Chapter 3 Lists, Stacks, and Queues

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Chapter 3Lists, Stacks, and Queues

• Abstract Data Types (ADTs)
• Lists
• Stacks
• Queues

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Array

• An array is a data structure that holds multiple
  values of the same type.
• The length of an array is established when the
  array is created (at runtime). After creation, an
  array is a fixed-length structure.
• Array Creation
• int a
• a new int10
• int b new int10
• int c a
• int d 1, 2, 3, 4

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• Example 1 Programming with array
• public class MyData
• public static void main(String args)
• int data 1, 2, 3, 4, 5, 6, 7, 8, 9,
  10
• print(data)
• System.out.println( findMax(data) )
• System.out.println( sum(data) )
• public static void print(int d)
• for (int i 0 i lt d.length i )
• System.out.println( di )

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• public static int findMax(int d)
• int max
• for (max d0, int i 1 i lt d.length
  i)
• if (di gt max) max di
• return max
• public static int findMin(int d)
• int min
• for (min d0, int i 1 i lt d.length
  i)
• if (di gt min) min di
• return min

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• public static int sum(int d)
• int sum 0
• for (int i 0 i lt d.length i)
• sum di
• return sum

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• Example 2 Programming with a new data type
  (MyData)
• public class MyProg
• public static void main(String args)
• MyData data new Mydata()
• for (int i 0 i lt 10 i)
• data.add(i)
• data.print()
• System.out.println( data.findMax() )
• System.out.println( data.sum() )

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• public class MyData
• private int data
• private int size
• MyData()
• data new int100
• size 0
• public void add( int x )
• datasize x
• size

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• public int findMax()
• int max
• for (max data0, int i 1 i lt size i)
• if (datai gt max) max datai
• return max
• public int findMin()
• int min 0
• for (min data0, int i 1 i lt size i)
• if (datai gt min) min datai
• return min

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• public int sum()
• int sum 0
• for (int i 0 i lt size i)
• sum datai
• return sum
• public void print()
• for (int i 0 i lt size i )
• System.out.println( datai )

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Abstract Data Types (ADTs)

• Data values
• Operations to perform on the values
• Examples
• MyData ( data integer values, operations add,
  print, findMax, findMin, sum)
• Set (data members, operations union,
  intersect, isMember)
  
• String (data string of characters, operations
  print, append, find)

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Lists

• A set of data objects
• The data objects (elements) are arranged in some
  order
• Data A1, A2, A3, . . . , AN
• Operations insert, remove, find, findKth

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Array Implementation of List

• Insert
• insert(10,4)

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• Remove
• remove(52)

• printList

printList() prints 34 12 10 16 12
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• findKth

findKth(2) returns 12

• find

find(16) returns 4
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• Example 3 Array Implementation of List
• public class MyProg
• public static void main(String args)
• ListArray data new ListArray()
• for (int i 1 i lt 10 i)
• data.insert(i, i)
• data.remove( data.findMax() )
• data.printList()

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• public class ListArray
• private int data
• private int size
• ListArray()
• data new int100
• size 0
• public void insert(int x, int i)
• for (int n size n gt i n--)
• datan1 datan
• datai x
• size

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• public void remove(int x)
• int n
• for (n find(x) n ! -1 n lt size n)
• datan datan1
• size--
• public int find(int x)
• int i
• for (i 1 i lt size i)
• if (datai x) break
• if (i gt size) return -1 else return i

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• public int findKth(int k)
• return datak
• public int findMax()
• int max data1
• for (int i 2 i lt size i)
• if (datai gt max) max datai
• return max
• public void printList()
• for (int i 1 i lt size i )
• System.out.println( datai )

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Array Implementation of List

• Size of the list must be known in order to
  allocate an array with sufficient size
• All elements are adjacent in memory
• printList and find take linear time O(N)
• findKth takes constant time O(1)

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Array Implementation of List

• insert must push the tail of the list down
• remove must shift the tail of the list up
• insert and remove take linear time O(N)
• N successive inserts requires quadratic time
  O(N2)
• Expensive

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Linked Lists

• A linked list consists of nodes
  (not necessarily adjacent in memory)
• Each node contains
• data
• link (object reference) to the next node

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Linked Lists with header node
empty list
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Three Classes in Linked List
LinkedList
LinkedListItr
header
current
ListNode
ListNode
ListNode
ListNode
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Objects in Linked List
theList
theItr
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public class LinkedList private ListNode
header public LinkedList( ) public boolean
isEmpty( ) public void makeEmpty( )
public LinkedListItr zeroth( ) public
LinkedListItr first( ) public LinkedListItr
find( Object x ) public void remove( Object
x ) public LinkedListItr findPrevious(
Object x ) public void insert( Object x,
LinkedListItr p )
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class ListNode Object element ListNode
next ListNode ( Object theElement )
this( theElement, null )
ListNode ( Object theElement, ListNode n )
element theElement next
n
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public class LinkedListItr ListNode
current LinkedListItr( ListNode theNode )
current theNode public boolean isPastEnd(
) return current null public Object
retrieve( ) return isPastEnd( ) ? Null
current.element public void advance( ) if
(!isPastEnd( ) ) current current.next
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public class MyProg public static void main(
String args ) LinkedList
theList new LinkedList( )
LinkedListItr theItr theList.zeroth( )
int i printList( theList )
for( i 0 i lt 10 i )
theList.insert( new MyInteger( i ), theItr
) printList( theList )
theItr.advance( )
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for( i 0 i lt 10 i 2 ) theList.remove(
new MyInteger( i ) ) for( i 0 i lt 10 i
) if( ( i 2 0 ) ! (
theList.find( new MyInteger( i ) ).isPastEnd( ) )
) System.out.println( "Find
fails!" ) printList( theList )
// end main // end class MyProg
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Linked Lists
insert
remove
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public class LinkedList private ListNode
header public LinkedList( ) header new
ListNode( null ) public boolean isEmpty( )
return header.next null public void
makeEmpty( ) header.next null public
LinkedListItr zeroth( ) return new
LinkedListItr( header )
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public LinkedListItr first( ) return new
LinkedListItr( header.next ) public void
insert( Object x, LinkedListItr p ) if( p !
null p.current ! null ) p.current.next new
ListNode( x, p.current.next ) public
LinkedListItr find( Object x ) / 1/
ListNode itr header.next / 2/ while(
itr ! null !itr.element.equals( x ) ) / 3/
itr itr.next / 4/ return new
LinkedListItr( itr )
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public LinkedListItr findPrevious( Object x )
/ 1/ ListNode itr header / 2/
while( itr.next ! null !itr.next.element.equal
s( x ) ) / 3/ itr itr.next / 4/
return new LinkedListItr( itr ) public
void remove ( Object x ) LinkedListItr p
findPrevious( x ) if( p.current.next ! null )
p.current.next
p.current.next.next // Bypass deleted node
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public static void printList( LinkedList theList
) if( theList.isEmpty( ) ) System.out.print(
"Empty list" ) else
LinkedListItr itr theList.first( )
for( !itr.isPastEnd( ) itr.advance( )
) System.out.print(
itr.retrieve( ) " " )
System.out.println( )
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public static void main( String args )
LinkedList theList new LinkedList(
) LinkedListItr theItr
theList.zeroth( ) int i
printList( theList ) for( i 0 i lt
10 i )
theList.insert( new MyInteger( i ), theItr )
printList( theList )
theItr.advance( )
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for( i 0 i lt 10 i 2 ) theList.remove(
new MyInteger( i ) ) for( i 0 i lt 10 i
) if( ( i 2 0 ) ! (
theList.find( new MyInteger( i ) ).isPastEnd( ) )
) System.out.println( "Find
fails!" ) printList( theList )
// end main // end class LinkedList
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Linked List

• Size of the list is not known when the list is
  created
• All elements need not be adjacent in memory
• Often require less memory space than array
• printList, find and findPrevious take linear time
  O(N)
• insert and remove take constant time O(1)

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Circular linked list
Doubly linked list
Double circular linked list
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Example Polynomial

• aNxN aN-1xN-1 aN-2xN-2 . . . a1x1 a0
• P1(x) 10x1000 5x14 1
• P2(x) 3x1990 - 2x1492 11x 5
• Can be implemented by using array or linked list

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Array Implementation of Polynomial

• Array of coefficients

x0
x1
x2
x3
x4
P1(x) 15x4 x3 5x 120
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Array Implementation of Polynomial
public class Polynomial public Polynomial( )
public void insertTerm( int coef, int exp )
public void zeroPolnomial( ) public
Polynomial add( Polynomial rhs ) public
Polynomial multiply( Polynomial rhs ) public
void print( ) public static final int
MAX_DEGREE 100 private int coeffArray
new int MAX_DEGREE 1 private int highPower
0
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public Polynomial add( Polynomial rhs
) Polynomial sum new Polynomial(
) sum.highPower max( highPower, rhs.highPower
) for( int i sum.highPower igt 0 i--
) sum.coeffArray i coeffArray i

rhs.coeffarray i return sum
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Linked List Implementation of Polynomial
P1(x) 10x1000 5x14 1
P2(x) 3x1990 - 2x1492 11x 5
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Linked List Implementation of Polynomial
public class Literal int coefficient int
exponent public class Polynomial private
LinkedList terms public Polynomial( )
public void insertTerm( int coef, int exp )
public void zeroPolnomial( ) public
Polynomial add( Polynomial rhs ) public
Polynomial multiply( Polynomial rhs ) public
void print( )
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Bucket Sort

• Sort N integers in the range 1 to M
• Use M buckets, one bucket for each integer i
• Bucket i stores how many times i appears in the
  input. Initially, all buckets are empty.
• Read input and increase values in buckets
• Finally, scan the buckets and print the sorted
  list

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Bucket Sort
3, 1, 3, 5, 8, 7, 4, 2, 9, 5, 4, 10, 4
1
1
1
2
3
2
0
1
1
1
1, 2, 3, 3, 4, 4, 4, 5, 5, 7, 8, 9, 10
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Radix Sort

• Bucket sort needs M max - min 1 buckets
• If M gtgt N, lots of buckets are not used
• Radix sort needs less buckets than bucket sort
• Performs several passes of bucket sort
  one pass for each digit
• Sort by the least significant digit first

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2
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Radix Sort

• More than one (possibly different) number could
  fall into the same bucket
• When several numbers enter a bucket, they enter
  in sorted order
• Numbers in each bucket is kept in a list
• Use 10 lists

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Multilists
Problem

• A university with 40,000 students and 2,500
  courses
• First report lists, for each class, the
  registered students
• Second report lists, for each student, the
  classes that the student is registered

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Multilists
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Cursor Implementation of Linked Lists

• Instead of calling new each time a node is
  needed, lots of nodes are created at the
  beginning
• Getting a node from the collection ( alloc ) and
  returning a node to the collection ( free ) are
  implemented by the programmer

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Cursor Implementation of Linked Lists
Allocation
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Cursor Implementation of Linked Lists
Two Lists
Deallocation (free)
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public class CursorList private static int
alloc( ) private static void free( )
public CursorList( ) header alloc( )
cursorSpace header .next 0 private int
header static CursorNode cursorSpace privat
e static final int SPACE_SIZE
100 static cursorSpace new CursorNode
SPACE_SIZE for( int i 0 i lt SPACE_SIZE
iI ) cursorSpace i new CursorNode(
null, i1 ) cursorSpace SPACE_SIZE - 1
.next 0
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private static int alloc( ) int p
cursorSpace 0 .next cursorSpace 0 .next
cursorSpace p .next if ( p 0 ) throw new
OutOfMemoryError( ) return p private static
void free( int p ) cursorSpace p .element
null cursorSpace p .next cursorSpace 0
.next cursorSpace 0 .next p
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Stack
POP
5
5
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Stack

• A special kind of list
• Only the element at the end of the list (called
  the top of stack) can be operated on
• Only three operations
• PUSH put one element on the top of the stack
• POP take one element from the top of the
  stack
• TOP see the value of the element on the top
• Last In, First Out (LIFO)

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Balancing Symbols

• Check whether pairs of symbols are balanced
• Balanced ( ), , , ( ( ) ), (
  )
• Unbalanced ( (, ( ) , )

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Balancing Symbols Algorithm

• Read characters until end of file
• For an opening symbol, push it onto the stack
• For an closing symbol, pop the stack
• Report an error if
• Stack empty when trying to pop
• Popped symbol is not the corresponding opening
  symbol
• Stack is not empty when end of file is reached

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Balancing Symbols
( )
)
( ( ( ) )
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Postfix Expressions

• Normal 1 2 3 4 5
  ( ( (1 2) 3 ) 4 ) 5 65
• With Parentheses 1 ( 2 3 ) ( 4 5 )
  ( 1 ( 2 3 ) ) ( 4 5 ) 27
• Postfix Expression 1 2 3 4 5
  ( 1 ( ( 2 3 ) ( 4 5 ) ) ) 27

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Evaluation of Postfix Expressions

• When a number is seen, it is pushed onto the
  stack
• When an operator is seen, the operator is applied
  to the two numbers that are popped from the
  stack. The result is pushed onto the stack

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Postfix Expressions
Example 1 2 3 4 5
4 5
4 5



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Infix to Postfix Conversion

• Infix a b c ( d e f ) g
• Postfix a b c d e f g

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Infix to Postfix Conversion

• When an operand is seen, print it.
• When an operator is seen, pop the stack and
  print. until a lower-priority operator or ( is
  found. Then, push the operator onto the stack.
• When a ( is seen, push it onto the stack.
• When a ) is seen, pop the stack and print until a
  ( is popped. ( and ) are not printed.
• When input is empty, pop the stack and print
  until it is empty

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Infix to Postfix Conversion
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Infix to Postfix Conversion
Input a b c ( d e f ) g Output a b
c d e f g
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Method Calls
a ( ) . . . b( ) . . .
b( ) . . . c( ) . . .
c( ) . . .
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Method Calls
a . . call b . .
return
b . . call c . .
return
c . . . return
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Method Calls and Stack
a 10 . . . 11 call b 12 . . .
b 101 . . . 102 call c 103 . . .
c 223 . . . 224 return
b 102 call c 103 . . . 104 return
a 10 . . . 11 call b 12 . . .
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Method Calls

• When a call is made to a new method, the calling
  routine must save
• current location ( return address )
• register values
• local variables
• call and return are balancing symbols

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Activation Record (Stack Frame)
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Exception Handling in Java (page 16)

• Exception is a mechanism to catch errors and take
  action on the errors.
• An exception is thrown when an error condition
  occurs.
• An exception is propagated back through the
  calling sequence until some routing catches it.

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• try
• // code that might cause an exception
• statements
• catch (exception_type identifier)
• // exception handler for an exception type
• statements
• catch (exception_type identifier)
• // exception handler for another exception type
• statements

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Underflow and Overflow Exceptions

• Underflow exception signals an illegal attempt to
  extract from an empty collection
• Overflow exception signal that a capacity has
  been exceeded.
• public void pop( ) throws Underflow
• if( isEmpty( ) ) throw new Underflow( )
• topOfStack topOfStack.next

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Linked List Implementation of Stacks
public class StackLi private
ListNode topOfStack public
StackLi( ) topOfStack null
public boolean isfull( )
return false public boolean isEmpty(
) return topOfStack null
public void makeEmpty( ) topOfStack
null public void push( Object
x ) public Object topAndPop( )
public Object top( )
public void pop( )
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Linked List Implementation of Stacks
public static void main( String args )
StackLi s new StackLi( )
for( int i 0 i lt 10 i )
s.push( new MyInteger( i ) )
while( !s.isEmpty( ) )
System.out.println( s.topAndPop( ) )

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Linked List Implementation of Stacks
public void push( Object x )
topOfStack new ListNode( x, topOfStack )
public Object topAndPop( )
if( isEmpty( ) ) return null
Object topItem topOfStack.element
topOfStack topOfStack.next return
topItem
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Linked List Implementation of Stacks
public Object top( )
if( isEmpty( ) ) return null
return topOfStack.element
public void pop( ) throws Underflow
if( isEmpty( ) ) throw new Underflow(
) topOfStack topOfStack.next

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Array Implementation of Stacks
public class StackAr private
Object theArray private int
topOfStack static final int
DEFAULT_CAPACITY 10 public StackAr(
) this( DEFAULT_CAPACITY ) public
StackAr( int capacity ) theArray
new Object capacity topOfStack
-1
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Array Implementation of Stacks
public boolean isEmpty( ) return
topOfStack -1 public boolean
isFull( ) return topOfStack
theArray.length - 1 public void
makeEmpty( ) topOfStack -1 public
void push( Object x ) public
Object topAndPop( ) public Object
top( ) public void pop( )

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Array Implementation of Stacks
public static void main( String args )
StackAr s new StackAr( 12 )
try for(
int i 0 i lt 10 i )
s.push( new MyInteger( i ) )
catch( Overflow e ) System.out.println(
"Unexpected overflow" ) while(
!s.isEmpty( ) )
System.out.println( s.topAndPop( ) )

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Array Implementation of Stacks
public void push( Object x ) throws
Overflow if( isFull( ) )
throw new Overflow( ) theArray
topOfStack x public Object
topAndPop( ) if( isEmpty( )
) return null Object topItem top(
) theArray topOfStack-- null
return topItem
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Array Implementation of Stacks
public void pop( ) throws Underflow
if( isEmpty( ) ) throw new Underflow(
) theArray topOfStack-- null
public Object top( )
if( isEmpty( ) ) return null
return theArray topOfStack
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Queue

• Queue is a special kind of list
• Two operations
• Enqueue insert an element at the end
• Dequeue delete an element at the front
• O(1) running times for both operations
• First-Come First-Served

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Application of Queues

• A queue of requests waiting for a service
• Examples
• Event Simulation queues at phone booth, bank
• Job scheduling print jobs submitted to a printer
• Buffering keyboard buffer

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Array Implementation of Queues
enqueue
dequeue
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Circular Array
enqueue
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Empty Queue
2 entries
dequeue 10 1 entry left
dequeue 11 0 entry left
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Array Implementation of Queues
public class QueueAr private Object
theArray private int currentSize
private int front private int
back static final int
DEFAULT_CAPACITY 10 public QueueAr( )
this( DEFAULT_CAPACITY)
public QueueAr( int capacity ) public
boolean isEmpty( ) return currentSize
0 public boolean isFull( )
return currentSize theArray.length
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Array Implementation of Queues
public void makeEmpty( )
public Object getFront( ) public void
enqueue( Object x ) throws Overflow
public int increment( int x)
public Object dequeue( )
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public static void main( String args )
QueueAr q new QueueAr( )
try for( int i 0
i lt 10 i ) q.enqueue( new
MyInteger( i ) )
catch( Overflow e ) System.out.println(
"Unexpected overflow" ) while(
!q.isEmpty( ) )
System.out.println( q.dequeue( ) )
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public QueueAr( int capacity ) theArray
new Object capacity makeEmpty(
) public void makeEmpty( ) currentSize
0 front 0 back -1
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public void enqueue( Object x ) throws
Overflow if ( isFull( ) ) throw new
Overflow( ) back increment( back )
theArray back x currentSize private
int increment( int x ) if ( x
theArray.length ) x 0 return x
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public Object dequeue( ) if ( isEmpty( ) )
return null currentSize-- Object
frontItem theArray front theArray
front null front increment( front )
return frontItem public Object getFront(
) if( isEmpty( ) ) return null
return theArray front
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Linked List Implementation of Queues
Exercise.