Chapter 15: Advanced Topics:
Introducing Data Structures
and Recursion
Visual Basic .NET Programming: From
Problem Analysis to Program Design
Objectives
• Create linked lists
• Create a stack
• Create a queue
• Understand recursion
• Write recursive methods
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Introducing Data Structures
• Linked list
– List of object instances that are linked together
– Objects may be added to:
• Beginning
• End
• Somewhere in between
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Introducing Data Structures
(continued)
• Stack
– Can be implemented as specialized case of linked
list
– Objects are added and removed only at beginning
of list
– Employs LIFO logic
• Last in, first out
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Introducing Data Structures
(continued)
• Queue
– Implemented as linked list
– Objects added at end and removed from beginning
– Employ FIFO logic
• First in, first out
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Creating Linked Lists
• Node
– Each instance in linked list contains
• Data
• Reference attribute linking it to next node
• Maintain references to first and last item in list
– To facilitate access
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Creating Linked Lists
(continued)
• Self-referencing class
– Class that references instances of itself
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Creating a Stack
• Stack can be implemented as LinkedList
– LIFO structure:
• Add and remove nodes from only beginning of
Stack
– Employ inheritance to create Stack class
• As subclass of LinkedList
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Exploring the FCL Stack Class
• Stores nodes as instances of Object
• Methods:
– Push
– Pop
– Peek
– ToArray
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Creating a Queue
• Queue can be implemented as linked list
• Objects added only at end
• Removed only from beginning
– Employing FIFO logic
• Enqueue
– Add object
• Dequeue
– Remove object
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Creating a Queue (continued)
• Placing common attributes and methods in
superclass eliminates redundancy in subclasses
– Count and IsEmpty added to superclass
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Exploring the FCL Queue class
• Queue class
– Stores nodes as instances of Object
• Methods:
– Enqueue
– Dequeue
– Peek
– ToArray
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Programming Example:
Reservation Application
• Implements reservation system
• Reservation class methods:
– MakeReservation
– CancelReservation
– ListReservations
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Understanding Recursion
•
•
•
Programming technique in which method calls
itself
For some problems recursive approach leads to
simple and elegant solution
Recursive problem-solving approach
– Divides complex problem into successively
smaller but similar subproblems
– Solves each subproblem
– Assembles result
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Example 15-8: Using a
Recursive Method to Simulate
Opening Boxes
Module OpenBoxesRecursively
Sub Main()
'open largest box (size 10)
OpenBox(10)
System.Console.WriteLine(”Done”)
End Sub
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Example 15-8: Using a
Recursive Method to Simulate
Opening Boxes (continued)
Sub OpenBox(ByVal boxSize As Integer)
If boxSize = 0 Then
System.Console.WriteLine(”No more boxes”)
Else
System.Console.WriteLine(”Box “ & boxSize & _
“ opened”)
OpenBox(boxSize - 1)
End If
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(Continued)
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Example 15-8: Using a
Recursive Method to Simulate
Opening Boxes (continued)
•
Recursive algorithm must have stopping point
– Called base case
– When encountered, recursion stops
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Example 15-8: Using a
Recursive Method to Simulate
Opening Boxes (continued)
•
Each time recursive method calls itself
– Fresh copy of the method created
– Each copy has own set of values and parameters
– Remains unfinished until base case is recognized
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Example 15-8: Using a
Recursive Method to Simulate
Opening Boxes (continued)
•
Upon each return
– Execution resumes within that copy at line of
code immediately following recursive call
•
Recursion is similar to iteration
– Any problem that can be solved iteratively can
also be solved recursively, and vice versa
– Recursive solutions are less efficient
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Writing Recursive Methods
• Write recursive method:
– Must think recursively
– Think of problem in terms of series of successively
smaller but virtually identical subproblems
– Smallest subproblem must be one that can be
solved directly
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Computing Factorials
• Classic example of recursion involves computing
factorials
• Definition:
– n! = n * (n – 1) * (n – 2) * . . . * 1, where n is a
positive integer
– 0! = 1
• Thinking recursively:
– 4! can be defined as 4 * 3!
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Computing Factorials
(continued)
• Calculating factorials can produce a number that is
too large to be represented in memory space
allocated to a particular variable
– 12! is largest factorial that can be computed using
Integer data type to hold result
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(Continued)
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Displaying a Directory Tree
• Generate and display tree containing directories
and subdirectories on hard drive
• Depending on size of your hard drive and speed of
your computer
– Initially creating directory tree may take a few
minutes
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Sorting an Array
• Recursive methods are frequently used for array
processing
• Quicksort
– Recursive technique for sorting one-dimensional
array
– Begins by selecting array element to serve as pivot
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Sorting an Array (continued)
• Quicksort (continued)
– Position pivot such that
• All array elements to right are greater than or equal
to pivot
• All array elements to left are less than or equal to
pivot
– Elements to right and left of pivot form subarrays
• Sort them using Quicksort
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Programming Example:
Towers of Hanoi
• Classic computer science problem
• Priests in Far Eastern temple were given task of
moving stack of 64 disks from one pole to another
• Each disk was slightly different size
– Disks were arranged on pole from top to bottom in
order of increasing size
– Intermediate pole also available to hold disks
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Programming Example:
Towers of Hanoi (continued)
• Priests were to move all 64 disks to third pole
using the following rules:
– Only one disk can be moved at a time
– Removed disk must be placed on one of other poles
– Under no circumstance may larger disk be placed
upon smaller disk
• Priests were told that world would end when they
completed their task
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Programming Example:
Towers of Hanoi (continued)
• Recursive algorithm:
– Move top n-1 disks from pole 1 to pole 2, using
pole 3 to temporarily hold disks
– Move bottom (nth) disk from pole 1 to pole 3
– Move n-1 disks on pole 2 to pole 3, using pole 1 to
temporarily hold disks
• Number of moves required to move the disks is
264-1
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Summary
• Linked list
– List of object instances that are linked together
– Each instance is called a node
• Stack
– Can be implemented as special form of LinkedList
– LIFO structure
– FCL provides Stack class
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Summary (continued)
• Queue
– Implemented as linked list with objects added at
end and removed from beginning
– Employ FIFO logic
– FCL includes Queue class
• Recursive problem-solving approach
– Divides problem into series of smaller problems
– Solves each subproblem
– Assembles result
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