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

NAME
     std::ranges::is_heap_until - std::ranges::is_heap_until

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 I

	    is_heap_until( 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 ranges::borrowed_iterator_t<R>

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

	Examines  the  range [first, last) and finds the largest range beginning
     at first
	which is 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
	The  upper  bound of the largest range beginning at first which is a max
     heap. That
	is, the last iterator it for which range [first, it) is a max heap  with
     respect to
	comp and proj.

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_until_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 I
	     operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
	 {
	     std::iter_difference_t<I> n{ranges::distance(first, last)}, dad{0},
     son{1};
	     for (; son != n; ++son)
	     {
		 if (std::invoke(comp, std::invoke(proj, *(first + dad)),
				       std::invoke(proj, *(first + son))))
		     return first + son;
		 else if ((son % 2) == 0)
		     ++dad;
	     }
	     return first + n;
	 }

	 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 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 is_heap_until_fn is_heap_until {};

Example
	The example renders a given vector as a (balanced) Binary tree.

     // Run this code

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

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

      void draw_bin_tree(auto first, auto last)
      {
	  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 auto size{std::ranges::distance(first, last)};
	  const int m{static_cast<int>(std::ceil(std::log2(1 + size)))};
	  for (int i{}; i != m; ++i)
	      tier(i, m, first, last);
      }

      int main()
      {
	  std::vector<int> v{3, 1, 4, 1, 5, 9};
	  std::ranges::make_heap(v);

	  // probably mess up the heap
	  v.push_back(2);
	  v.push_back(6);

	  out("v after make_heap and push_back:\n");
	  draw_bin_tree(v.begin(), v.end());

	  out("the max-heap prefix of v:\n");
	  const auto heap_end = std::ranges::is_heap_until(v);
	  draw_bin_tree(v.begin(), heap_end);
      }

Output:
      v after make_heap and push_back:
	     9
	 aaaaa'aaaa
	 5	 4
       aaa'aa	aaa'aa
       1   1   3   2
      aa'a aa'a aa'a aa'a
      6
      the max-heap prefix of v:
	 9
       aaa'aa
       5   4
      aa'a aa'a
      1 1 3 2

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

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