CS5539 Data Structures and Algorithms

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CS5539Data Structures and Algorithms

• Lecture 15
• Linear Structures

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Queues

• A queue is a sequence of elements where
• Nodes can only be removed from the head/front
• Nodes can only be added to the tail/end
• A queue is thus a first-in, first-out structure
  (FIFO)
• A queue has a length
• the number of elements it contains
• If a queue is empty it has length zero

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Reading

• Watt and Brown Chapter 7 Queues
• Watt and Brown Chapter 8 Lists

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Queue Behaviour
no queue
front back 0 elements
Fred
Fred joins queue
front back Fred 1 element
Joe joins queue
front Fred back Joe 2 elements
Harry joins queue
front Fred back Harry 3 elements
Fred catches bus
front Joe back Harry 2 elements
Barney joins queue
front Joe back Barney 3 elements
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Typical Operations

• OPERATION PRE-CONDITION POST-CONDITION
• append (Object item)q not full queue1,
• item added at end queue
• remove() q not empty queue 1, item at
  front removed
• front() q not empty queue same
• isEmpty() none queue same
• back() q not empty queue same
• isFull() none queue same

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Specification of a Queue ADT

• Associated ADTs Boolean, Element

• Operations
• create Queue
• append Element Queue Queue
• front Queue Element
• remove Queue Queue
• isEmpty Queue Boolean

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Specification of a Queue ADT

• Requirements
• isEmpty(create) true
• For every x,q isEmpty(append(x,q)) false
• front(append(x,create)) x
• For every x,q!create front(append(x,q))
  front(q)
• remove(append(x,create)) create
• For every x,q!create remove(append(x,q))
  append(x,remove(q))

• Exceptions
• front(create) is illegal
• remove(create) is illegal

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Linked List Implementation

• public class Queue
• private class SLLnode
• Object element
• SLLnode succ
• private SLLnode(Object element, SLLnode succ)
• this.element element
• this.succ succ
• private SLLnode front, rear
• // The methods go here ...

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Array Implementation

• public class Queue
• private Object items
• private int length, front, back
• public queue (int maxsize)
• items new Object maxsize
• length 0
• front 0
• rear 0

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Methods (Array Implementation)

• public void append(Object item)
• if (length items.length) makeLonger()
• itemsrear item
• if (rear items.length)
• rear 0
• length

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Methods (Array Implementation)

• public Object remove()
• if (length 0)
• throw new NoSuchElementException()
• Object firstItem itemsfront
• itemsfront null
• if (front items.length)
• front 0
• length--
• return firstItem

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Methods (Array Implementation)

• public Object front()
• if (length 0)
• throw new NoSuchElementException()
• return itemsfront
• public boolean isEmpty()
• return (length 0)

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Array Implementation
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Lists

• Operations on a list vary according to
  application
• There may be more than one operation of the same
  name but with different number and types of
  parameters
• eg
• adding a new item at a specific position
• this needs 2 parameters position and element
• adding a new item at the end
• this needs 1 parameter element

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Lists Implementation

• Array
• Means maximum size bounded list
• Linked List
• Any size unbounded list but requires links to
  both first and last elements

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Time Complexities and Implementations
Array O(1) O(1) O(1) O(n) O(n)
Linked list O(n) O(n) O(1) O(n) O(n)

• Operation
• get
• set
• add at end
• addanywhere
• remove