1. MIS 131 Introduction to Algorithms and Programming 2017/2018 Fall - Chapter 2 – Algorithms, Pseudocodes and Flowcharts 1

2. In this chapter, you will learn:
Objectives
In this chapter, you will learn:
To understand basic problem solving techniques.
Inputs and outputs of a proglem
Concept of variables
To be able to develop algorithms through the process of top-down, stepwise refinement.
To be able to convert the algorithm to pseudocode and flowcharts

3. Before writing a program:
2.1 Introduction
Before writing a program:
Have a thorough understanding of the problem
Carefully plan an approach for solving it
The program should be carifully designed
While writing a program:
Know what “building blocks” are available
Use good programming principles

4. Algorithm: procedure in terms of
2.2 Algorithms
Computing problems
All can be solved by executing a series of actions in a specific order
Algorithm: procedure in terms of
Actions to be executed
The order in which these actions are to be executed
Program control
Specify order in which statements are to be executed

5. Dack of Cards
In a game - dack of cards
each player pull a card at the top of the dack
read the task written on it
perform the task
then pull the next card on the top of the dack

6. Example 2.1 Registration
A real life example
Describe steps of registration to an universty
step by step description of how a new commer is to register to an universty

7. Example 2.1. Registering to an University Algorithm
1 Obtain required forms
2 Fill out the forms
3 Other required materials are prepaired
identification, diploms
4 Registration fee is paid
5 forms are submited to the relevent person
6 if something is mising
goto step 2
7 Sign the agrement
8 Registration is complete

8. When each step is compleated
Notice that
When each step is compleated
next step is passed
it is also possible to branch a previous or later step
in this example from step 6 to srep 2
The action in each step may depend on a condition
in step 6 if everything is OK continue otherwise branch to step 2
Each of these steps may consists of sub steps
ex: step 2 fill out forms: there may be three different forms
each of which may be a sub step of step 2
2a : a from for registration office
2b : a form for university hospital
2c : a form for university library

9. Example 2.2 Calculating area of a regtangle
Calcuating area of a rectangle
Algortihm:
1- Start
2- Get value of hight
3- Get value of width
4- Multiply hight by width to obtain area
5- Display the resulting area to the screen
6- Stop

10. Note
Without performing steps 2 and 3
Step 4 can not be performed
Similarly
Without performing steps 4
Step 5 can not be performed
But
Steps 2 and 3 can be interchanged

11. Pick up a real life situation that interest you for example:
Exercis 2.1
Pick up a real life situation that interest you
for example:
driveing a car
cooking egg or cake
Construct the algorithm to someone who does not have any idea obout that situation

12. 2.3 Pseudocode Pseudocode
Artificial, informal language that helps us develop programs
One step closer to programming languages
Similar to everyday English on one side and programming languages on the other side
Not actually executed on computers
Helps us “think out” a program before writing it
Easy to convert into a corresponding C program
Consists only of executable statements

13. Pseudocode for Example 2.2
1 Start
2 a Display “enter height of the rectange”
2 b Input heigth
3 a Display “enter width of the rectange”
3 b Input width
4 Set area = height * width
5 Display “the area of the regtanle” , area
6 Stop or end

14. In the algorithm :in step 2 In the pseudocode14
Note That
In the algorithm :in step 2
Getting the height from the user
In the pseudocode
first write a message to be displayed in the screen
informing the user what to enter as an input
Then let the user enter a real number and press ENTER key
The number entered by the user is stored in the variable heigth
Similarly for getting width of the rectangle – in step 3

15. The user first see the message15
When the pseudocode is implemented in any programming languare such as Java, C# or Python
The user first see the message
“Enter heitht of the rectanvge ”
in the computers screen
The user is expected to enter real number for the height end press ENTER key
The Input heigth statement
obtains the chacters entered by the user converts into a numerical variable called height to be used in subsequent steps of the pseudocode or program

16. Building Blocks Input output transfer
Calculations in between - processing
Decision making
Iteration
Variables
Store data in memory
different types in different languages
İntegers, real, character, string ...
Input: obtain a value from the user and store in a variable
enter a value for radius of a circle to compute its area
enter your name lastname id number
make a choice Yes/No to save or not

17. Variables numerical variables Strings : Store data in memory
different types in different languages
Integers, real, character, string, logical (tgru or false) ...
numerical variables
heigth, width, age totalSales
Strings :
Name, last name, address,
“Bertan” , “Badur”,
usually presented in quats “.....”

18. what is your age or weight
Variable in daily iife
what is your name?
stored in your memory as a string
what is your age or weight
you know the meaning of age or weight
stroded as an integer or real and changes over time
What is your GPA
you know wht GPA is but not yet has a value as a new studeent
What is your garbay score
this does not make a sense to you
no such think in your memory
when asked you are supprised or hesitate to answer
BUT A COMPUTER PRGRAM FAİLS

19. Output: display the results of the problem
Outtput
Output: display the results of the problem
some variables
display area
constant messages
Display “welcome to Java”
Display “you failed to register”
expressions
Display pi*r2
or a mixture of them
Display “the area is:“, area
E.g.: displays when the value of area is 200
the area is: 200

20. Calculations - processing
aritmetic and logical computations
intermediate resulst are also in variables
E.g.:
Set area = hight*width
area is the product of hight and width
Set valueAddedTax = taxRate*basePayment
Set total = total + new grade
add new grade to the total

21. 2.4 Control Structures Sequential execution Transfer of control
Statements executed one after the other in the order written
Transfer of control
When the next statement executed is not the next one in sequence
Overuse of goto statements led to many problems
Bohm and Jacopini
All programs written in terms of 3 control structures
Sequence structures: Built into Java. Programs executed sequentially by default
Selection structures: Java has three types: if, if…else, and switch
Repetition structures: Java has three types: while, do…while and for

22. Simple Building Blocks
We will start with
input
get data from the user
store in variables
process or calculation
Store the results in variables
output
dsiplay message and/or variables to the screen
Variables of different types
Stored in memory

23. Single-entry/single-exit control structures
2.3 Flowcharts
Flowchart
Graphical representation of an algorithm
Drawn using certain special-purpose symbols connected by arrows called flowlines
Rectangle symbol (action symbol):
Indicates any type of action
Oval symbol:
Indicates the beginning or end of a program or a section of code
Single-entry/single-exit control structures
Connect exit point of one control structure to entry point of the next (control-structure stacking)
Makes programs easy to build

24. Flowchart Symbols start or end calculation flow decision making output
input

25. Example 2.3 Foreign Exchange Problem
The amount of $ in your hand makes how meny TL
1 $ 3.44 TL
Inputs::
amount of dollar in your hand
Output:
How much does the dollar worth in terms of TL
:Limitations
1 dolar is 3.44 TL forex rate is constant
just convert to TL

26. Ex 2.13 Algorithm of exchange rate calculation26
Ex 2.13 Algorithm of exchange rate calculation
1 Start
2 Define the forex rate
3 Get dollar amount
4 TL correspondence of the dollar is computed
TL = dollar * exchage rate
5 dsiplay TL
6 Stop or End
What variables are needed?
dollar, TL
exchange rate?

27. 3a Display “Enter dollar in your hand” 3b Input dollar 27
Pseudocode
1 Start
2 Set forexRate = 3.45
3a Display “Enter dollar in your hand”
3b Input dollar
4 Set tl = dollar * forexRate
5 Display “your”, dollar , “worths”, tl
6 Stop or End

28. Variables ForexRate dollar tl a real number set at the begining28
Variables
ForexRate
a real number set at the begining
fixed it does not change
dollar
dollar in the hand of the user
real input
every run of the program has a different value tl
calculated TL amout for the dollar with the dixed forexRate

29. Limitations and Extensions29
Limitations and Extensions
Limitations:
every time a new $ is given the algorithme start from begining
if the user enters a negative value it prints a negative NTL
if the user enters a character it fails to compute
Note:
should the exchange rate be asekd as a second input or is it fixed As it is not chaning very often but it may change hourly
Exercise:
Modify the algorithm when the for ex rate change as well
Extension of the problem
given NTL the user mey want to chose the forex ohter then dollar to purchase

30. Ex 2.4. Length conversion
What is the equivanent of a given inch in term of cm
Inputs:
inch
Output:: cm
Limitations:
just between inch and cm
Note: relation between c.m. and inch is constant and 1 inch is 2.54 cm

31. Ex 2.5. Area and circunference of circle
Given a radius of a circle calcualte its area and circunference
Inputs:
radius
Output:
area and circkunference
Note has two outputs
Limitations:
only for circle
Note:Pi is a universal constant as well

32. Area and Circunference of circle32
Area and Circunference of circle
1 Start
2 Set the value of pi =
2 Get radius
4 Compute area and circunference
4.a area = pi * (radius)2
4b circunf. = 2 * pi * radius
5 display area and circunference to the screen
6 Stop or end
What are variables?
radius, area, circunference
What about pi
its value does not change – universan constant
What are the limitations of the algorithm?

33. Pseudocode for Cirlcle33
Pseudocode for Cirlcle
1 Start
2 Set pi = 3.14
3a Display “Enter radius”
3b Input radius
4a Set area = pi * radius2
4b Set circunference = 2 * pi * radius
5a Display “Area of the circle is” , area
5b Display “Circunference of the circle is”, circunference
6 Stop

34. Ex 2.7 Display a Fixed message
Display your signiture to the screen
when run always displays your name, last name, address and to the screen
Limitation: only one signiture for you
No input, no variables
Output
Name: Bertan
Last name: Badur
Address: Bogazici University
E-male:

35. Ex 2.8 Asking and displaying your personal information
Task: ask name lastname and age
dispay to the screeen
Inputs : name, lastName – String
age - integer
Output: A messge that change according to your name last name and age but has some fixed characters
Example output
Name: İrem
Last Name : Badur
Age: 9

36. Algorithm
1 Start
2 Ask and get name, last name and age of a person
2a ask and get neme
2b ask and get last name
2c ask and get age
3 Dispay personal information in a forfmated way to the screen
3a dispay name
3b dispay last name
3c dispay age
4 Stop

37. Pseudocode
1 Start
2a i Display “Enter your name”
2a ii Input name
2b i Display “Enter your last name”
2b ii Input lastName
2c i Display “Enter your age”
2c ii Input age
3a Display “Name:” , name
3b Display “Last Name:”, lastName
3c Display “Age:”, age
4 Stop

38. Variables name , lastName age String – set of characters
integer your age

39. Flowchart
Draw the flowchart

40. Ex 2.9. Exam grades Computes exam statistics Inputs: Outputs: Limits:
student grades
Outputs:
avgerage, min, max, letter grades, ...
Limits:
only for one exam

41. A Simple Grade Average Calculation Problem
Task: There are only three students in a class
Ali, Ahmet and Nazlı. Get their exam grades from the user and calculate and display the class average to the screen.

42. Algorithm A class consisting of three students: Ali,Ahmet, Nazlı42
Algorithm
A class consisting of three students: Ali,Ahmet, Nazlı
1 Start
2 Get Ali’s grade
3 Get Ahmet’s grade
4 Get Nazlı’s grade
5 Compute the average grade
Average grade = (Ali’s grade + Ahmet’s grade + Nazlı’s grade)/3
6 Display the average grade
7 End
Variables:
Ali’s grade, Ahmet’s grade, Nazlı’s grade,
average grade

43. Pseudocode and variables
1 Start
2a Declare Integer alisGrade
2b Declare Integer ahmetsGrade
2c Declare Integer nazlisGrade
2d Declare Real average
3a Display “Enter Ali’s grade”
3b Input alisGrade
4a Display “Enter Ahmet’s grade”
4b Input ahmetsGrade
5a Display “Enter Nazli’s grade”
5b Input nazlisGrade

44. Pseudocode and variables (cont.)
6 Set average = (alisGrade + ahmetsGrade +
nazlisGrade)/3
7 Display “the class average” , average
End
Variables
alisGrade, ahmetsGrede and nazlisGrade are declared as integers
average is declared as Real
Note that: if this pseudocode is implemented in Java or C programming languages
sum of three integers is an integer dividing by 3
you may lose the remainder because of ineger division

45. Solution
Declare the student grades as Real variables
average = ( ) / 3
here average is
if grades are declared as integers
average = ( ) / 3
here average is

46. Another Important feature
In step 6 of the pseudocode
average can be computed in one asignment statement
or it can be computed is steps as follows
6a Set sum = alisGrade
6b Set sum = sum + ahmetsGrade
6c Set sum = sum + nazlisGrade
6d average = sum / 3
How do you get rid of the information lose due to integer division ?

47. Ex 2.10. Purchase Note prices of goods are not inputs
what is total payment after a sale
Inputs:
products SKU and amounts
Outut:
invoice total payment value added tax
Note prices of goods are not inputs

48. two products apple and pair Value added tax Input: Output: Variables:48
Purchase Problem tasl
two products apple and pair
prices are given not chaning
Value added tax
tax rate is constant
Input:
AmoutApple, AmountPair – asked to user
Output:
netPay, VAT, grossPay – calculated and printed
Variables:
PriceApple, PricePair – fixed
VAT Rate – fixed

49. Purchase Problem Algorithm49
Purchase Problem Algorithm
1 Start
2a define prices for the two goods
PriceApple = 4, PricePair = 5
2b define value added tax rate
VATRate = 0.18
3 get amount of apple and pair purchased from the user
4 Calculate net payment
netPay = PriceApple*AmountApple + PricePair*AmountPair
5 Calculate VAT
VAT ? netPay*VATRate
6 Calculate gross payment
grossPay = netPay + VAT
7 print net psyment, VATand total payment to screen
8 End

50. you can declare them a constants 50
pseudocode flowchart
Exercise to you
Note if you are sure that value of a variable will not change through out the program,
you can declare them a constants
many programming languages including Java has a syntax for constants
any attempt to change the value of a constant is a syntax error
Examples of well known constants
pi = , e = 2.713
speed of light, Avagadro number

51. Constants in pseudocodes
Constant Integer priceApple = 4
Constant Real pi = 3.14

52. Notes Purchase Problem52
Notes Purchase Problem
Note that
calculating net Paymnet can be performed in two steps as
4a Set netPay = PriceApple*AmountApple
4b Set netPay = netPay + PricePair*AmountPair

53. Ex 2.11.Tax Calculation Compute the tax burden Inputs: Output:
yearly income
Output:
tax burden
Note: tax rate is given

54. Ex. 2.12 Interest calculation
Depositing some money calculate interest earned on that
Inputs:
Principle
term
yearly interest rate
Output:
money
interest earned :

55. Suppose a language does not support mode 55
Exercise
Suppose a language does not support mode
In Java mode is implemented by %
14 % 3 = 2
12 % 3 = 0
How do you imlement mode if it is not supported by the language syntax

56. Mode opperation give the remainder Ex 10 mode 3 = 1 9 mode 3 = 0 56
Solution
Mode opperation give the remainder
Ex 10 mode 3 = 1
9 mode 3 = 0
Suppose mode is not supported by the syntax of a programming labnguage
How would you imlement mode?
Set modeab = a mode b
Set modeab = a – (a / b) * b
E.g.: if a = 8, b = 3
a mode b = 8 node 3 = 2
a – (a / b) * b = 8 – (8 / 3) * 3 = 8 – 2*3 = 2

57. Ex 2.13 ATM Problem
Consider a customer intending to withdraw money from an ATM, enters the amount she wnnt to withdrow
available types of notes are say:
100,50,20,10...
assume ATM pays as much 100 as possible then pays the remaining with 50 s and so on
Write the algorithm of money withdrawing problem.How much of the money is paid with what type of notes
and remainging money that can not be paid at all
E.g.: 643 TL is paid with
6 100s, 0 50s, 2 20s and 3 TL can not be paid

58. ATM Problem Hint
Hint: at each step try to identify how much of the money is paid with say by 100s and what is the remaining amount

59. ATM Input and outputs Input: Output: money from the user
how many 100 TL
how many 50 TL
how many 20 TL
how much not paid

60. ATM: Algorithm
1 Start
2 Get money from the user
3a Determine how many 100s are paid
3b Determine remaining money not paid by 100s
4a Determine how many 50s are paid
4b Determine remaining not paid by 50s
5a Determine how many 20s are paid
5b Determine how remaining not paid by 20s
6 Determine money that can not be paid at all
7 Display the results
8 End

61. ATM: variables Variables input - money61
ATM: variables
Variables
input - money
output - howMany100, howMany50, howMany20, notPaid
remaining - used for intermediate calculations

62. Pseudocode of Step 3a and 3b
3a determine how many 100s are paid
3b determine remaining money not paid by 100s
remaining = money
3a howMany100 = remaining / 100
3b remaining = remaining mode 100
Example suppose money is 455
remaining = money: remaining becomes 455
howMany100 = 455 / 100 = 4 – integer division
remaining = remaining mode 100
remaining becomes 55

63. Complete the pseudocode Draw the flowchart Write the Java program63
Exercise
Complete the pseudocode
Draw the flowchart
Write the Java program

64. Exercise Time expression 1
Given a duration of time in hours, munite and seconds expres it in total seconds
E.g.:
given 2 hours, 3 minutes and 5 seconds
it is 7385 seconds
given 2 hours, 0 munites and 30 seconds
it is 7230 seconds
given 0 hours, 20 munites and 40 seconds
it is 1240 seconds

65. Exercise: Time expresion 265
Exercise: Time expresion 2
Given a duration of time in seconds Expres it in hours, munite and seconds
E.g.:
given 7385 seconds
it is: 2 hours, 3 minutes and 5 seconds
given 7230 seconds
it is 2 hours, 0 munites and 30 seconds
given 1240 seconds
it is 0 hours, 20 munites and 40 seconds

66. Exercise: Exchange of values of variables
Given two int type variables
a, b hodling values
E.g.: a = 5, b = 10
Change their values
At the end of the change
a becomes 10 , b becomes 5
i) By using a temporary variable
İi) Without using a temporary variable

67. Exercise: Reverse of an Integer
Given a three digit integer
Examples: 174, 810, 400, 956
print it in reverse order
Examples 174 to 471, 956 to 659, 400 to 4, 810 to 18
Hint:: try to get its first digit, second digit and third digit
then try to construct the reverse number

68. Input and output Input: Output: a three digit integer from the user
its reverse

69. 7 Display reverse to the screen 8 End
Algorithm 1
1 Start
2 get number from user
3 determine ones
4 determine tens
5 determine hundrends
6 compute reverse as
reverse = 100*hundreds+10*tens+ones
7 Display reverse to the screen
8 End

70. Variables for Algorithm 170
Variables for Algorithm 1
Variables
number– input from user
reverse – output to screen
ones, tens, hundreds, remaining

71. Set remaining = number // take a copy of number 3 determine ones:
Hard of the Algorithm 1
Set remaining = number // take a copy of number
3 determine ones:
3a Set ones = remaining mode 10
3b Set remaining = remaining / 10
Example:
number is 743
remaing is 743
ones is 743 mode 10 = 3
remaining is 743 / 10 74
perform step 4 amd 5 to find tens and hudereds

72. Algorithm 2 1 Start 2 get number from user 3 determine hundrends
4 determine tens
5 determine ones
6 compute reverse as
invnumber = 100*hundreds+10*tens+ones
7 Display reverse
8 end

73. Set remaining = number // copy of money 3 determine hundreds:
Algorithm 2
Set remaining = number // copy of money
3 determine hundreds:
3a Set hundreds = remaining / 100
3b Set remaining = remaining mode 100
Example:
number is 743
remaing is 743
hundreds is 743 / 100 = 7
remaining is 743 mode 100 = 43
perform step 4 amd 5 to find tens and ones

74. Algorithm 3
1 Start
2 initialize reverse to zero
3 get number from user
4a determine ones
4b update remainder
4c update reverse
5a determine tens
5b update remainder
5c update reverse

75. Algorithm 3 (contg.) 6a determine hundrends 6b update remainder75
Algorithm 3 (contg.)
6a determine hundrends
6b update remainder
6c update reverse
7 print reverse
8 end

76. Hard of Algorithm 3
initially reverse variable is set to 0
4a determine ones:
Set ones = remaining mode 10
4b update remainder
Set remaining = remaining / 10
4c updata reverse
Set reverse = 10*reverse + ones // inverse becomes ones

77. just before 5 inverse is ones 5a determine tens: 77
Hard of Algorithm 3
just before 5 inverse is ones
5a determine tens:
Set tens = remaining mode 10
5b update remainder
Set remaining = remaining / 10
5c updata reverse
Set reverse = 10*reverse + tems // inverse becomes ones