CS187 Programming with Data Structures 9' Trees all kinds

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CS187 Programming with Data Structures9. Trees
(all kinds)

• Oliver Brock
• UMass Amherst
• Spring 2009

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Overview (mostly for people who missed class)

• In this class (or classes) we will do the
  following
• Repeat what we know about trees
• Traverse trees
• Learn about the following data structures
• Binary Search Trees
• Heaps
• Priority Queues
• http//webpages.ull.es/users/jriera/Docencia/AVL/A
  VL20tree20applet.htm

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(No Transcript)
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Terminology

• gtgtDefinition?ltlt
• Root
• Leaf
• Node
• Child
• Parent
• Sibling

• arity
• full
• complete
• pre/in/post order traversal

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From previous classes

• Implementation of binary tree
• Different traversals
• (Remember the relationship with stacks and
  queues?)

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Binary Search Tree Example
How does the definition of a binary tree change
for a binary search tree?
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Search Tree Interface from the textbook
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Binary Search Tree
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Methods of BST

• find
• insert (called add in the textbook)
• delete
• deleted node has no children (easy)
• deleted node has one child (easy)
• deleted node has two children
• Left child has no right child use child to
  overwrite deleted node
• Otherwise find largest node in right subtree
  (how?) and move it to deleted node

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Removing the Rat
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Heap
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Methods of Heaps

• insert
• remove (only highest priority item)
• find? lets see

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Inserting an Item into a Heap
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Removing an Item from a Heap
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Implementing a Heap as an ArrayList
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Properties of Heaps

• Always complete (why?)
• How can we find an element?
• How do we have to change the definition of BST?
• if node has index p then left child is at 2p1
  and right child is at 2p2 (why?)

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Inserting into a Heap Implemented as an ArrayList
(continued)
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Priority Queue
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Questions

• When would you use a BST?
• When would you use a PQ?
• Can you implement a PQ using a BST?