Priority Queues

The ADT

• A homogenous collection of Comparable Objects
• Operations
• void insert (const Comparable & x) inserts object x into the queue
• void deleteMin ( ) removes the element with minimum priority
• void deleteMin (Comparable &x) removes the element with minimum
  priority and returns it in x
• const Comparable & findMin ( ) const returns the minimum element
• bool isEmpty ( ) const
• bool isFull ( ) const
• void makeEmpty ( )
• construct from an initial set of element
  
  

Possible Implementations

1. Sorted List   -- too slow
2. Binary Search Tree -- overkill
3. Balanced Binary Search Tree (a later topic)

Binary Heaps

A complete binary tree with the additional property that at every vertex,
neither child is smaller than the vertex.  ( a partial ordering)

Concepctually a complete binary tree, but implemented as an array.

Properties -- for vertex at index i

• left child is at index 2i
• right child is at index 2i + 1
• parent is at |_ i / 2_|