# push_heap

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 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.

### See also

`make_heap`, `pop_heap`, `sort_heap`, `is_heap`, `sort`

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