1. Introduction to Programming
Algorithms
Andreas Savva

2. What is an algorithm?
An Algorithm is a detailed sequence of simple steps that are needed to solve a problem.
It is a step-by-step solution to a problem.

3. Mathematical Example
Problem: What is the value of x in the following equation?
5x – 10 = 30
Algorithm (Solution):
Step 1: 5x =
Step 2: 5x = 40
Step 3: x = 40/5
Step 4: x = 8

4. Making a cake Step 1: Preheat oven to 200 degrees.
Step 2: Mix the eggs with the sugar.
Step 3: Add the butter, flour, and the rest of the ingredients.
Step 4: Stir for 5 minutes.
Step 5: Put the mixture into a baking pan and cook it in a 175 degrees for 40 minutes.
Step 6: Keep it in the pan for 15 minutes to cool down.
Step 7: Serve with vanilla ice-cream.

5. Algorithms The Problem: How will the robot go to the file folder?
Step 1: Move 3 squares and turn right.
Step 2: Move 1 square and turn left.
Step 3: Move 2 squares and turn left.
Step 4: Move 2 squares and turn right.
etc.
The Problem: How will the robot go to the file folder?

6. Representation of Algorithms
Verbal representation
Pseudo-code
Flowchart

7. Verbal representation of Algorithms
Example: Write an algorithm to read and calculate the average of three numbers.
Algorithm:
Step 1: Ask for the first number.
Step 2: Ask for the second number.
Step 3: Ask for the third number.
Step 4: Add the three numbers to find their sum.
Step 5: Divide the sum by 3.
Step 6: Display the result.

8. Flowcharts - graphical representation of an algorithm
Start – Finish
Input – Output
Processing
Sub-programs (Separate flowchart)
Choice Statements (Question, Decision)
Comments
Flow

9. Flowchart G R Sum a Average b c Start Read a Read b Read c
Sum  a + b + c
Average  Sum / 3
Display Average
Finish

10. Structures
For the solution of a problem we use three basic structures:
Sequential structure
Conditional structure
Repetitive structure

11. Example 2
Write an algorithm to read two numbers and display the appropriate message if the two numbers are equal or not.
Read a.
Read b.
If a = b then display that the two numbers are equal.
Else display that the two numbers are NOT equal.

12. Conditional Structure Start Read a Read b FALSE a = b ? TRUE Display:
”The two numbers
are not equal”
Display:
”The two numbers
are equal”
Finish

13. Example 3
Write an algorithm to read two numbers a and b and find the sum of all the numbers between a and b inclusive. i.e.
a = 3, b = 7, Sum = = 25
a = 1, b = 100, Sum = … = 5,050
Read a, b
Sum  0
Counter  a
If Counter > b then Goto 8
Sum  Sum + Counter
Counter  Counter + 1
Goto 4
Display Sum

14. Repetitive Structure Start Read a, b Sum  0 i  a i is the Counter
i > b ?
TRUE
FALSE
Sum  Sum + i
i  i + 1
Display Sum
Finish

15. Exercises Design a flowchart for the following problems:
Calculate the weekly salary of an employee, when the employee-name, working-hours, and rate-per-hour are given. If the working-hours exceed 40, the rate-per-hour is double than the normal hour.
Given 4 numbers X1, X2, X3, and X4, find and display the smaller one.
Given two numbers A and B. Calculate and display the remainder of their division B:A. (Hind: Keep subtracting A from B until you find a smaller number than A. i.e. for the division 20:6 it will be 20 – 6 = 14; 14 – 6 = 8; 8 – 6 = 2; so Remainder = 2).