# what is a binary heap?

Frederik Vig

Greenhorn

Posts: 1

Svend Rost

Ranch Hand

Posts: 904

posted 10 years ago

Hi,

A binary heap is a complete binary tree.

Let me elaborate:

- It's a heap, so every node n (other than the root), is greater than it's

parent.

- It's a complete binary tree, that is it's a tree T, where all the levels

in the tree have the maximum number of nodes possible.

Example:

Feel free to reply back, if you need further explaination.

/Svend Rost

A binary heap is a complete binary tree.

Let me elaborate:

- It's a heap, so every node n (other than the root), is greater than it's

parent.

- It's a complete binary tree, that is it's a tree T, where all the levels

in the tree have the maximum number of nodes possible.

Example:

Feel free to reply back, if you need further explaination.

/Svend Rost

Adam Vinueza

Ranch Hand

Posts: 76

posted 10 years ago

Another way of talking about a binary heap is as a binary tree which has the property of being

The space property of binary heaps makes them complete binary trees,

Any decent data structures text should have basic information on binary heaps. They're usually just called heaps in your more basic texts, and are often discussed in the context of sorting, because binary heaps provide an efficient means for sorting items. A very good and comprehensive discussion is in the chapter on Heapsort in the big Intro to Algorithms book by Cormen et al.

[ May 31, 2005: Message edited by: Adam Vinueza ]

*heap-ordered*and*left-to-right filled*. A tree is heap-ordered if, given an ordering operator, the parent node is no later in the ordering than its children. Being left-to-right filled means that if there is a space available on a level, nodes are added left-to-right.The space property of binary heaps makes them complete binary trees,

*except possibly for the lowest level*. It is the heap property that makes them heaps.Any decent data structures text should have basic information on binary heaps. They're usually just called heaps in your more basic texts, and are often discussed in the context of sorting, because binary heaps provide an efficient means for sorting items. A very good and comprehensive discussion is in the chapter on Heapsort in the big Intro to Algorithms book by Cormen et al.

[ May 31, 2005: Message edited by: Adam Vinueza ]