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std::ranges::make_heap(3)      C++ Standard Libary     std::ranges::make_heap(3)

NAME
     std::ranges::make_heap - std::ranges::make_heap

Synopsis
	Defined in header <algorithm>
	Call signature
	template< std::random_access_iterator I, std::sentinel_for<I> S,

		  class Comp = ranges::less, class Proj = std::identity >
	requires  std::sortable<I,  Comp, Proj> 			     (1)
     (since C++20)
	constexpr I

	    make_heap( I first, S last, Comp comp = {}, Proj proj = {} );
	template< ranges::random_access_range R, class Comp =
	ranges::less,

		  class Proj = std::identity  > 			     (2)
     (since C++20)
	requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
	constexpr ranges::borrowed_iterator_t<R>

	    make_heap( R&& r, Comp comp = {}, Proj proj = {} );

	Constructs a max heap in the range [first, last).

	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 make the heap from
	r	    - the range of elements to make the heap from
	pred	    - predicate to apply to the projected elements
	proj	    - projection to apply to the elements

Return value
	An iterator equal to last.

Complexity
	Given N = ranges::distance(first, last), at  most  \(\scriptsize  3\cdot
     N\)3*N
	comparisons and \(\scriptsize 6\cdot N\)6*N projections.

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.

Example
     // Run this code

      #include <algorithm>
      #include <cmath>
      #include <functional>
      #include <iostream>
      #include <vector>

      void out(const auto& what, int n = 1)
      {
	  while (n-- > 0)
	      std::cout << what;
      }

      void print(auto rem, auto const& v)
      {
	  out(rem);
	  for (auto e : v)
	      out(e), out(' ');
	  out('\n');
      }

      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"); };
	      if (!(n /= 2))
		  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 h{1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9};
	  print("source: ", h);

	  std::ranges::make_heap(h);
	  print("\n" "max-heap: ", h);
	  draw_heap(h);

	  std::ranges::make_heap(h, std::greater{});
	  print("\n" "min-heap: ", h);
	  draw_heap(h);
      }

Output:
      source: 1 6 1 8 0 3 3 9 8 8 7 4 9 8 9

      max-heap: 9 8 9 8 8 4 9 6 1 0 7 1 3 8 3
	     9
	 aaaaa'aaaa
	 8	 9
       aaa'aa	aaa'aa
       8   8   4   9
      aa'a aa'a aa'a aa'a
      6 1 0 7 1 3 8 3

      min-heap: 0 1 1 8 6 3 3 9 8 8 7 4 9 8 9
	     0
	 aaaaa'aaaa
	 1	 1
       aaa'aa	aaa'aa
       8   6   3   3
      aa'a aa'a aa'a aa'a
      9 8 8 7 4 9 8 9

See also
	ranges::is_heap       checks if the given range is a max heap
	(C++20) 	      (niebloid)
	ranges::is_heap_until finds the largest subrange that is a max heap
	(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)
	make_heap	      creates a max heap out of a range of elements
			      (function template)

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