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push_heap

push_heap PrototypePush_heap is an overloaded name; there are actually two push_heap functions.

template <class RandomAccessIterator>
void push_heap(RandomAccessIterator first, RandomAccessIterator last);

template <class RandomAccessIterator, class StrictWeakOrdering>
void push_heap(RandomAccessIterator first, RandomAccessIterator last,
               StrictWeakOrdering comp);

DescriptionPush_heap adds an element to a heap [1]. It is assumed that [first, last - 1) is already a heap; the element to be added to the heap is *(last - 1).

The two versions of push_heap differ in how they define whether one element is less than another. The first version compares objects using operator<, and the second compares objects using a function object comp. The postcondition for the first version is that is_heap(first, last) is true, and the postcondition for the second version is that is_heap(first, last, comp) is true.

Definition Defined in the standard header algorithm, and in the nonstandard backward-compatibility header algo.h. Requirements on types For the first version:

RandomAccessIterator is a model of Random Access Iterator.
RandomAccessIterator is mutable.
RandomAccessIterator's value type is a model of LessThan Comparable.
The ordering on objects of RandomAccessIterator's value type is a strict weak ordering, as defined in the LessThan Comparable requirements.

For the second version:

RandomAccessIterator is a model of Random Access Iterator.
RandomAccessIterator is mutable.
StrictWeakOrdering is a model of Strict Weak Ordering.
RandomAccessIterator's value type is convertible to StrictWeakOrdering's argument type.

Preconditions For the first version:

[first, last) is a valid range.
[first, last - 1) is a valid range. That is, [first, last) is nonempty.
[first, last - 1) is a heap. That is, is_heap(first, last - 1) is true.

For the second version:

[first, last) is a valid range.
[first, last - 1) is a valid range. That is, [first, last) is nonempty.
[first, last) is a heap. That is, is_heap(first, last - 1, comp) is true.

Complexity Logarithmic. At most log(last - first) comparisons. Example

int main()
{
  int A[10] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };

  make_heap(A, A + 9);
  cout << "[A, A + 9)  = ";
  copy(A, A + 9, ostream_iterator<int>(cout, " "));
  
  push_heap(A, A + 10);
  cout << endl << "[A, A + 10) = ";
  copy(A, A + 10, ostream_iterator<int>(cout, " "));
  cout << endl;
}

The output is

[A, A + 9)  = 8 7 6 3 4 5 2 1 0 
[A, A + 10) = 9 8 6 3 7 5 2 1 0 4

Notes

[1] A heap is a particular way of ordering the elements in a range of random access iterators [f, l). The reason heaps are useful (especially for sorting, or as priority queues) is that they satisfy two important properties. First, *f is the largest element in the heap. Second, it is possible to add an element to a heap (using push_heap), or to remove *f, in logarithmic time. Internally, a heap is a tree represented as a sequential range. The tree is constructed so that that each node is less than or equal to its parent node.

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