Lesson 66: Worked Examples of Algorithms

Example 1: Sequence Algorithm

Write an algorithm to calculate the sum of the first n positive integers.

1. Input n
2. Initialize sum = 0
3. For i = 1 to n
4. sum = sum + i
5. Output sum

Example 2: Selection Algorithm

Write an algorithm to find the maximum of two numbers.

1. Input a and b
2. If a > b then
3. Output a
4. Else
5. Output b

Example 3: Iteration Algorithm

Write an algorithm to calculate the factorial of a given number n.

1. Input n
2. Initialize factorial = 1
3. For i = 1 to n
4. factorial = factorial x i
5. Output factorial

Example 4: Recursion Algorithm

Write an algorithm to calculate the Fibonacci sequence up to the nth term.

1. Input n
2. If n = 1 then
3. Output 0
4. Else if n = 2 then
5. Output 1
6. Else
7. Output fib(n-1) + fib(n-2)

Designing Solutions

Use structured diagrams and pseudocode to construct solutions. Decompose problems into smaller parts and design a solution for each part. For example, a grade management system can be designed using structured diagrams and pseudocode in the same way.