std::ranges::is_heap

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 bool is_heap( 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 bool is_heap( R&& r, Comp comp = {}, Proj proj = {} );	(2)	(since C++20)

Checks if the elements in range [first, last) are 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

true if the range is max heap, false otherwise.

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_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

#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);
 
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);
}
 
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()); }
}

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

Compiler support
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Technical specifications
Symbols index
External libraries

ranges::is_heap_until (C++20)	finds the largest subrange that 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 (C++11)	checks if the given range is a max heap (function template)