CSC 212

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CSC 212

• Trees Recursion

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Announcements

• Midterm grades were generally good
• Wide distributions of scores, however
• Will hand back at end of class
• Will not discuss individual situations until
  office hours today

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Announcements

• Homework 3 results werenot good
• Read the homework FAQ regularly
• Do not edit my code, unless stated explicitly
• Do more tests than what Tester includes
• But definitely do tests included with Tester
• Tester checks if code compiles and meets minimum
  functionality
• Comment your code
• One assignment submitted without a name

4
Announcements

• Homework 3 results werenot good
• Can (re-)submit homework until Thursday before
  lab
• I can resend any files people submitted
• Unless you forgot to include your name
• Todays lecture includes several important
  examples of how to solve problem 3

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Trees

• Tree data structure represents a hierarchical
  relationship
• Computer directory

csc212/
murders.todo1K
homeworks/
programs/
LLQueue.java10K
DLNode.java25K
fail.txt3K
really_fail.txt2K
Tree.java20K
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Trees

• Tree data structure represents a hierarchical
  relationship
• Computer directories
• Object hierarchy

Mammal
Cat
Ape
Lion
Human
Chimpanzee
Professors
Yankee Fan
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Trees

• Tree data structure represents a hierarchical
  relationship
• Computer directory
• Object hierarchy
• Tournament

Canisius
Marist
Canisius
Marist
Fairfield
Niagra
Canisius
Siena
Fairfield
Rider
Niagra
Canisius
Manhattan
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Overloaded Term Node

• We use Node for our linked lists
• Each of the individual links are a Node
• Implement Position
• Also use Node for trees
• Each of the locations in the tree are a Node
• Still implement Position
• Node usually used for any of these items
• Class implementing Position is called Node

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Node for Trees

• Position ADT still defines single method
• element() return Object that Position stores
• When used for a tree next and prev may not
  make sense
• Instead defines parent children

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Tree Relationships

• Node A is root of the tree
• Root node is the nodeat the top or start
  oftree

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Tree Relationships

• Nodes B, C, D are childrenof Node A
• Node A is parent ofNodes B, C, D
• Node B is sibling ofNode C D
• Parent-child relationsare what define a
  treestructure

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Tree Relationships

• Nodes A, B, C, F areinternal nodes
• A node is internal ifit has 1 or more children

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Tree Relationships

• Nodes D, E, G, H, I, J Kare external nodes or
  leaves
• A node is a leaf if it hasno children
• Every node is eitherexternal or internal

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Tree Properties

• Height of tree is longest distance from leaf to
  root
• Height of this tree is 4

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Node Properties

• Depth of a node isthe number of levelsin tree
  above it
• Root depth always 0
• Depth of Node B is 1
• Depth of Node H is 2

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Tree Relationships

• Trees are a recursive structure
• Every node in the tree definesit own subtree
• Node C is the rootnode of this subtree

subtree
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Tree Relationships

• Trees and subtrees do not needto be very large
• Node D is the root of a rather boring subtree

subtree
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Binary Tree

• Binary Tree is a tree where each Node can have at
  most 2 children
• Nodes in a binary tree can have 0, 1, or 2
  children
• Refer to one child as the left child and other
  as right child

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Object-Oriented Design

• Important principle of object-oriented design is
  encapsulation
• Hide implementation details
• Rely upon already defined classes methods
• Maximizes code reusability
• Minimizes amount of testing needed
• The key is to write as little code as needed

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Implementing a Binary Tree

• Binary tree could be implemented using linked
  data structure
• public class BTNode implements Position
  protected Object elementprotected BTNode
  parent, left, right// Define constructor, get
  set methods...
• Implementation is similar to linked-list

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Link-based Binary Tree

• Conceptual Tree Actual Tree

?
B
A
C
?
?
?
D
?
?
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Vector-based implementation

• Could implement using a Vector
• Root node stored at rank 0
• Left subchild at rank 1
• Right subchild at rank 2
• Left subchilds left subchild at rank 3
• Left subchilds right subchild at rank 4
• Right subchilds left subchild at rank 5
• Right subchilds right subchild at rank 6

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Vector-based Implementation

• For a node at rank n
• Left subchild at rank (2n)1
• Right subchild at rank (2n) 2
• Need to add empty ranksfor this to work

0
1
2
5
4
3
6
9
8
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Vector-based Implementation

• Binary tree could be implemented using linked
  data structure
• public class BTNode implements Position
  protected Object elementprotected boolean
  parent, left, rightprotected int rank//
  Define constructor, get set methods...
• parent, left, right fields are true if
  parent/child exists

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Vector-based Implementation

• How should we start this implementation?
• public class BTVector extends Vector implements
  BinaryTree
• or
• public class BTVector implements BinaryTree
  protected Vector vect

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Vector-based Implementation

• How should we start this implementation?
• public class BTVector extends Vector implements
  BinaryTree
• or
• public class BTVector implements BinaryTree
  protected Vector vect

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Vector-based Implementation

• How should we start this implementation?
• public class BTVector extends LLVector implements
  BinaryTree
• Violates the encapsulation principle!
• Exposes the trees implementation
• This also violates my laziness principle
• Requires us to learn LLVectors implementation
• Need to write and test Vector Binary Tree
  methods
• Remember goal is write as little code as possible

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BTVector class

• public class BTVector implements BinaryTree /
  vect holds the nodes in the tree. /protected
  Vector vect/ size equals the number of
  elements in the tree. Empty slots mean cannot
  use vect.size(). / protected int size// No
  need to define root field public BTVector()
  vect new LLVector() size 0

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BTVector, continued

• public Position root() throws EmptyTreeException
  Position retVal nullif (size 0) throw
  new EmptyTreeException()try retVal
  (Position)(vect.elemAtRank(0)) catch
  (BoundaryViolationException e) // We know
  this exception cannot be thrown, but // the
  try-catch block is needed since the // compiler
  cannot know this.return retVal

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BTVector, continued

• public Position insertLeft(Position v, Object
  e)...if ((BTNode)v).getLeft()) throw new
  InvalidPositionException()BTNode retVal new
  BTNode()int parentRank (BTNode)v).getRank()
  retVal.setParent(true)(BTNode)v).setLeft(true)
  retVal.setRank((parentRank 2)
  1)sizetry vect.insertAtRank(retVal.getRa
  nk(), retVal) catch (Exception e) // Still
  not needed return retVal

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Viva la Laziness!

• How was LLVector implemented?
• Do you care?
• Should you care?
• Is BTVector a good class name?

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Binary Search Tree

• Binary Search Trees are specialization of a
  Binary Tree
• BSTs order the data in its nodes
• Left child defines subtree whose nodes store
  elements with value less than the parent node
• Right child define subtree with greater elements

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• Position recursiveInsert(Position node, String
  name)Position child// For class, we will
  assume tree is not empty// Returns -1 if less,
  0 if equal, 1 if greaterif (name.compareTo((Str
  ing)node.element()) lt 0) child
  left(node)else child right(node)if (child
  ! null) return recursiveInsert(child,
  name)else if (name.compareTo((String)node.elemen
  t())lt0) return insertLeft(node, name)else
  return insertRight(node, name)

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Binary Tree Implementation

• How is the Binary Tree implemented?
• How do you know?
• Did it matter?

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• Position recursiveInsert(Position node, String
  name)Position child// For class, we assume
  the tree is not empty and // ignore handling
  exceptions.// Returns -1 if less, 0 if equal,
  1 if greaterif (name.compareTo((String)node.eleme
  nt()) lt 0) child left(node)else child
  right(node)if (child ! null) return
  recursiveInsert(child, name)else if
  (name.compareTo((String)node.element())lt0)
  return insertLeft(node, name)else return
  insertRight(node, name)
• Works with any binary tree implementation!

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Daily Quiz

• Build binary trees representing tournaments of 1,
  2, 4, 8, 16
• How many games must the champion win?
• How many games are played in total?
• Are there/what are the relationships between
• Number of teams
• Total number of games played
• Number of games team must win to win tournament