Algorithms

An algorithm is a finite set of clear, well-defined instructions designed to solve a problem or perform a task. Algorithms are fundamental in mathematics and computer science because they provide a step-by-step method to achieve a result.

 Characteristics of an Algorithm:

• Definiteness: Each step must be clear and unambiguous.
• Finiteness: It must finish after a finite number of steps.
• Input: It should accept zero or more inputs.
• Output: It should produce at least one output.
• Effectiveness: Each step must be basic and executable.

Represent Algorithms:

• Pseudocode: Uses structured English-like statements.
• Flowchart: Diagram using standard symbols for processes, decisions, and flow.
• Natural Language: A written step-by-step explanation.

Common Algorithm Examples in Mathematics:

• Finding the HCF (Greatest Common Divisor) – Euclidean Algorithm
• Finding the LCM (Least Common Multiple)
• Sorting numbers (Bubble sort, Selection sort)
• Searching for a number in a list (Linear search, Binary search)

Steps to Write an Algorithm:

1. Understand the problem clearly.
2. Define the input and output.
3. Write the steps in a logical order.
4. Check if the algorithm covers all possible cases.
5. Test the algorithm with examples.

START
  SET sum = 0
  FOR i = 1 TO 5
    READ number
    sum = sum + number
  NEXT i
  average = sum / 5
  PRINT average
END