Lecture 017

Heap

A heap is a balanced binary tree

Shape of Heap:

• 

• Highest priority at root

• perfectly balanced

• 

• 

Heap the word:

• a type of binary tree

• priority queue where priorities are integers

  • min-heap: smaller = high priority (mostly)
  • max-heap: bigger = high priority

• allocated memory

Sifting Up (adding elements)

1. added element in one place that maintain the shape invariants
2. swap with its parent until violation is fixed
3. There is always at most one violation

Swapping(Sifting) Down (removing elements O(log n))

1. remove element on the root
2. swap right most leaf to maintain shape
3. swap root with its child with highest priority
4. This guarantees there are always at most two violations

Implementation

Arithmetic to Navigate the Tree

In practice:

• stack unbounded

• queues can be either

• priority queues are often bounded