std::ranges::is_heap_until() algorithm

since C++20

Simplified

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

// (2)
constexpr ranges::borrowed_iterator_t<R>
    is_heap_until( 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:
  • (1) - std::indirect_strict_weak_order<std::projected<I, Proj>>
  • (2) - std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>, Proj>>
• Proj - (none)

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

Detailed

// (1)
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)
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 = {} );

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 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 examine.
r	The range of elements to examine.
pred	Predicate to apply to the projected elements.
proj	The 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.

Exceptions

(none)

Possible implementation

is_heap_until(1) and is_heap(2)

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 {};

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 <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);

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);
}

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);
}

Possible 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