std::ranges::is_heap_until

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< std::projected<I, Proj>> Comp = ranges::less > constexpr I is_heap_until( I first, S last, Comp comp = {}, Proj proj = {} );	(1)	(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 = {} );	(2)	(since C++20)

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 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 may not be specified when calling any of them.
None of them is visible to argument-dependent lookup.
When one of them is found by normal unqualified lookup for the name to the left of the function-call operator, it inhibits argument-dependent lookup.

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

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.

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_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.

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);
 
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); }
}

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

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Technical specifications
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External libraries

ranges::is_heap (C++20)	checks if the given range is a max heap (niebloid)
ranges::make_heap (C++20)	creates a max heap out of a range of elements (niebloid)
ranges::push_heap (C++20)	adds an element to a max heap (niebloid)
ranges::pop_heap (C++20)	removes the largest element from a max heap (niebloid)
ranges::sort_heap (C++20)	turns a max heap into a range of elements sorted in ascending order (niebloid)
is_heap_until (C++11)	finds the largest subrange that is a max heap (function template)