Programming fundamentals lecture 4

ALGORITHMS AND FLOWCHARTS

ALGORITHMS AND FLOWCHARTS

• A typical programming task can be divided into two phases:

• Problem solving phase– produce an ordered sequence of steps that describe

solution of problem– this sequence of steps is called an algorithm

• Implementation phase – implement the program in some programming language

Steps in Problem Solving

• First produce a general algorithm (one can use pseudocode)

• Refine the algorithm successively to get step by step detailed algorithm that is very close to a computer language.

• Pseudocode is an artificial and informal language that helps programmers develop algorithms. Pseudocode is very similar to everyday English.

Pseudocode & Algorithm

• Example 1: Write an algorithm to determine a student’s final grade and indicate whether it is passing or failing. The final grade is calculated as the average of four marks.


Pseudocode:• Input a set of 4 marks• Calculate their average by summing and dividing by 4• if average is below 50

Print “FAIL”else

Print “PASS”


• Detailed Algorithm • Step 1: Input M1,M2,M3,M4

Step 2: GRADE (M1+M2+M3+M4)/4 Step 3: if (GRADE < 50) then

Print “FAIL” else

Print “PASS”endif

The Flowchart

A Flowchart– shows logic of an algorithm– emphasizes individual steps and their

interconnections– e.g. control flow from one action to the next

Flowchart Symbols

Basic

Oval

Parallelogram

Rectangle

Diamond

Hybrid

Name Symbol Use in Flowchart

Denotes the beginning or end of the program

Denotes an input operation

Denotes an output operation

Denotes a decision (or branch) to be made. The program should continue along one of two routes. (e.g. IF/THEN/ELSE)

Denotes a process to be carried oute.g. addition, subtraction, division etc.

Flow line Denotes the direction of logic flow in the program

Example

PRINT“PASS”

Step 1: Input M1,M2,M3,M4Step 2: GRADE (M1+M2+M3+M4)/4 Step 3: if (GRADE <50) then

Print “FAIL” else

Print “PASS” endif

START

InputM1,M2,M3,M4

GRADE(M1+M2+M3+M4)/4

ISGRADE<50

PRINT“FAIL”

STOP

YN

Example 2

• Write an algorithm and draw a flowchart to convert the length in feet to centimeter.

Pseudocode:• Input the length in feet (Lft)• Calculate the length in cm (Lcm) by multiplying

LFT with 30• Print length in cm (LCM)

Example 2

Algorithm • Step 1: Input Lft• Step 2: Lcm Lft x 30 • Step 3: Print Lcm

START

InputLft

Lcm Lft x 30

PrintLcm

STOP

Flowchart

Example 3

Write an algorithm and draw a flowchart that will read the two sides of a rectangle and calculate its area.

Pseudocode • Input the width (W) and Length (L) of a rectangle• Calculate the area (A) by multiplying L with W• Print A

Example 3

Algorithm • Step 1: Input W,L• Step 2: A L x W • Step 3: Print A

START

InputW, L

A L x W

PrintA

STOP

Example 4

• Write an algorithm and draw a flowchart that will calculate the roots of a quadratic equation

• X=(-b + sqrt (b2 -4ac))/2a• X=(-b - sqrt (b2 -4ac))/2a

2 0ax bx c

Example 4

Pseudocode: • Input the coefficients (a, b, c) of the quadratic

equation• Calculate d• Calculate x1• Calculate x2• Print x1 and x2

Example 4

• Algorithm: • Step 1: Input a, b, c• Step 2: d sqrt ( )• Step 3: x1 (–b + d) / (2 x a)• Step 4: x2 (–b – d) / (2 x a)• Step 5: Print x1, x2

START

Inputa, b, c

d sqrt(b x b – 4 x a x c)

Printx1 ,x2

STOP

x1 (–b + d) / (2 x a)

X2 (–b – d) / (2 x a)

4b b a c

DECISION STRUCTURES

• The expression A>B is a logical expression• it describes a condition we want to test• if A>B is true (if A is greater than B) we take the

action on left• print the value of A • if A>B is false (if A is not greater than B) we take the

action on right• print the value of B

DECISION STRUCTURES

isA>B

Print BPrint A

Y N

IF–THEN–ELSE STRUCTURE

• The structure is as followsIf condition then

true alternative else

false alternativeendif

IF–THEN–ELSE STRUCTURE

• The algorithm for the flowchart is as follows:If A>B then

print Aelse

print Bendif

isA>B

Print BPrint A

Y N

Relational Operators

Relational Operators

Operator Description> Greater than

< Less than

= Equal to

Greater than or equal to Less than or equal to

Not equal to

Example 5 • Write an algorithm that reads two values, determines the

largest value and prints the largest value with an identifying message.

ALGORITHMStep 1: Input VALUE1, VALUE2Step 2: if (VALUE1 > VALUE2) then

MAX VALUE1else

MAX VALUE2endif

Step 3: Print “The largest value is”, MAX

Example 5

MAX VALUE1

Print“The largest value is”, MAX

STOP

Y N

START

InputVALUE1,VALUE2

MAX VALUE2

isVALUE1>VALUE2

NESTED IFS

• One of the alternatives within an IF–THEN–ELSE statement– may involve further IF–THEN–ELSE statement

Example 6

• Write an algorithm that reads three numbers and prints the value of the largest number.

Example 6Step 1: Input N1, N2, N3Step 2: if (N1>N2) then

if (N1>N3) then MAX N1 [N1>N2, N1>N3]

else MAX N3 [N3>N1>N2]

endifelse

if (N2>N3) then MAX N2 [N2>N1, N2>N3]

else MAX N3 [N3>N2>N1]

endifendif

Step 3: Print “The largest number is”, MAX

Example 6

• Flowchart: Draw the flowchart of the above Algorithm.

Example 7

• Write and algorithm and draw a flowchart to a) read an employee name (NAME), overtime

hours worked (OVERTIME), hours absent (ABSENT) and

b) determine the bonus payment (PAYMENT).

Example 7

Bonus Schedule

OVERTIME – (2/3)*ABSENT Bonus Paid

>40 hours>30 but 40 hours>20 but 30 hours>10 but 20 hours 10 hours

$50$40$30$20$10

Step 1: Input NAME,OVERTIME,ABSENTStep 2: if (OVERTIME–(2/3)*ABSENT > 40) then PAYMENT 50 else if (OVERTIME–(2/3)*ABSENT > 30) then

PAYMENT 40 else if (OVERTIME–(2/3)*ABSENT > 20) then PAYMENT 30 else if (OVERTIME–(2/3)*ABSENT > 10) then PAYMENT 20 else PAYMENT 10 endif

Step 3: Print “Bonus for”, NAME “is $”, PAYMENT

Example 7

• Flowchart: Draw the flowchart of the above algorithm?

Simple Program Design, Fourth Edition Chapter 2

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Objectives

• In this chapter you will be able to:

• Introduce common words, keywords, and meaningful names when writing pseudocode

• Define the three basic control structures as set out in the Structure Theorem

• Illustrate the three basic control structures using pseudocode


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• When designing a solution algorithm, you need to keep in mind that a computer will eventually perform the set of instructions written

• If you use words and phrases in the pseudocode which are in line with basic computer operations, the translation from pseudocode algorithm to a specific programming language becomes quite simple

How to Write Pseudocode


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Six Basic Computer Operations

1 A computer can receive information– When a computer is required to receive

information or input from a particular source, whether it is a terminal, a disk or any other device, the verbs Read and Get are used in pseudocode

Read => Input from a recordGet => Input from keyboard

Example pseudocode

Read student nameGet system dataRead number1, number2Get tax_code


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1 A computer can receive information– Usually an output Prompt instruction is required

before an input Get instruction

Example pseudocode

Prompt for student_markGet student_mark


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2 A computer can put out information– When a computer is required to supply

information or output to a device, the verbs Print, Write, Put, Output, or Display are used in pseudocode

– Print => send output to printer– Write => send out to file– Put, Output, Display => send to screen

Example pseudocodePrint ‘Program Completed’Write customer record to master fileOutput total taxDisplay ‘End of data’


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Six Basic Computer Operations3 A computer can perform arithmetic

– Most programs require the computer to perform some sort of mathematical calculation, or formula, and for these, a programmer may use either actual mathematical symbols or the words for those symbols

– To be consistent with high-level programming languages, the following symbols can be written in pseudocode:+ for Add - for Subtract* for Multiply / for Divide ( ) for Parentheses

– When writing mathematical calculations for the computer, standard mathematical ‘order of operations’ applies to pseudocode and most computer languages


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4 A computer can assign a value to a variable or memory location

– There are three cases where you may write pseudocode to assign a value to a variable or memory location:

1. To give data an initial value in pseudocode, the verbs Initialize or Set are used

2. To assign a value as a result of some processing the symbols ‘=‘ or ‘’ are written

3. To keep a variable for later use, the verbs Save or Store are used


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4 A computer can assign a value to a variable or memory location

Example pseudocode

Initialize total_price to zeroSet student_count to zeroTotal_price = cost_price + sales_taxTotal_price cost_price + sales_taxStore customer_num in last_customer_num


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5 A computer can compare two variables and select one or two alternate actions

– An important computer operation available to the programmer is the ability to compare two variables and then, as a result of the comparison, select one of two alternate actions

– To represent this operation in pseudocode, special keywords are used: IF, THEN, and ELSE


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6 A computer can repeat a group of actions

– When there is a sequence of processing steps that need to be

repeated, two special keywords, DOWHILE and ENDDO, are

used in pseudocode

– The condition for the repetition of a group of actions is

established in the DOWHILE clause, and the actions to be

repeated are listed beneath it


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Meaningful Names• All names should be meaningful• A name given to a variable is simply a method of identifying a particular

storage location in the computer• The uniqueness of a name will differentiate it from other locations• Often a name describes the type of data stored in a particular variable• Most programming languages do not tolerate a space in a variable name,

as a space would signal the end of the variable name and thus imply that there were two variables


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The Structure Theorem

• The Structure Theorem states that it is possible to write any computer program by using only three basic control structures that are easily represented in pseudocode: – Sequence– Selection– Repetition


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The Three Basic Control Structures1 Sequence

– The sequence control structure is the straightforward execution of one processing step after another

– In pseudocode, we represent this construct as a sequence of pseudocode statements

2 Selection– The selection control structure is the presentation of a condition and the

choice between two actions; the choice depends on whether the condition is true or false

– In pseudocode, selection is represented by the keywords IF, THEN, ELSE, and ENDIF


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The Three Basic Control Structures

3 Repetition

– The repetition control structure can be defined as the presentation of a set of instructions to be performed repeatedly, as long as a condition is true

– The basic idea of repetitive code is that a block of statements is executed again and again, until a terminating condition occurs

– This construct represents the sixth basic computer operation, namely to repeat a group of actions


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Summary• In this chapter, six basic computer operations were listed, along

with pseudocode words and keywords to represent them

• These operations were: to receive information, put out information, perform arithmetic, assign a value to a variable, decide between two alternate actions, and repeat a group of actions

• The Structure Theorem was introduced; it states that it is possible to write any computer program by using only three basic control structures: sequence, selection, and repetition

Someone Stole a Cookie from the Cookie Jar

Problem: Momma had just filled the cookie jar when the 3 children went to bed. That night one child woke up, ate half of the cookies and went back to bed. Later, the second child woke up, ate half of the remaining cookies, and went back to bed. Still later, the third child woke up, ate half of the remaining cookies, leaving 3 cookies in the jar. How many cookies were in the jar to begin with?

Someone Stole a Cookie from the Cookie Jar (cont’d)

• Information available:– Three children– Each one ate half of the cookies– Three cookies remaining

• Information needed:– Original number of cookies

• Calculations:– For each child, multiply the number of remaining cookies

by two.

Specific Solution to the Problem• First, we solve the specific problem to help us

identify the steps.

– 3 cookies left X 2 = 6 cookies left after 2nd child

– 6 X 2 = 12 cookies left after 1st child– 12 X 2 = 24 = original number of cookies

A Generic Algorithm

• What is a generic algorithm for this problem?

An algorithm that will work with any number of remaining cookies

ANDthat will work with any number of children.

Generic Algorithm for Cookie Problem

• Get number of children.• Get number of cookies remaining.• While there are still children that have not

raided the cookie jar, multiply the number of cookies by 2 and reduce the number of children by 1.

• Display the original number of cookies.

Test The Generic Algorithm

• Try the algorithm on paper with:– Four children and six cookies remaining.– Two children with two cookies remaining.

• If you did not get the correct answer, modify the algorithm so that you get the correct answer.

Pseudocode• When we broke down the previous problem

into steps, we expressed each step as an English phrase.

• We can think of this as writing pseudocode for the problem.

• Typically, pseudocode is a combination of English phrases and formulas.

Pseudocode (con’t)• Pseudocode is used in

– designing algorithms– communicating an algorithm to the customer– converting an algorithm to code (used by the

programmer)– debugging logic (semantic) errors in a solution

before coding (hand tracing)• Let’s write the Cookie Problem algorithm using

a more formal pseudocode and being more precise.

Improved PseudocodeDisplay “Enter the number of children: “Read <number of children>Display “Enter the number of cookies remaining: “Read <cookies remaining><original cookies> = <cookies remaining>While (<number of children> > 0)

<original cookies> = <original cookies> X 2<number of children> = <number of children> - 1

End_WhileDisplay “Original number of cookies = “, <original cookies>

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Programming fundamentals lecture 4