Transcript Chapter 3 Lists, Stacks, and Queues

Chapter 3
Lists, 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 fixedlength structure.
Array Creation
int [] a;
a = new int[10];
int [] b = new int[10];
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 < d.length; i++ ) {
System.out.println( d[i] );
}
}
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public static int findMax(int [] d) {
int max;
for (max = d[0], int i = 1; i < d.length; i++) {
if (d[i] > max) max = d[i];
}
return max;
}
public static int findMin(int [] d) {
int min;
for (min = d[0], int i = 1; i < d.length; i++) {
if (d[i] > min) min = d[i];
}
return min;
}
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public static int sum(int [] d) {
int sum = 0;
for (int i = 0; i < d.length; i++)
sum += d[i];
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 < 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 int[100];
size = 0;
}
public void add( int x ) {
data[size] = x;
size++;
}
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public int findMax() {
int max;
for (max = data[0], int i = 1; i < size; i++)
if (data[i] > max) max = data[i];
return max;
}
public int findMin() {
int min = 0;
for (min =data[0], int i = 1; i < size; i++)
if (data[i] > min) min = data[i];
return min;
}
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public int sum() {
int sum = 0;
for (int i = 0; i < size; i++)
sum += data[i];
return sum;
}
public void print() {
for (int i = 0; i < size; i++ )
System.out.println( data[i] );
}
}
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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)
10
34
12
52
16
12
34
12
52
10
16
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12
• Remove
remove(52)
34
12
52
10
16
12
• printList
printList() prints 34 12 10 16 12
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• findKth
34
12
10
16
12
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 <= 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 int[100];
size = 0;
}
public void insert(int x, int i) {
for (int n = size; n >= i; n--)
data[n+1] = data[n];
data[i] = x;
size++;
}
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public void remove(int x) {
int n;
for (n = find(x); n != -1 && n < size; n++)
data[n] = data[n+1];
size--;
}
public int find(int x) {
int i;
for (i = 1; i <= size; i++)
if (data[i] == x) break;
if (i > size) return -1; else return i;
}
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public int findKth(int k) {
return data[k];
}
public int findMax() {
int max = data[1];
for (int i = 2; i <= size; i++)
if (data[i] > max) max = data[i];
return max;
}
public void printList() {
for (int i = 1; i <= size; i++ )
System.out.println( data[i] );
}
}
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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
A1
A2
A3
header
empty list
header
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Three Classes in Linked List
LinkedList
LinkedListItr
header
current
A1
ListNode
ListNode
A2
ListNode
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A3
ListNode
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Objects in Linked List
theList
theItr
LinkedList
current
header
ListNode
next
element
Object
LinkedListItr
ListNode
next
element
Object
ListNode
next
element
Object
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ListNode
next
element
Object
25
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 < 10; i++ ) {
theList.insert( new MyInteger( i ), theItr );
printList( theList );
theItr.advance( );
}
}
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for( i = 0; i < 10; i += 2 ) theList.remove( new MyInteger( i ) );
for( i = 0; i < 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
A1
A2
A3
insert
A1
A2
A3
x
remove
A1
A2
x
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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.equals( 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 < 10; i++ ) {
theList.insert( new MyInteger( i ), theItr );
printList( theList );
theItr.advance( );
}
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for( i = 0; i < 10; i += 2 ) theList.remove( new MyInteger( i ) );
for( i = 0; i < 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
A1
A2
A3
Doubly linked list
A1
A2
A3
Double circular linked list
A1
A2
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A3
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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
120
5
0
1
15
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; i>= 0; i-- )
sum.coeffArray[ i ] = coeffArray[ i ] +
rhs.coeffarray[ i ];
return sum;
}
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Linked List Implementation of Polynomial
10 1000
P1
14
1
0
P1(x) = 10x1000 + 5x14 + 1
3 1990
P2
5
-2 1492
11
1
5
0
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
2
3
2
0
1
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 >> 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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0
1 512 343
8
729
1 216 27
0 512 125
64
27
8
1
0 125 216 343
64 125 216
343
27
8 729
64
512
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729
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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
S1
S2
S3
S4
C1
C2
C3
C4
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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
freeList
Allocation
freeList L1
freeList L1
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Cursor Implementation of Linked Lists
Two Lists
freeList L1
L2
Deallocation (free)
freeList L1
L2
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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;
private static final int SPACE_SIZE = 100;
static
{
cursorSpace = new CursorNode[ SPACE_SIZE ];
for( int i = 0; i < SPACE_SIZE; iI++ )
cursorSpace[ i ] = new CursorNode( null, i+1 );
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
4
3
2
1
PUSH 5
POP
5
5
4
3
2
1
5
4
3
2
1
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3
2
1
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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 * + +
*45*++
3
2
1
45*++
*++
++
+
6
1
5
4
6
1
20
6
1
26
1
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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
Input
Action
operand
Print it
operator
Pop and print until a lower precedence operator or a
( is found. Push the operator.
(
Push
)
Pop and print until a ( is found. Pop (.
are not printed
empty
( and )
pop and print all
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Infix to Postfix Conversion
Input
a+b*c+(d*e+f)*g
Output
abc*+de*f+g*+
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Method Calls
a()
{
...
b( );
...
}
b( )
{
...
c( );
...
}
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c( )
{
...
}
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Method Calls
a:
b:
.
.
call b
.
.
return
c:
.
.
call c
.
.
return
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.
.
return
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a:
10: . . .
11: call
b
12: . . .
Method
Calls
and
Stack
c:
b:
101: . . .
102: call
c
223: . . .
224:
return
103: . . .
1
2
b:
102: call c
103: . . .
104: return
103
1
2
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a:
10: . . .
11: call
b
12: . . .
1
2
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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)
return address
previous frame
arguments
local variables
return address
previous frame
arguments
local variables
return address
previous frame
arguments
local variables
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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
public boolean
public boolean
public void
StackLi( )
{ topOfStack = null; }
isfull( )
{ return false; }
isEmpty( )
{ return topOfStack == null; }
makeEmpty( ) { topOfStack = null; }
public void
public Object
public Object
public void
push( Object x ) { }
topAndPop( ) { }
top( ) { }
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 < 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 < 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
1
2
front
enqueue
1
3
back
2
3
front
dequeue
4
back
2
front
3
4
back
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Circular Array
7
8
9
front
enqueue
11
back
7
10
back
8
9
10
front
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Empty Queue
2 entries
dequeue 10
1 entry left
11
10
back
front
11
front back
dequeue 11
0 entry left
back
front
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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( )
public QueueAr( int capacity )
public boolean isEmpty( )
public boolean isFull( )
{ this( DEFAULT_CAPACITY); }
{}
{ return currentSize == 0 }
{ return currentSize == theArray.length; }
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Array Implementation of Queues
public void
public Object
public void
public int
public Object
makeEmpty( ) { }
getFront( ) { }
enqueue( Object x ) throws Overflow { }
increment( int x) { }
dequeue( ) { }
}
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public static void main( String [ ] args )
{
QueueAr q = new QueueAr( );
try
{
for( int i = 0; i < 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.
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