PriorityQueue: Tree Implementation
- Enumerate the structure and order properties of the binary heap.
We are going to explore a tree-based implementation of PriorityQueue. This implementation is called a Binary Heap (or simply a Heap).
A heap has the following properties:
- Structure (shape) property: heap is a complete binary tree.
The structure property implies the height of the tree is $\Omicron(\lg n)$.1
- Order (heap) property: the element stored at each node has a higher priority (is considered "better") than its children.
The order property implies the "best" element is always at the root.
1 We know the height of a perfect binary tree is $\Omicron(\lg n)$. We should prove the complete binary tree also has a logarithmic height. We'll leave that to you to justify this. The proof is not difficult but it is beyond the scope of this course.