Download Java Classes

A Binary Search
Tree
Implementation
Chapter 27
Slides by Steve Armstrong
LeTourneau University
Longview, TX
2007, Prentice Hall
Chapter Contents
• Getting Started
 An Interface for the Binary Search Tree
 Duplicate Entries
 Beginning the Class Definition
• Searching and Retrieving
• Traversing
• Adding an Entry
 Recursive Implementation
 Iterative Implementation
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Chapter Contents
• Removing an Entry …






Whose Node is a leaf
Whose Node Has One Child
Whose Node has Two Children
In the Root
Recursive Implementation
Iterative Implementation
• Efficiency of Operations
 Importance of Balance
 Order in Which Nodes Are Added
• Implementation of the ADT Dictionary
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Getting Started
• A binary search tree is a binary tree
 Nodes contain Comparable objects
• For each node in the tree
 The data in a node is greater than the data in
the node's left subtree
 The data in a node is less than the data in the
node's right subtree
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Getting Started
Fig. 27-1 A binary search tree of names.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
An Interface for the
Binary Search Tree
• Includes common operations of a tree
• Also includes basic database operations





Search
Retrieve
Add
Remove
Traverse
• View source code for
SearchTreeInterface
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
An Interface for the
Binary Search Tree
Fig. 27-2 Adding an entry that matches an entry
already in a binary tree … continued →
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
An Interface for the
Binary Search Tree
Fig. 27-2 Adding an entry that matches an entry
already in a binary tree.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Duplicate Entries
If duplicates are allowed,
place the duplicate in the
entry's right subtree.
Fig. 27-3 A binary search tree with duplicate entries.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Beginning the Class Definition
• View source code of BinarySearchTree
• Note
 Derived from BinaryTree
 Call by constructor to protected method
setRootNode (inherited from BinaryTree)
• Other methods
 contains
 getEntry
 add
 remove
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Searching and Retrieving
• Like performing a binary search of an
array
• For a binary array
 Search one of two halves of the array
• For the binary search tree
 You search one of two subtrees of the binary
search tree
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Searching and Retrieving
• View search algorithm
 Root node of tree or subtree enables
manipulation of descendant nodes
• Note implementation in methods
 getEntry
 findEntry
• Method contains simply calls getEntry
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Traversing
• The SearchTreeInterface provides
the method getInorderIterator
 Returns an inorder iterator
• Our class is a subclass of BinaryTree
 It inherits getInorderIterator
 This iterator traverses entries in ascending
order
 Uses the entries' method compareTo
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Adding an Entry
Fig. 27-4 (a) A
binary search tree;
(b) the same tree
after adding Chad.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Adding an Entry Recursively
Fig. 27-5 Recursively adding Chad to smaller subtrees
of a binary search tree … continued →
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Adding an Entry Recursively
Fig. 27-5 (ctd.)
Recursively adding
Chad to smaller
subtrees of a binary
search tree.
Click to view recursive
method addEntry
Click to view iterative
method addEntry
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry
• The remove method must receive an
entry to be matched in the tree
 If found, it is removed
 Otherwise the method returns null
• Three cases
 The node has no children, it is a leaf (simplest
case)
 The node has one child
 The node has two children
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry, Node a Leaf
Fig. 27-6 (a) Two possible configurations of leaf
node N; (b) the resulting two possible
configurations after removing node N.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry,
Node Has One Child
Fig. 27-6 (a) Two possible configurations of leaf node N; (b) the
resulting two possible configurations
after removing node N.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry,
Node Has Two Children
Fig. 27-8 Two possible configurations of node N
that has two children.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry,
Node Has Two Children
Fig. 27-9 Node N and its subtrees; (a) entry a is
immediately before e, b is immediately after e; (b) after
deleting the node that contained a and replacing e with a.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry,
Node Has Two Children
Fig. 27-10 The largest entry a in node N's left subtree
occurs in the subtree's rightmost node R.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry,
Node Has Two Children
Fig. 27-11 (a) A binary search tree; (b)
after removing Chad;
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry,
Node Has Two Children
Fig. 27-11 (c) after removing Sean;
(d) after removing Kathy.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Removing an Entry in the Root
Fig. 27-12 (a) Two possible configurations of a root that
has one child; (b) after removing the root.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Recursive Implementation
• Details similar to adding an entry
• The public remove method calls a private
recursive remove method
 The public remove returns removed entry
 Private remove must return root of revised tree
 Thus use parameter that is an instance of
ReturnObject to return the value the public remove
needs
• View source code for recursive implementation
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Iterative Implementation
• To locate the desired entry
 The remove method given entry to be
matched
 If remove finds the entry, it returns the entry
 If not, it returns null
• The compareTo method used to make
comparisons with the entries in the tree
• View source code for iterative
implementation
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Efficiency of Operations
• Operations add, remove, getEntry require
a search that begins at the root
• Maximum number of comparisons is
directly proportional to the height, h of the
tree
• These operations are O(h)
• Thus we desire the shortest binary search
tree we can create from the data
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Efficiency of Operations
Fig. 27-13 Two
binary search trees
that contain the
same data.
Shorter tree has
efficiency O(log n)
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Importance of Balance
• Completely balanced
 Subtrees of each node have exactly same
height
• Height balanced
 Subtrees of each node in the tree differ in
height by no more than 1
• Completely balanced or height balanced
trees are balanced
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Importance of Balance
Fig. 27-14 Some binary trees that are height balanced.
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Importance of Balance
• The order in which entries are added
affect the shape of the tree
• If entries are added to an empty binary
tree
 Best not to have them sorted first
 Tree is more balanced if entries are in random
order
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X
Implementation of the ADT
Dictionary
• Recall interface for a dictionary (Ch. 17)
• Consider an implementation of the ADT
dictionary that uses a binary search tree
• Note methods
 add
 remove
 Use of iterator
Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X