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| Category: algorithms | | Component type: function |
Prototype
Push_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);
Description
Push_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 functors 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 RandomAccessIterator.
-
RandomAccessIterator is mutable.
-
RandomAccessIterator's value type is a model of LessThanComparable.
-
The ordering on objects of
RandomAccessIterator's value type is a strict weak ordering, as defined in the LessThanComparable requirements.
For the second version:
-
RandomAccessIterator is a model of RandomAccessIterator.
-
RandomAccessIterator is mutable.
-
StrictWeakOrdering is a model of StrictWeakOrdering.
-
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 RandomAccessIterator [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.
See also
make_heap, pop_heap, sort_heap, is_heap, sort
