# std::ranges::push_heap

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< cpp‎ | algorithm‎ | ranges

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`,` 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 inhibited.

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`,` 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 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

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);

    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("┌"), 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());
    }

Output:

    source vector v: 1 6 1 8 0 3
    after make_heap: 8 6 3 1 0 1
       8
     ┌─┴─┐
     6   3
    ┌┴┐ ┌┴┐
    1 0 1
    before push_heap: 8 6 3 1 0 1 9
       8
     ┌─┴─┐
     6   3
    ┌┴┐ ┌┴┐
    1 0 1 9
    after push_heap: 9 6 8 1 0 1 3
       9
     ┌─┴─┐
     6   8
    ┌┴┐ ┌┴┐
    1 0 1 3

### See also

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

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