# pop_heap

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 function object `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 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)` 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 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.

[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`

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