# std::ranges::is_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 Proj = std::identity, std::indirect_strict_weak_order< std::projected<I, Proj>> Comp = ranges::less > constexpr bool is_heap( I first, S last, Comp comp = {}, Proj proj = {} ); | (1) | (since C++20)
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 bool is_heap( R&& r, Comp comp = {}, Proj proj = {} ); | (2) | (since C++20)

Checks if the elements in range `[`first`,` last`)` are 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

true if the range is max heap, false otherwise.

### 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_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 bool operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
        {
            return (last == ranges::is_heap_until(first, last,
                                                  std::move(comp), std::move(proj)));
        }

        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 bool 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_fn is_heap {};

### Example

Run this code

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

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

    void draw_heap(auto const& v);

    int main()
    {
        std::vector<int> v {3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8};

        out("initially, v:\n");
        for (auto i : v) std::cout << i << ' ';
        out('\n');

        if (!std::ranges::is_heap(v))
        {
            out("making heap...\n");
            std::ranges::make_heap(v);
        }

        out("after make_heap, v:\n");
        for (auto t {1U}; auto i : v)
            std::cout << i << (std::has_single_bit(++t) ? " │ " : " ");

        out("\n" "corresponding binary tree is:\n");
        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("┐"); };
            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 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:

    initially, v:
    3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8
    making heap...
    after make_heap, v:
    9 │ 8 9 │ 6 5 8 9 │ 3 5 3 5 3 4 7 2 │ 1 2 3 1
    corresponding binary tree is:
                   9
           ┌───────┴───────┐
           8               9
       ┌───┴───┐       ┌───┴───┐
       6       5       8       9
     ┌─┴─┐   ┌─┴─┐   ┌─┴─┐   ┌─┴─┐
     3   5   3   5   3   4   7   2
    ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
    1 2 3 1

### See also

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::push_heap (C++20) | adds an element to a max heap (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)
is_heap (C++11) | checks if the given range is a max heap (function template)

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