, auto const& v)
{
    out(rem);
    for (auto e : v)
        out(e), out(' ');
    out('\n');
}

int main()
{
    std::vector h {1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9};
    print("source: ", h);

    std::ranges::make_heap(h);
    print("\n" "max-heap: ", h);
    draw_heap(h);

    std::ranges::make_heap(h, std::greater {});
    print("\n" "min-heap: ", h);
    draw_heap(h);
}

void draw_heap(auto const& v)
{
    auto bails = [](int n, int w)
    {
        auto b = [](int w) { out("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
        if (!(n /= 2))
            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());
}

Possible Output

source: 1 6 1 8 0 3 3 9 8 8 7 4 9 8 9

max-heap: 9 8 9 8 8 4 9 6 1 0 7 1 3 8 3
       9
   ┌───┴───┐
   8       9
 ┌─┴─┐   ┌─┴─┐
 8   8   4   9
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
6 1 0 7 1 3 8 3

min-heap: 0 1 1 8 6 3 3 9 8 8 7 4 9 8 9
       0
   ┌───┴───┐
   1       1
 ┌─┴─┐   ┌─┴─┐
 8   6   3   3
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
9 8 8 7 4 9 8 9