Welcome to CIS 068 !

1
Welcome to CIS 068 !
Lesson 11 Data Structures 2
2
Overview

• Description, Usage and Application of
• Queues and Stacks

3
Queues

• FIFO (first in first out) Structure

in
3
2
1
out
4
Queues

• Java Interface

5
Queues Implementation 1

• 1. Implementation as Linked List

in
out
1
2
3
(null)
6
Adding an Element
in
out
in
out
in
out
2
(null)
1
1
(null)
(null)

• Adding an element E
• If in null in E, out E, E.link null
• else in.link E, in E, E.link null

7
Removing an Element
in
out
in
out
in
out
2
1
2
(null)
(null)
(null)

• Removing an element
• If out null throw EmptyQueueException
• else
• Eout, outout.link
• If out null in null
• return E

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Queues Implementation 2
2. Implementation as Circular Array
Capacity 6
Index !
3
4
5
in
---
out
1
2
size 5
List-Size 5
9
Circular Array Adding an Element E
in
out
out
9
9
10
10
11
11
12
12
13
13
E14
in
14
---
size 6
size 5
If size capacity return error (or increase
capacity automatically) else arrayinE size
in (in1)capacity
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Circular Array Removing an Element
out
---
9
out
10
10
11
11
12
12
13
13
in
in
---
---
size 4
size 5
If size 0 throw EmptyQueueException else E
arrayout size -- out (out1)capacity
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Stacks

• LIFO (first in first out) Structure

top
3
2
1
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Stacks
Java Interface
13
Stack Implementation 1

• 1. Implementation as Linked List

top
3
2
1
(null)
14
Adding an Element E
2
1
top
(null)
2
1
top
E3
(null)
Adding an Element E E.link top top E
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Removing an Element
2
1
top
3
(null)
2
1
top
(null)
return 3
Removing an Element E if topnull throw
EmptyQueueException else Etop top
top.link return E
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Stack Implementation 2

• 2. Implementation as Array

Capacity 6
Index !
---
---
top
4
3
2
1
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Adding / Removing
---
---
top
4
3
2
1
Adding an Element E If top capacity return
error (or increase capacity automatically) else
arraytop E top
Removing an Element If top 0 throw
EmptyQueueException else top -- return
arraytop
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Application 1

• Checking for Balanced Parantheses
• Task
• Determine whether expression is balanced with
  respect to parantheses
• Allow for different symbols of parentheses
• ( )

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Algorithm
20
Algorithm

• Expression
• (ab-cd(ab))
• Stack
• (
• (
• (
• (
• ((
• (

Error !
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Application 2
Evaluating a Postfix Expression Postfix
expression Why ? No brackets necessary !
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PN / RPN

• Prefix / Postfix Expression History
• PREfix Notation (also called Polish Notation)
  invented in the 1920's by Polish mathematician
  Jan Lukasiewicz,
• writing operators in front of their operands,
  instead of between them, makes brackets
  unnecessary
• Postfix Expression Reverse Polish Notation
  (RPN) operators appear behind their operands
• Proposed in the late 1950's by the Australian
  philosopher and early computer scientist Charles
  L. Hamblin
• Advantage the operators appear in the order
  required for computation.

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HP9100A
Engineers at the Hewlett-Packard company realised
that RPN could be used to simplify the
electronics of their calculators at the expense
of a little learning by the user. The first
"calculator" to use RPN was the HP9100A, which
was introduced in 1968 Price 4900
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Evaluation Algorithm

• Evaluate Expression from left to right
• If symbol read is operand push onto the stack
• If symbol read is operator
• pop two operators
• Evaluate using operator
• Push result on stack
• Final value on stack is final result
• (remark works only on binary operators)

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Evaluation Algorithm
Example