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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 CSC 244 Concepts of Algorithms3
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Concepts of AlgorithmsCSC-244 Unit Zero
Pseudo code, Flowchart and Algorithm
Master PrinceComputer College
Qassim University K.S.A.
General Information• Instructor: Shahid Iqbal Lone• Tel: 0541-924839• E-mail:
[email protected]• Discussion / Lectures/mailing GROUP:
CSC-244 at yahoo group• Text Books:
Introduction to Algorithm Second Edition by
Thomas H. CormenCharles E. Leiserson
Ronald L. RivestClifford Stein
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
CSC 244 Concepts of Algorithms 3
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.
CSC 244 Concepts of Algorithms 4
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.
CSC 244 Concepts of Algorithms 5
Pseudocode & AlgorithmPseudocode:• 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”
CSC 244 Concepts of Algorithms 6
Pseudocode & Algorithm• Detailed Algorithm • Step 1: Input M1,M2,M3,M4
Step 2: GRADE (M1+M2+M3+M4)/4
Step 3: if (GRADE < 50) thenPrint “FAIL”
elsePrint “PASS”
endif
CSC 244 Concepts of Algorithms 7
The Flowchart• (Dictionary) A schematic representation of a sequence of
operations, as in a manufacturing process or computer program.
• (Technical) A graphical representation of the sequence of operations in an information system or program. Information system flowcharts show how data flows from source documents through the computer to final distribution to users. Program flowcharts show the sequence of instructions in a single program or subroutine. Different symbols are used to draw each type of flowchart.
CSC 244 Concepts of Algorithms 8
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
CSC 244 Concepts of Algorithms 9
Flowchart Symbols
CENG 213 Data Structures 10
Example-1
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” endifStep 4: End
START
InputM1,M2,M3,M4
GRADE(M1+M2+M3+M4)/4
ISGRADE<50
STOP
YN
CSC 244 Concepts of Algorithms 11
PRINT“FAIL”
PRINT“PASS”
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)
CSC 244 Concepts of Algorithms 12
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
CSC 244 Concepts of Algorithms 13
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
CSC 244 Concepts of Algorithms 14
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
CSC 244 Concepts of Algorithms 15
Example 4
• Write an algorithm and draw a flowchart that will calculate the roots of a quadratic equation
• Hint: d = sqrt ( ), and the roots are: • x1 = (–b + d)/2a and x2 = (–b – d)/2a
2 0ax bx c 2 4b ac
CSC 244 Concepts of Algorithms 16
Example 4
Pseudocode: • Input the coefficients (a, b, c) of the
quadratic equation• Calculate d• Calculate x1 • Calculate x2• Print x1 and x2
CSC 244 Concepts of Algorithms 17
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
CSC 244 Concepts of Algorithms 18
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
CSC 244 Concepts of Algorithms 19
DECISION STRUCTURES
isA>B
Print BPrint A
Y N
CSC 244 Concepts of Algorithms 20
IF–THEN–ELSE STRUCTURE
• The structure is as followsIf condition then
true alternative else
false alternativeendif
CSC 244 Concepts of Algorithms 21
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
CSC 244 Concepts of Algorithms 22
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
CSC 244 Concepts of Algorithms 23
Example 5
MAX VALUE1
Print“The largest value is”, MAX
STOP
Y N
START
InputVALUE1,VALUE2
MAX VALUE2
isVALUE1>VALUE2
CSC 244 Concepts of Algorithms 24
NESTED IF’S
• One of the alternatives within an IF–THEN–ELSE statement– may involve further IF–THEN–ELSE statement
CSC 244 Concepts of Algorithms 25
Example 6
• Write an algorithm that reads three numbers and prints the value of the largest number.
CSC 244 Concepts of Algorithms 26
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
CSC 244 Concepts of Algorithms 27
Example 6
• Flowchart: Draw the flowchart of the above Algorithm.
CSC 244 Concepts of Algorithms 28
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).
CSC 244 Concepts of Algorithms 29
Example 7
Bonus ScheduleOVERTIME – (2/3)*ABSENT Bonus Paid
>40 hours>30 but 40 hours>20 but 30 hours>10 but 20 hours 10 hours
S.R. 50S.R. 40S.R. 30S.R. 20S.R. 10
CSC 244 Concepts of Algorithms 30
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 S.R.”, PAYMENT
CSC 244 Concepts of Algorithms 31
Example 7
• Flowchart: Draw the flowchart of the above algorithm?
CSC 244 Concepts of Algorithms 32
33
Problem Statement
Convert a decimal number into binary
Convert 75 to Binary
75237 1218 129 024 122 021 020 1
1001011
remainder
CSC 244 Concepts of Algorithms 34
We will write down the pseudo code for this problem in a formal way.
CSC 244 Concepts of Algorithms 35
36
Solution in Pseudo Code
1. Let the decimal number be an integer x, x > 02. Let the binary equivalent be an empty string y3. Repeat while x > 0 {
Determine the quotient & remainder of x ÷ 2y = CONCATENATE( remainder, y )x = quotient
}4. Print y5. Stop
CSC 244 Concepts of Algorithms
Q: Is this the only possible algorithm for converting a decimal number into a binary representation?
If not, then is this the best?In terms of speed?In terms of memory requirement?In terms of ease of implementation?
You must ask these questions after writing any algorithm!
CSC 244 Concepts of Algorithms 37
38
Tips on Writing Good Pseudo Code• Use indention for improved clarity
• Do not put “code” in pseudo code – make your pseudo code computer language independent
• Don’t write pseudo code for yourself – write it in an clear fashion so that anyone of the team member with a reasonable knowledge can understand and implement it.
• Prefer formulas over English language descriptions
CSC 244 Concepts of Algorithms
Start
Find quotient& remainder
of x ÷ 2
INPUT x
x>0 ?
Print y
Stop
y = CONC(remainder, x)x = quotient
x is the decimal numbery is the binary equivalent
Flowchart of Decimalto Binary Conversion
Yes
No
CSC 244 Concepts of Algorithms 39
Start
Find quotient & remainder of x ÷ 2
Get x
Print y
Stop
y = CONC(remainder, x)x = quotient
x is the decimal numbery is the binary equivalent
Another Flowchart of Decimalto Binary Conversion
CSC 244 Concepts of Algorithms 40
While x > 0
Example 8Write a program that asks the user to enter a temperature reading in centigrade and then prints the equivalent Fahrenheit value.
fahrenheitPrompt for centigrade valueRead centigrade valueCompute fahrenheit valueDisplay fahrenheit value
centigrade
OutputProcess InputSTOP
inputCentcentigrade
calcFahfahrenheit = (1.8*centigrade) + 32
outputFahfahrenheit
STARTConvert centigrade to fahrenheit
PSEUDOCODE:Display "Enter Centigrade: "Input centigradeFahrenheit = 1.8 * centigrade + 32Display "Centigrade to Fahrenheit = " fahrenheit
CSC 244 Concepts of Algorithms 41
END
CSC 244 Concepts of Algorithms 42