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 inhibited.
   In practice, they may be implemented as function objects, or with special 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 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.

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("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
         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
    ┌───┴───┐
    8 9
  ┌─┴─┐ ┌─┴─┐
  8 8 4 9
 ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
 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
    ┌───┴───┐
    1 1
  ┌─┴─┐ ┌─┴─┐
  8 6 3 3
 ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
 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)