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std::is_heap

Defined in header `<algorithm>`
	(1)
template< class RandomIt > bool is_heap( RandomIt first, RandomIt last );		(since C++11) (until C++20)
template< class RandomIt > constexpr bool is_heap( RandomIt first, RandomIt last );		(since C++20)
template< class ExecutionPolicy, class RandomIt > bool is_heap( ExecutionPolicy&& policy, RandomIt first, RandomIt last );	(2)	(since C++17)
	(3)
template< class RandomIt, class Compare > bool is_heap( RandomIt first, RandomIt last, Compare comp );		(since C++11) (until C++20)
template< class RandomIt, class Compare > constexpr bool is_heap( RandomIt first, RandomIt last, Compare comp );		(since C++20)
template< class ExecutionPolicy, class RandomIt, class Compare > bool is_heap( ExecutionPolicy&& policy, RandomIt first, RandomIt last, Compare comp );	(4)	(since C++17)

Checks whether the elements in range [first, last) are a max heap.

1) Elements are compared using operator<.

3) Elements are compared using the given binary comparison function comp.

2,4) Same as (1,3), but executed according to policy. These overloads do not participate in overload resolution unless

`std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>` is `true`.	(until C++20)
`std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>` is `true`.	(since C++20)

Parameters

first, last	-	the range of elements to examine
policy	-	the execution policy to use. See execution policy for details.
comp	-	comparison function object (i.e. an object that satisfies the requirements of Compare) which returns `true` if the first argument is less than the second. The signature of the comparison function should be equivalent to the following: `bool cmp(const Type1 &a, const Type2 &b);` While the signature does not need to have `const &`, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) `Type1` and `Type2` regardless of value category (thus, `Type1 &` is not allowed, nor is `Type1` unless for `Type1` a move is equivalent to a copy (since C++11)). The types Type1 and Type2 must be such that an object of type RandomIt can be dereferenced and then implicitly converted to both of them.
Type requirements
-`RandomIt` must meet the requirements of LegacyRandomAccessIterator.

Return value

true if the range is max heap, false otherwise.

Complexity

Linear in the distance between first and last.

Exceptions

The overloads with a template parameter named ExecutionPolicy report errors as follows:

If execution of a function invoked as part of the algorithm throws an exception and ExecutionPolicy is one of the standard policies, std::terminate is called. For any other ExecutionPolicy, the behavior is implementation-defined.
If the algorithm fails to allocate memory, std::bad_alloc is thrown.

Notes

A max heap is a range of elements [f, l) that has the following properties:

With N = l - f, for all 0 < i < N, f[(i - 1) / 2] does not compare less than f[i].
A new element can be added using std::push_heap, in \(\scriptsize \mathcal{O}(\log N)\)𝓞(log N) time.
The first element can be removed using std::pop_heap, in \(\scriptsize \mathcal{O}(\log N)\)𝓞(log N) time.

Example

#include <algorithm>
#include <bit>
#include <iostream>
#include <vector>
 
int main()
{
    std::vector<int> v {3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9};
 
    std::cout << "initially, v:\n";
    for (auto i : v)
        std::cout << i << ' ';
    std::cout << '\n';
 
    if (!std::is_heap(v.begin(), v.end()))
    {
        std::cout << "making heap...\n";
        std::make_heap(v.begin(), v.end());
    }
 
    std::cout << "after make_heap, v:\n";
    for (auto t{1U}; auto i : v)
        std::cout << i << (std::has_single_bit(++t) ? " | " : " ");
    std::cout << '\n';
}

Output:

initially, v:
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9
making heap...
after make_heap, v:
9 | 6 9 | 5 5 9 7 | 1 1 3 5 8 3 4 2 |

is_heap_until (C++11)	finds the largest subrange that is a max heap (function template)
make_heap	creates a max heap out of a range of elements (function template)
push_heap	adds an element to a max heap (function template)
pop_heap	removes the largest element from a max heap (function template)
sort_heap	turns a max heap into a range of elements sorted in ascending order (function template)
ranges::is_heap (C++20)	checks if the given range is a max heap (niebloid)