std::ranges::is_heap(3)

NAME
std::ranges::is_heap - std::ranges::is_heap

Synopsis
   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< (since
             std::projected<I, Proj>> Comp = ranges::less > (1) C++20)
   constexpr bool
       is_heap( I first, S last, Comp comp = {}, Proj proj = {} );
   template< ranges::random_access_range R, class Proj = std::identity,
   std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>, (since
   Proj>> (2) C++20)
             Comp = ranges::less >
   constexpr bool
       is_heap( R&& r, Comp comp = {}, Proj proj = {} );
   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 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.

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)
 {
     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());
 }
 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);
 }

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

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