std::is_heap(3)

NAME
std::is_heap - std::is_heap

Synopsis
   Defined in header <algorithm>
   template< class RandomIt > (since C++11)
   bool is_heap( RandomIt first, RandomIt last ); (until C++20)
   template< class RandomIt >
   constexpr bool is_heap( RandomIt first, RandomIt (since C++20)
   last );
   template< class ExecutionPolicy, class RandomIt
   > (2) (since C++17)
   bool is_heap( ExecutionPolicy&& policy, RandomIt
   first, RandomIt last );
   template< class RandomIt, class Compare > (1) (since C++11)
   bool is_heap( RandomIt first, RandomIt last, (until C++20)
   Compare comp );
   template< class RandomIt, class Compare >
   constexpr bool is_heap( RandomIt first, RandomIt (3) (since C++20)
   last, Compare comp );
   template< class ExecutionPolicy, class RandomIt,
   class Compare > (4) (since C++17)
   bool is_heap( ExecutionPolicy&& policy, RandomIt
   first, RandomIt last, Compare comp );
   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>>
   (until C++20)
   std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>
   (since C++20) is true.

Parameters
   first, last - the range of elements to examine
   policy - the execution policy to use. See execution policy for details.
                  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);
   comp -
                  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
// Run this code
 #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 │

See also
   is_heap_until finds the largest subrange that is a max heap
   (C++11) (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 checks if the given range is a max heap
   (C++20) (niebloid)