堆（Heap）和二叉堆（Binary heap）

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堆（Heap）：

The operations commonly performed with a heap are:

• create-heap: create an empty heap
• heapify: 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 (aka, peek)
• 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.
• meld(h1,h2): Return the heap formed by taking the union of the item-disjoint heaps h1 and h2. Melding destroys h1 and h2.
• size: return the number of items in the heap.
• isEmpty(): returns true if the heap is empty, false otherwise.
• ExtractMin() or ExtractMax(): Returns the node of minimum value from a min heap [or maximum value from a max heap] after removing it from the heap
• Union(): Creates a new heap by joining two heaps given as input.
• Shift-up: Move a node up in the tree, as long as needed (depending on the heap condition: min-heap or max-heap)
• Shift-down: Move a node down in the tree, similar to Shift-up

二叉堆（Binary heap）

A binary heap is a heap data structure created using a binary tree. It can be seen as a binary tree with two additional constraints:

Shape property

A binary heap is a complete binary tree; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right.

Heap property

All nodes are either greater than or equal to or less than or equal to each of its children, according to a comparison predicate defined for the heap.

Heaps with a mathematical "greater than or equal to" (≥) comparison predicate are called max-heaps; those with a mathematical "less than or equal to" (≤) comparison predicate are called min-heaps. Min-heaps are often used to implement priority queues.

堆（Heap）和二叉堆（Binary heap）

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原文地址：http://www.cnblogs.com/utank/p/4286263.html