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

NAME
     std::ranges::push_heap - std::ranges::push_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

	    push_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>

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

	Inserts  the  element at the position last - 1 into the max heap defined
     by the range
	[first, last - 1).

	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 defining the heap to modify
	r	    - the range of elements defining the heap to modify
	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  \(\scriptsize
     \log{(N)}\)log(N)
	comparisons and \(\scriptsize 2\log{(N)}\)2log(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.

Possible implementation
     struct push_heap_fn {
	 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>
	 constexpr I
	     operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
	 {
	     const auto n{ranges::distance(first, last)};
	     const auto length{n};
	     if (n > 1)
	     {
		 I last{first + n};
		 n = (n - 2) / 2;
		 I i{first + n};
		 if (std::invoke(comp, std::invoke(proj, *i),  std::invoke(proj,
     *--last)))
		 {
		     std::iter_value_t<I> v {ranges::iter_move(last)};
		     do
		     {
			 *last = ranges::iter_move(i);
			 last = i;
			 if (n == 0)
			     break;
			 n = (n - 1) / 2;
			 i = first + n;
		     }
		     while  (std::invoke(comp,	std::invoke(proj,  *i), std::in-
     voke(proj, v)));
		     *last = std::move(v);
		 }
	     }
	     return first + length;
	 }

	 template<ranges::random_access_range R, class Comp = ranges::less,
		  class Proj = std::identity>
	 requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
	 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 push_heap_fn push_heap {};

Example
     // Run this code

      #include <algorithm>
      #include <cmath>
      #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<int> v{1, 6, 1, 8, 0, 3,};
	  print("source vector v: ", v);

	  std::ranges::make_heap(v);
	  print("after make_heap: ", v);
	  draw_heap(v);

	  v.push_back(9);

	  print("before push_heap: ", v);
	  draw_heap(v);

	  std::ranges::push_heap(v);
	  print("after push_heap: ", v);
	  draw_heap(v);
      }

Output:
      source vector v: 1 6 1 8 0 3
      after make_heap: 8 6 3 1 0 1
	 8
       aaa'aa
       6   3
      aa'a aa'a
      1 0 1
      before push_heap: 8 6 3 1 0 1 9
	 8
       aaa'aa
       6   3
      aa'a aa'a
      1 0 1 9
      after push_heap: 9 6 8 1 0 1 3
	 9
       aaa'aa
       6   8
      aa'a aa'a
      1 0 1 3

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::make_heap     creates a max heap out of a range of elements
	(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)
	push_heap	      adds an element to a max heap
			      (function template)

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