TK1924 Program Design & Problem Solving Session 2011/2012 L5: Stacks.

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

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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

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Stacks (cont’d.)

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Stacks (cont’d.)

Stack Operations

• In the abstract class stackADT:– initializeStack– isEmptyStack– isFullStack– push– top– pop

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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

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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

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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

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Implementation of Stacks as Arrays (cont'd.)

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Initialize Stack

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Empty Stack

• If stackTop is 0, the stack is empty

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Full Stack

• The stack is full if stackTop is equal to maxStackSize

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Push

• Store the newItem in the array component indicated by stackTop

• Increment stackTop• Must avoid an overflow

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Push (cont'd.)

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Return the Top Element

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Pop

• Simply decrement stackTop by 1• Must check for underflow condition

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Pop (cont’d.)

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Pop (cont’d.)

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Copy Stack

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Constructor

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Destructor

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 name3.5 Bill3.6 John2.7 Lisa3.9 Kathy3.4 Jason3.9 David3.4 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 Bill3.6 John2.7 Lisa3.9 Kathy3.4 Jason3.9 David3.4 Jack

highestGPA

3.9

Kathy

David

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100

[0]

[1]

[2]

[3]

:

:

[98]

[99]

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

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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

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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 * +

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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

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Application of Stacks: Postfix Expressions Calculator (cont'd.)

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• Example: 6 3 + 2 * =

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

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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

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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

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Main Algorithm

• Pseudocode:

• We will write four functions:– evaluateExpression, evaluateOpr, discardExp, and printResult

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Function evaluateExpression

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Function evaluateOpr

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Function evaluateOpr (cont’d.)

Function discardExp

• This function is called whenever an error is discovered in the expression

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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

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Function printResult (cont’d.)

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)

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Nonrecursive Algorithm to Print a Linked List Backward

• Let us now execute the following statements:

• Output:20 15 10 5

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Nonrecursive Algorithm to Print a Linked List Backward

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)

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