Heaps

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Heaps
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What is a Heap?

• A heap is another specialized form of a binary
  tree.
• In a heap, every descendant of a node is smaller
  than that node (maxheap) or larger than that node
  (minheap).
• Since this is also a data structure based on
  comparisons, objects in the heap must also be
  Comparable.

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Heap Operations

• public void add (Comparable c)
• public Comparable removeMax()
• public Comparable getMax()
• public boolean isEmpty()
• public int getSize()
• public void clear()

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This is not The Heap

• Unlike the stack, The Heap where java objects
  are stored is not an instance of this ADT.

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Array Based Implementation

• Although a heap is a special instance of a binary
  tree, it has the added benefit of also being a
  complete binary tree.
• This means that we can store the tree in an array
  in a most convenient fashion.

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Calculating Hierarchy

• Since the tree is complete, we can locate either
  the children or the parent of any node by using a
  simple computation on the nodes number.
• The children of a node (if any) are located at 2i
  and 2i1.
• The parent of a node (excluding the root, of
  course) is at i/2.

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Basic Concepts

• To add to the heap, add at the last index and
  bubble up
• To remove from the heap, swap the last index and
  the first, and bubble down.