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 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
   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 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_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::iterator_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("┌"), 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 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
    ┌───┴───┐
    5 4
  ┌─┴─┐ ┌─┴─┐
  1 1 3 2
 ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
 6
 the max-heap prefix of v:
    9
  ┌─┴─┐
  5 4
 ┌┴┐ ┌┴┐
 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)