algorithms & flowcharts

ALGORITHMS AND FLOWCHARTSALGORITHMS AND FLOWCHARTS

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

Problem solving phaseProblem solving phase produce an ordered sequence of steps that produce an ordered sequence of steps that

describe solution of problemdescribe solution of problem this sequence of steps is called an this sequence of steps is called an algorithmalgorithm

Implementation phaseImplementation phase implement the program in some programming implement the program in some programming

languagelanguage

Steps in Problem SolvingSteps in Problem Solving

First produce a general algorithm (one can First produce a general algorithm (one can use use pseudocodepseudocode) )

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

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

PseudocodePseudocode & Algorithm& Algorithm

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


PseudocodePseudocode:: Input a set of 4 marksInput a set of 4 marks Calculate their average by summing and Calculate their average by summing and

dividing by 4dividing by 4 if average is below 50if average is below 50

Print “FAIL”Print “FAIL”elseelse

Print “PASS”Print “PASS”


Detailed Algorithm Detailed Algorithm Step 1: Step 1: Input M1,M2,M3,M4Input M1,M2,M3,M4

Step 2: Step 2: GRADE GRADE (M1+M2+M3+M4)/4 (M1+M2+M3+M4)/4

Step 3: Step 3: if (GRADE < 50) thenif (GRADE < 50) thenPrint “FAIL”Print “FAIL”

elseelsePrint “PASS”Print “PASS”

endifendif

The FlowchartThe Flowchart

(Dictionary) A schematic representation of (Dictionary) A schematic representation of a sequence of operations, as in a a sequence of operations, as in a manufacturing process or computer manufacturing process or computer program.program.

The FlowchartThe Flowchart

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

interconnectionsinterconnections e.g. control flow from one action to the e.g. control flow from one action to the

nextnext

Flowchart Symbols Flowchart Symbols

BasicOval

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

ExampleExample

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<5

0

PRINT“FAIL”

STOP

YN

Example 2Example 2

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

PseudocodePseudocode:: Input the length in feet (Lft)Input the length in feet (Lft) Calculate the length in cm (Lcm) by Calculate the length in cm (Lcm) by

multiplying LFT with 30multiplying LFT with 30 Print length in cm (LCM)Print length in cm (LCM)

Example 2Example 2

AlgorithmAlgorithm Step 1: Input LftStep 1: Input Lft Step 2: Step 2: Lcm Lcm Lft x 30 Lft x 30 Step 3: Step 3: Print LcmPrint Lcm

START

InputLft

Lcm Lft x 30

PrintLcm

STOP

Flowchart

Example 3 Example 3

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

PseudocodePseudocode Input the width (W) and Length (L) of a Input the width (W) and Length (L) of a

rectanglerectangle Calculate the area (A) by multiplying L Calculate the area (A) by multiplying L

with Wwith W Print APrint A

Example 3Example 3

AlgorithmAlgorithm Step 1: Step 1: Input W,LInput W,L Step 2: Step 2: A A L x W L x W Step 3: Step 3: Print APrint A

START

InputW, L

A L x W

PrintA

STOP

Example 4 Example 4

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

Hint: Hint: dd = sqrt ( ), and the roots = sqrt ( ), and the roots are: are: xx11 = (– = (–bb + + dd)/2)/2aa and and xx22 = (– = (–bb – – dd)/2)/2aa

2 0ax bx c 2 4b ac

Example 4Example 4

PseudocodePseudocode: : Input the coefficients (a, b, c) of the Input the coefficients (a, b, c) of the

quadratic equationquadratic equation Calculate Calculate dd Calculate Calculate xx11 Calculate Calculate x2x2 Print Print xx1 and 1 and x2x2

Example 4Example 4

AlgorithmAlgorithm: : Step 1: Step 1: Input a, b, cInput a, b, c Step 2: Step 2: dd sqrt ( sqrt (

)) Step 3: Step 3: xx1 1 (– (–bb + + dd) / (2 x ) / (2 x aa)) Step 4: Step 4: xx2 2 (– (–bb – – dd) / (2 x ) / (2 x aa)) Step 5: Step 5: Print Print xx1, 1, xx22

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 DECISION STRUCTURES

The expression A>B is a logical expressionThe expression A>B is a logical expression it describes ait describes a condition condition we want to testwe want to test if A>B is true (if A is greater than B) if A>B is true (if A is greater than B)

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

B) B) we take the action on rightwe take the action on right print the value of Bprint the value of B

DECISION STRUCTURESDECISION STRUCTURES

isA>B

Print B

Print A

Y N

IF–THEN–ELSE STRUCTUREIF–THEN–ELSE STRUCTURE

The structure is as followsThe structure is as follows

If condition then If condition then

true alternative true alternative

else else

false alternativefalse alternative

endifendif

IF–THEN–ELSE STRUCTUREIF–THEN–ELSE STRUCTURE

The algorithm for the flowchart is as The algorithm for the flowchart is as follows:follows:

If A>B then If A>B then print Aprint A

else else print Bprint B

endifendif

isA>B

Print B

Print A

Y N

Relational OperatorsRelational Operators

Relational OperatorsRelational Operators

OperatorOperator DescriptionDescription>> Greater thanGreater than

<< Less than Less than

== Equal toEqual to

Greater than or equal toGreater than or equal to

Less than or equal toLess than or equal to

Not equal toNot equal to

Example 5 Example 5 Write an algorithm that reads two values, Write an algorithm that reads two values,

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

ALGORITHMALGORITHMStep 1: Step 1: InputInput VALUE1, VALUE2 VALUE1, VALUE2Step 2: Step 2: if (if (VALUE1 > VALUE2) VALUE1 > VALUE2) then then

MAX MAX VALUE1 VALUE1elseelse

MAX MAX VALUE2 VALUE2endifendif

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

Example 5 Example 5

MAX VALUE1

Print“The largest value is”,

MAX

STOP

Y N

START

InputVALUE1,VALUE2

MAX VALUE2

isVALUE1>VALUE2

NESTED IFS NESTED IFS

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

statement statement

Example 6Example 6

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

Example 6Example 6

Step 1: Step 1: InputInput N1, N2, N3N1, N2, N3Step 2: Step 2: if (if (N1>N2) N1>N2) thenthen

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

elseelse MAX MAX N3 N3 [N3>N1>N2][N3>N1>N2]

endifendifelse else

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

elseelse MAXMAX N3 N3 [N3>N2>N1][N3>N2>N1]

endifendifendifendif

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

Example 6Example 6

Flowchart: Draw the flowchart of Flowchart: Draw the flowchart of the above Algorithm.the above Algorithm.

Example 7Example 7

Write and algorithm and draw a Write and algorithm and draw a flowchart to flowchart to

a)a) read an employee name (NAME), read an employee name (NAME), overtime hours worked (OVERTIME), overtime hours worked (OVERTIME), hours absent (ABSENT) andhours absent (ABSENT) and

b)b) determine the bonus payment determine the bonus payment (PAYMENT). (PAYMENT).

Example 7Example 7

Bonus ScheduleBonus Schedule

OVERTIME – (2/3)*ABSENTOVERTIME – (2/3)*ABSENT Bonus PaidBonus Paid

>40 hours>40 hours>30 but >30 but 40 hours 40 hours>20 but >20 but 30 hours 30 hours>10 but >10 but 20 hours 20 hours 10 hours10 hours

$50$50$40$40$30$30$20$20$10$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 7Example 7

Flowchart: Draw the flowchart of Flowchart: Draw the flowchart of the above algorithm?the above algorithm?

Flowchart with Flowchart with looploop

Start

Is light less than 50? Turn lamp on

Yes

No


Start


Yes

No

Turn lamp off


Start


Yes

No

Turn lamp off

Beep

ScenariosScenarios

An automatic bell rings in a shop An automatic bell rings in a shop when somebody enterswhen somebody enters

Gates open when somebody Gates open when somebody approaches themapproaches them

The turnstile at the fun park The turnstile at the fun park registers people as they want to registers people as they want to enter and displays a green lightenter and displays a green light

7.6 T2a

algorithms & flowcharts

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