TK1924
Program Design & Problem Solving
Session 2011/2012
L5: Stacks
Objectives
In this chapter, you will:
• Learn about stacks
• Examine various stack operations
• Learn how to implement a stack as an array
• Discover stack applications
• Learn how to use a stack to remove recursion
2
Stacks
• Stack: list of homogenous elements
– Addition and deletion occur only at one end,
called the top of the stack
• Example: in a cafeteria, the second tray can be
removed only if first tray has been removed
– Last in first out (LIFO) data structure
• Operations:
– Push: to add an element onto the stack
– Pop: to remove an element from the stack
3
Stacks (cont’d.)
4
Stacks (cont’d.)
5
Stack Operations
• In the abstract class stackADT:
– initializeStack
– isEmptyStack
– isFullStack
– push
– top
– pop
6
Implementation of Stacks as Arrays
• First element can go in first array position,
the second in the second position, etc.
• The top of the stack is the index of the last
element added to the stack
• Stack elements are stored in an array
• Stack element is accessed only through
top
• To keep track of the top position, use a
variable called stackTop
7
Implementation of Stacks as Arrays
(cont'd.)
• Because stack is homogeneous
– You can use an array to implement a stack
• Can dynamically allocate array
– Enables user to specify size of the array
• The class stackType implements the
functions of the abstract class
stackADT
8
UML Class Diagram of class
stackType
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Implementation of Stacks as Arrays
(cont'd.)
• C++ arrays begin with the index 0
– Must distinguish between:
• The value of stackTop
• The array position indicated by stackTop
• If stackTop is 0, the stack is empty
• If stackTop is nonzero, the stack is not
empty
– The top element is given by stackTop - 1
10
Implementation of Stacks as Arrays
(cont'd.)
11
Initialize Stack
12
Empty Stack
• If stackTop is 0, the stack is empty
13
Full Stack
• The stack is full if stackTop is equal to
maxStackSize
14
Push
• Store the newItem in the array
component indicated by stackTop
• Increment stackTop
• Must avoid an overflow
15
Push (cont'd.)
16
Return the Top Element
17
Pop
• Simply decrement stackTop by 1
• Must check for underflow condition
18
Pop (cont’d.)
19
Pop (cont’d.)
20
Copy Stack
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Constructor
22
Destructor
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Stack Header File
myStack.h
– Place definitions of class and functions (stack
operations) together in a file
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Programming Example: Highest
GPA
• Input: program reads an input file with
each student’s GPA and name
3.5
3.6
2.7
3.9
3.4
3.9
3.4
Bill
John
Lisa
Kathy
Jason
David
Jack
• Output: the highest GPA and all the names
associated with the highest GPA
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Programming Example: Problem
Analysis and Algorithm Design
• Read the first GPA and name of the student
– This is the highest GPA so far
• Read the second GPA and student name
– Compare this GPA with highest GPA so far
• New GPA is greater than highest GPA so far
– Update highest GPA, initialize stack, add to stack
• New GPA is equal to the highest GPA so far
– Add name to stack
• New GPA is smaller than the highest GPA
– Discard
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Programming Example: Problem
Analysis and Algorithm Design (cont’d.)
3.5
3.6
2.7
3.9
3.4
3.9
3.4
Bill
John
Lisa
Kathy
Jason
David
Jack
3.9
[99]
highestGPA
[98]
:
:
[3]
maxStackSize 100
[2]
stackTop 1
list
David
[1]
Kathy
[0]
27
Application of Stacks: Postfix
Expressions Calculator
• Infix notation: usual notation for writing
arithmetic expressions
– The operator is written between the operands
– Example: a + b
– The operators have precedence
• Parentheses can be used to override precedence
28
Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Prefix (Polish) notation: the operators are
written before the operands
– Introduced by the Polish mathematician Jan
Lukasiewicz
• Early 1920s
– The parentheses can be omitted
– Example: + a b
29
Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Reverse Polish notation: the operators
follow the operands (postfix operators)
– Proposed by the Australian philosopher and
early computer scientist Charles L. Hamblin
• Late 1950's
– Advantage: the operators appear in the order
required for computation
– Example: a + b * c
• In a postfix expression: a b c * +
30
Application of Stacks: Postfix
Expressions Calculator (cont'd.)
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Postfix notation has important applications
in computer science
– Many compilers first translate arithmetic
expressions into postfix notation and then
translate this expression into machine code
• Evaluation algorithm:
– Scan expression from left to right
– When an operator is found, back up to get the
operands, perform the operation, and
continue
32
Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Example: 6 3 + 2 * =
33
Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Symbols can be numbers or anything else:
– +, -, *, and / are operators
• Pop stack twice and evaluate expression
• If stack has less than two elements  error
– If symbol is =, the expression ends
• Pop and print answer from stack
• If stack has more than one element  error
– If symbol is anything else
• Expression contains an illegal operator
34
Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Examples:
7 6 + 3 ; 6 - =
• ; is an illegal operator
14 + 2 3 * =
• Does not have enough operands for +
14 2 3 + =
• Error: stack will have two elements when we
encounter equal (=) sign
35
Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• We assume that the postfix expressions
are in the following form:
#6 #3 + #2 * =
– If symbol scanned is #, next input is a number
– If the symbol scanned is not #, then it is:
• An operator (may be illegal) or
• An equal sign (end of expression)
• We assume expressions contain only +, -,
*, and / operators
36
Main Algorithm
• Pseudocode:
• We will write four functions:
– evaluateExpression, evaluateOpr,
discardExp, and printResult
37
Function evaluateExpression
38
Function evaluateOpr
39
Function evaluateOpr (cont’d.)
40
Function discardExp
• This function is called whenever an error is
discovered in the expression
41
Function printResult
• If the postfix expression contains no
errors, the function printResult prints
the result
– Otherwise, it outputs an appropriate message
• The result of the expression is in the stack
and the output is sent to a file
42
Function printResult (cont’d.)
43
Nonrecursive Algorithm to Print a
Linked List Backward
• To print the list backward, first we need to get
to the last node of the list
– Problem: how do we get back to previous node?
• Links go in only one direction
– Solution: save a pointer to each of the nodes with
info 5, 10, and 15
• Use a stack (LIFO)
44
Nonrecursive Algorithm to Print a
Linked List Backward
45
Nonrecursive Algorithm to Print a
Linked List Backward
• Let us now execute the following
statements:
• Output:
20 15 10 5
46
Summary
• Stack: items are added/deleted from one
end
– Last In First Out (LIFO) data structure
– Operations: push, pop, initialize, destroy,
check for empty/full stack
– Can be implemented as array or linked list
– Middle elements should not be accessed
• Postfix notation: operators are written after
the operands (no parentheses needed)
47