Unit 11: Data Structures

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Unit 11 Data Structures

• We explore some simple techniques for organizing
  and managing information
• This unit focuses on
• Abstract Data Types (ADTs)
• queues
• stacks
• dynamic structures
• linked lists

syllabus
basic programming concepts
object oriented programming
topics in computer science
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Abstract Data Types

• An abstract data type (ADT) is an organized
  collection of information and a set of operations
  used to manage that information
• The set of operations define the interface to the
  ADT
• As long as the ADT accurately fulfills the
  promises of the interface, it doesn't really
  matter how the ADT is implemented

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Queues

• A queue is similar to a list but adds items only
  to the end of the list and removes them from the
  front
• It is called a FIFO data structure First-In,
  First-Out
• Analogy a line of people at a bank tellers
  window

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Interface for ADT Queue

• public interface Queue
• public int size()
• public boolean isEmpty()
• public Object front()
• throws QueueEmptyException
• public void enqueue(Object o)
• public Object dequeue()
• throws QueueEmptyException

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Stacks

• A stack ADT is also linear, like a list or queue
• Items are added and removed from only one end of
  a stack
• It is therefore LIFO Last-In, First-Out
• Analogy a stack of plates

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Stacks

• Stacks are often drawn vertically

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Interface for ADT Stack

• public interface Stack
• public int size()
• public boolean isEmpty()
• public Object peek()
• throws StackEmptyException
• public void push(Object o)
• public Object pop()
• throws StackEmptyException

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Push Implementation
elements
top 5
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Push Implementation
obj
elements
if (isFull()) throw Exception
top 5
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Push Implementation
obj
elements
if (isFull()) throw Exception elementstop
obj
top 5
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Push Implementation
elements
if (isFull()) throw Exception elementstop
obj top
top 6
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Queue Implementation - Musical Chairs

• Use an array of size n, and a rear index
• Elements are always inserted to rear
• Elements are removed from front, all other
  elements move as in musical chairs

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Circular Queue - Insert
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Circular Queue - Insert
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Circular Queue - Insert
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Circular Queue - Insert
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Circular Queue - Remove
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Circular Queue - Remove
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Circular Queue - Insert
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Circular Queue - Insert
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Circular Queue - Insert
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Circular Queue - Insert
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Circular Queue - Insert
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Circular Queue - Remove
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Circular Queue - Insert
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Circular Queue - Insert
what will happen if we add one more element?
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Circular Queue - Operations

• front and rear are always incremented modulu n
• queue is full if (rear 1) n front
• queue is empty if rear front
• in an array of size n, only n-1 cells can be
  utilized

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Static vs. Dynamic Structures

• A static data structure has a fixed size (this
  meaning is different than those associated with
  the static modifier)
• Arrays are static once you define the number of
  elements it can hold, it doesnt change
• A dynamic data structure grows and shrinks as
  required by the information it contains
• Example of dynamic data structures linked lists

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Object References

• Object reference is a variable that stores the
  address of an object
• A reference can also be called a pointer
• They are often depicted graphically

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References as Links

• Object references can be used to create links
  between objects
• Suppose a Student class contained a reference to
  another Student object

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References as Links

• References can be used to create a variety of
  linked structures, such as a linked list

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Generic Node Class

• class Node
• private Object element
• private Node next
• // two overloaded constructors
• public Node()
• this(null,null)
• public Node(Object element, Node next)
• this.element element
• this.next next
• // functionality methods
• void setElement(Object element) // ...
• void setNext(Node next) // ...
• Object getElement() // ...
• Node getNext() // ...

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A Linked Node Chain
head
null
next
element
SingleLinkedList
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Stack Implementation linked list
null
top
size 0
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push(Object obj)
top
size 0
obj
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push(Object obj) Node n new Node()
push(Object obj)
top
size 0
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj)
top
size 0
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj) n.setNext(top)
top
size 0
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj) n.setNext(top) top n
top
size 0
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj) n.setNext(top) top n
size
top
size 1
n
obj
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top
size 1
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push(Object obj)
top
size 1
obj
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push(Object obj) Node n new Node()
top
size 1
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj)
top
size 1
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj) n.setNext(top)
top
size 1
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj) n.setNext(top) top n
top
size 1
n
obj
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push(Object obj) Node n new Node()
n.setElement(obj) n.setNext(top) top n
size
top
size 2
n
obj
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top
size 2
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Object pop() if (isEmpty()) throw Exception
top
size 2
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Object pop() if (isEmpty()) throw
Exception Object temp
top
size 2
temp
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Object pop() if (isEmpty()) throw
Exception Object temp temp
top.getElement()
top
size 2
temp
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Object pop() if (isEmpty()) throw
Exception Object temp temp
top.getElement() top top.getNext()
top
size 2
temp
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Object pop() if (isEmpty()) throw
Exception Object temp temp
top.getElement() top top.getNext() size--
top
size 1
temp
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Object pop() if (isEmpty()) throw
Exception Object temp temp
top.getElement() top top.getNext()
size-- return temp
top
size 1
temp
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top
size 1
temp
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top
size 1
temp
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top
size 1
temp
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push() pop() size() ...
interface Stack
ArrayStack implements Stack ArrayStack(int
size) push() throws StackFullException pop()
isFull() size() ...
SinglyLinkedStack implements Stack push()
pop() size() ...
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Using a Stack Balanced Strings

• A single character string which is not an opening
  or a closing character is a balanced string
• If the strings s1 and s2 are balanced, then s1
  s2 (i.e., the concatenation of s1 and s2) is a
  balanced string
• If a string s is balanced , and cop,ccl is a
  matching pair of opening and closing characters,
  then cop s ccl is a balanced string

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Balanced String Verification Algorithm

• boolean isBalanced(String str)
• for each character c in str0 ... strlength-1
  
• if c is an opening character then
• push it onto the stack
• if c is a closing character then
• if the stack is empty, return false
• else // stack not empty
• pop the topmost character t from
  the stack
• if t and c do not match return
  false
• otherwise // c is not a closing character
• do nothing (skip the character).
• if the stack is empty, return true, else return
  false.

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Using a Queue ComputationSimulation

• public abstract void computeOneStep() - Performs
  a single computation step
• public abstract boolean isCompleted() - Returns
  true if the computation is completed, false
  otherwise
• public Object getResult() - Returns the result of
  this computation, null if computation is not
  completed

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An Iteration of a Time Sharing Machine
computation queue
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computation queue
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computation queue
K times
computeOneStep()
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computation queue
?
isCompleted()
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computation queue
No
?
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computation queue
?
Yes
getResult()
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Collection Classes

• The Java 2 platform contains a Collections API
• This group of classes represent various data
  structures used to store and manage objects
• Their underlying implementation is implied in the
  class names, such as ArrayList and LinkedList
• Several interfaces are used to define operations
  on the collections, such as List, Set, SortedSet,
  Map, and SortedMap

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When do we use dynamic structures?

• static
• insert and remove items from unsorted lists
• examine elements of lists

• dynamic
• insert and remove items from sorted lists
• length of list can change in orders of magnitude