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std::ranges::push_heap

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>
constexpr I
    push_heap( I first, S last, Comp comp = {}, Proj proj = {} );
 (1) (since C++20) 
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>
    push_heap( R&& r, Comp comp = {}, Proj proj = {} );
 (2) (since C++20)

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

In practice, they may be implemented as function objects, or with special 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,Β 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 \(\scriptsize \mathcal{O}(\log N)\)π“ž(log N) time.
  • The first element can be removed using ranges::pop_heap, in \(\scriptsize \mathcal{O}(\log N)\)π“ž(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::invoke(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

#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);
 
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);
}
 
void draw_heap(auto const& v)
{
    auto bails = [](int n, int w)
    {
        auto b = [](int w) { out("β”Œ"), out("─", w), out("β”΄"), 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());
}

Output:

source vector v: 1 6 1 8 0 3
after make_heap: 8 6 3 1 0 1
   8
 β”Œβ”€β”΄β”€β”
 6   3
β”Œβ”΄β” β”Œβ”΄β”
1 0 1
before push_heap: 8 6 3 1 0 1 9
   8
 β”Œβ”€β”΄β”€β”
 6   3
β”Œβ”΄β” β”Œβ”΄β”
1 0 1 9
after push_heap: 9 6 8 1 0 1 3
   9
 β”Œβ”€β”΄β”€β”
 6   8
β”Œβ”΄β” β”Œβ”΄β”
1 0 1 3

See also

(C++20)
 checks if the given range is a max heap
(niebloid)
(C++20)
 finds the largest subrange that is a max heap
(niebloid)
(C++20)
 creates a max heap out of a range of elements
(niebloid)
(C++20)
 removes the largest element from a max heap
(niebloid)
(C++20)
 turns a max heap into a range of elements sorted in ascending order
(niebloid)
adds an element to a max heap
(function template)

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