Introduction to Programming Algorithms Andreas Savva

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.

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

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.

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?

Representation of Algorithms Verbal representation Pseudo-code Flowchart

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.

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

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

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

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.

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

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 = 3 + 4 + 5 + 6 + 7 = 25 a = 1, b = 100, Sum = 1 + 2 + 3 + … + 100 = 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

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

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).