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**Introduction to Programming**

Algorithms Andreas Savva

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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.

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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

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**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.

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**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?

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**Representation of Algorithms**

Verbal representation Pseudo-code Flowchart

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**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.

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**Flowcharts - graphical representation of an algorithm**

Start – Finish Input – Output Processing Sub-programs (Separate flowchart) Choice Statements (Question, Decision) Comments Flow

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**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

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

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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.

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**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

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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

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**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

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**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).

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