Online Programming Server

 In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: If A is a parent node of B then key(A) is ordered with respect to key(B) with the same ordering applying across the heap. Either the keys of parent nodes are always greater than or equal to those of the children and the highest key is in the root node (this kind of heap is called max heap) or the keys of parent nodes are less than or equal to those of the children (min heap).
Note that, as shown in the graphic, there is no implied ordering between siblings or cousins and no implied sequence for an in-order traversal (as there would be in, e.g., a binary search tree). The heap relation mentioned above applies only between nodes and their immediate parents.
The maximum number of children each node can have depends on the type of heap, but in many types it is at most two. The heap is one maximally efficient implementation of an abstract data type called a priority queue. Heaps are crucial in several efficient graph algorithms such as Dijkstra's algorithm, and in the sorting algorithm heapsort.
A heap data structure should not be confused with the heap which is a common name for dynamically allocated memory. The term was originally used only for the data structure.

Heaps are usually implemented in an array, and do not require pointers between elements.

The operations commonly performed with a heap are:

    create-heap: create an empty heap
    (a variant) create-heap: create a heap out of given array of elements
    find-max or find-min: find the maximum item of a max-heap or a minimum item of a min-heap, respectively
    delete-max or delete-min: removing the root node of a max- or min-heap, respectively
    increase-key or decrease-key: updating a key within a max- or min-heap, respectively
    insert: adding a new key to the heap
    merge: joining two heaps to form a valid new heap containing all the elements of both.

Different types of heaps implement the operations in different ways, but notably, insertion is often done by adding the new element at the end of the heap in the first available free space. This will tend to violate the heap property, and so the elements are then reordered until the heap property has been reestablished. Construction of a binary (or d-ary) heap out of given array of elements may be preformed faster than a sequence of consecutive insertions into originally empty heap using the classic Floyd's algorithm, with the worst-case number of comparisons equal to 2N - 2s2(N) - e2(N) (for a binary heap), where s2(N) is the sum of all digits of the binary representation of N and e2(N) is the exponent of 2 in the prime factorization of N.