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std::ranges::is_heap(3)        C++ Standard Libary	 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  inhib-
     ited.

	In  practice,  they may be implemented as function objects, or with spe-
     cial 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  com-
     parator 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 \(\scriptsize
	    \mathcal{O}(\log N)\)dh(log N) time.
	  *  The  first  element  can  be  removed  using  ranges::pop_heap,  in
     \(\scriptsize
	    \mathcal{O}(\log N)\)dh(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::itera-
     tor_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("a"), out("a",  w),  out("a'"),	out("a",
     w), out("a"); };
	      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) ? " a " : " ");

	  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 a 8 9 a 6 5 8 9 a 3 5 3 5 3 4 7 2 a 1 2 3 1
      corresponding binary tree is:
		     9
	     aaaaaaaaa'aaaaaaaa
	     8		     9
	 aaaaa'aaaa	  aaaaa'aaaa
	 6	 5	 8	 9
       aaa'aa	aaa'aa	 aaa'aa   aaa'aa
       3   5   3   5   3   4   7   2
      aa'a aa'a aa'a aa'a aa'a aa'a aa'a aa'a
      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)

http://cppreference.com 	   2024.06.10		 std::ranges::is_heap(3)
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