# sort_heap

Category: algorithms | Component type: function

### Prototype

`Sort_heap` is an overloaded name; there are actually two `sort_heap` functions.

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

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

### Description

`Sort_heap` turns a heap [1] `[first, last)` into a sorted range. Note that this is not a stable sort: the relative order of equivalent elements is not guaranteed to be preserved.

The two versions of `sort_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`.

### Definition

Defined in the standard header algorithm, and in the nonstandard backward-compatibility header algo.h.

### Requirements on types

For the first version, the one that takes two arguments:

- `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, the one that takes three arguments:

- `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, the one that takes two arguments:

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

For the second version, the one that takes three arguments:

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

### Complexity

At most `N * log(N)` comparisons, where `N` is `last - first`.

### Example

    int main()
    {
      int A[] = {1, 4, 2, 8, 5, 7};
      const int N = sizeof(A) / sizeof(int);

      make_heap(A, A+N);
      copy(A, A+N, ostream_iterator<int>(cout, " "));
      cout << endl;

      sort_heap(A, A+N);
      copy(A, A+N, ostream_iterator<int>(cout, " "));
      cout << endl;
    }

### 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.

### See also

`push_heap`, `pop_heap`, `make_heap`, `is_heap`, `sort`, `stable_sort`, `partial_sort`, `partial_sort_copy`

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