3. stack - data structures using c++ by varsha patil

1Oxford University Press © 2012

Data Structures Using C++ by Dr Varsha Patil

3. Stack



Objectives

Understand all the aspects of a stack as data type including :

Last In, First Out (LIFO) data access Push, Pop, and other stack operations Contiguous implementation of a stack Learn realization of stack using arrays(: Contiguous stack) Learn to choose appropriate realization suitable for

practical applications Learn and implement the multi-stacks Use of stacks in expression conversion, recursion,

reversing data and many more



Introduction To Programming

A stack is an ordered list in which all insertions and deletions are made at one end, called the top

In computer programming processing of function calls and their terminations uses stack. Stack is used to remember the place where the call was made; so that it can return there after the function is complete



Following are some examples in which where we need to use stacks are generally used:

Applications that maintain a list of printing jobs waiting at the a network printer. Here we need to keep one queue which can hold all print requests from different users

Handling function calls in programs very often restricts the access only at one end. In such implementation we need to use stacks. We can keep track of the return address to earlier function after furnishing/finishing a function call using stacks If we intend to store a group of data together in a

sequential manner in computer’s memory, then arrays can be one of the possible data structures.



Arrays An array is a finite ordered collection of

homogeneous data elements which provides direct access (or random access) to any of its elements.

An array as a data structure is defined as a set of pairs (index, value) such that with each index a value is associated.

index — indicates the location of an element in an array.

value - indicates the actual value of that data element. Declaration of an array in ‘C++’:

int Array_A[20];



The Stack Full Condition (Stack Capacity =3)



The Pop Operation



The Empty Stack



The Get Top Operation



REPRESENTATION OF STACK S USING SEQUENTIAL ORGANIZATION

(ARRAYS)



A polish Mathematician Han Lukasiewicz suggested a notation called polish notation, which gives two alternatives to represent an arithmetic expression the notations are Postfix and prefix notation



Stack using Array

……….. C B A

p



Stacks Using Template A template is variable which can be

instantiated to any data type This data type could be build in or user defined

type



MULTIPLE STACKS

Initial configuration for two stacks in A[0],, …, A[n-1]

………..1 2 3 B A

Stack2Stack 1

A

Top1 =2 Top2=n-2

0 1 2 3 n-3 n-2 n-1

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Initial configuration for m stacks in A [0, …, n-1]

B[0]T[0]

B[1]T[1]

B[2]T[2]

B[m-1]T[m-1]

0 n/m 2[n/m] N-1

A

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Applications Of Stack

Convert infix expression to postfix and prefixexpressions

Evaluate the postfix expression Reverse a string Check well-formed (nested) parenthesis Reverse a string Process subprogram function calls Parse (analyze the structure) of computer

programs Simulate recursion In computations like decimal to binary

conversion In Backtracking algorithms (often used in

optimizationsand in games)

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Expression Evaluation And Conversion

The most frequent application of stacks is in evaluation of arithmetic expressions.

An arithmetic expression is made up of operands, operators, and delimiters.

When higher level programming language came into existence one of the major difficulty faced by computer scientists was to generate machine language instruction, which would properly evaluate any arithmetic expression.

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The following operators are written is in descending order of their precedence:

Exponentiation ^, Unary +, Unary –, and not ~

Multiplication * and division / Addition + and subtraction – <, £ , =, ¹, ³, > AND OR

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The Operators and priorities

Oxferd Univercity Data Structures in C++ by Dr. Varsha Patil

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Polish Notation and Expression

Conversion:

Polish Mathematician Han Lukasiewicz suggested a notation called pPolish notation, which gives two alternatives to represent an arithmetic expression, the notation are postfix and prefix notations

The fundamental property of Polish notation is that the order in which the operations are to be performed is determined by the positions of the operators and operands in the expression.

Hence the advantage is parenthesis is not required while writing expressions in pPolish notation



…The example expression in various forms-infix, prefix and postfix

The postfix expressions can be evaluated easily hence infix expression is converted into postfix expression using stack.

Oxford University Press © 2012Data Structures Using C++ by Dr Varsha Patil

Repetition Construct

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Relationship between Data, Data Structures, and Algorithms A data structure represents a set of data items with a

specific relationship between them The success of a software project often depends upon

the choices made in the representation of data and algorithms designed to process the data

The proper choice of a data structure can be a key point in the design of many algorithms



Flow ChartsA very effective tool to show the logic flow of a programA flow chart is a pictorial representation of an

algorithmIt hides all of the details of an algorithm by giving the picture; It shows how the algorithm flows from beginning to end



Flow Charts

Flow chart for adding three numbers



Analysis of Algorithms

Complexity of Algorithms Space Complexity Time Complexity Computing Time Complexity of Algorithm Big-O Notation



Space Complexity Amount of computer memory required during the

program execution, as a function of the input size Space complexity measurement which is space

requirement of an algorithm can be done at two different times:

Compile time and Execution time



Compile time space complexity

Compile time space complexity is defined as the storage requirement of a program at compile time

The space complexity = Space needed of compile time



Runtime space complexity

If program is recursive or uses dynamic variables or dynamic data structure then there is a need to determine space complexity at runtime

The memory requirement is summation of theprogram spacedata space andstack space



Time Complexity The time complexity of an algorithm is a measure of

how much time is required to execute an algorithm for a given number of inputs

Time Complexity T(P) is the time taken by program P and the sum of the compile and execution time



Best, Worst and Average Cases

The worst case : Complexity of the algorithm is the function defined by the

maximum number of steps taken on any instance of size n

The best case: Complexity of the algorithm is the function defined by the

minimum number of steps taken on any instance of size n

The average case: Complexity of the algorithm is the function defined by an

average number of steps taken on any instance of size n.



Computing Time Complexity of Algorithm

The total time taken by the algorithm or program is calculated using the sum of the time taken by each of executable statement in algorithm or programTime required by each statement depends on

Time required for executing it once. Number of times the statement is executed.



Software Engineering

Software Engineering is the establishment and use of sound engineering methods and principles to obtain reliable software that works on real machines.

A fundamental concept in Software Engineering is the Software Development Life

Cycle (SDLC)




Analysis PhaseDesign PhaseImplementation PhaseTesting PhaseVerification




Analysis PhaseDesign PhaseImplementation PhaseTesting PhaseVerification

System Development Phases



Analysis Phase

Define the UserDefine the NeedsDesign PhaseDefine the Methods



Design Phase

Modularity: The design phase uses a very well-established principle called modularity

The whole package is divided into small modules

Tools



Implementation Phase

Tools

flowchartPseudo CodeCoding



Testing Phase

Testing PhaseOnce the programs have been written, they must be tested. There are two types of testing:

Black box and White box



VerificationProgram verification is a process to prove that the program does what it is intended to do. It is said that 'even verification must be verified'. This means, along with system, tests made are to be verified. Also, every software quality must be verified.



Summary A stack is an ordered list in which all insertions and deletions are

made at one end, called the top Adding an element is called as pushing the element onto the stack.

The function, which does this, is called ‘push’. Removing an element from the stack is called as popping the

element from the stack and the function, which does this, is called ‘pop’

Stack can be implemented using arrays or using linked lists. For array implementation its size should be predefined and also it

cannot exceed run time Stack is used in wide number of applications such as recursion,

expression conversion, well -formed parenthesis check etc.. Program verification is a process to prove that the program does

what it is intended to do It is said that 'even verification must be verified' This means, along with system, tests made are to be verified. Also, every software quality must be verified



Summary The most frequent application of stack is in evaluation of arithmetic

expressions. The conventional way of writing the expression is called infix, because the binary operators occur in between the operands and unary operators precede their operand.

Polish Mathematician Han Lukasiewicz suggested a notation called Polish notion, which gives two alternatives to represent an arithmetic expression, the notations are postfix and prefix notations.

In postfix notation, the operator is written after its operands, whereas in prefix notation the operator precedes its operands.·

The postfix expressions can be evaluated easily hence infix expression is converted into postfix expression using stack.

In computer programming processing of function calls and their terminations uses stack.

Stack is used to remember the place where the call was made; so that it can return there after the function is complet the check etc..

Program verification is a process to prove that the program does what it is intended to do.

It is said that 'even verification must be verified'. This means, along with system, tests made are to be verified. Also, every software quality must be verified.



Key Terms Data Data type DATA OBJECT DATA STRUCTURE ABSTRACT DATA TYPE LINEAR DATA STRUCUTRE NON LINEAR DATA STRUCTURE ALGORITHM ASSEMBLER COMPILER Program Pseudo code Flowchart Software Engineering

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End of Chapter 3 …!

3. stack - data structures using c++ by varsha patil

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