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| Category: algorithms | | Component type: function |
Prototype
Pop_heap is an overloaded name; there are actually two pop_heap functions.
template <class RandomAccessIterator>
void pop_heap(RandomAccessIterator first, RandomAccessIterator last);
template <class RandomAccessIterator, class StrictWeakOrdering>
inline void pop_heap(RandomAccessIterator first, RandomAccessIterator last,
StrictWeakOrdering comp);
Description
Pop_heap removes the largest element (that is, *first) from the heap [1] [first, last). The two versions of pop_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 of pop_heap is that is_heap(first, last-1) is true and that *(last - 1) is the element that was removed from the heap. The postcondition for the second version is that is_heap(first, last-1, comp) is true and that *(last - 1) is the element that was removed from the heap. [2]
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) is a heap. That is, is_heap(first, last) 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, comp) is true.
Complexity
Logarithmic. At most 2 * log(last - first) comparisons.
Example
int main()
{
int A[] = {1, 2, 3, 4, 5, 6};
const int N = sizeof(A) / sizeof(int);
make_heap(A, A+N);
cout << "Before pop: ";
copy(A, A+N, ostream_iterator<int>(cout, " "));
pop_heap(A, A+N);
cout << endl << "After pop: ";
copy(A, A+N-1, ostream_iterator<int>(cout, " "));
cout << endl << "A[N-1] = " << A[N-1] << endl;
}
The output is
Before pop: 6 5 3 4 2 1
After pop: 5 4 3 1 2
A[N-1] = 6
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.
[2] Pop_heap removes the largest element from a heap, and shrinks the heap. This means that if you call keep calling pop_heap until only a single element is left in the heap, you will end up with a sorted range where the heap used to be. This, in fact, is exactly how sort_heap is implemented.
See also
make_heap, push_heap, sort_heap, is_heap, sort
