Pseudo Code for Calculating Factorial of a Non-Negative Integer

Definition

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n.

Logic Overview

1. Input: A non-negative integer n.
2. Output: The factorial of n (denoted as n!).
3. Calculation: Multiply all integers from 1 to n.
4. Edge Case: Factorial of 0 is defined as 1.

Pseudo Code

FUNCTION CalculateFactorial(n):
    IF n < 0 THEN
        RETURN "Error: Factorial of a negative number is undefined"
    
    SET factorial = 1
    
    FOR i FROM 1 TO n DO
        factorial = factorial * i
    
    RETURN factorial

Explanation of the Pseudo Code

1. Function Declaration: CalculateFactorial(n) defines a function taking one parameter n.
2. Error Handling:
   • Check if n is less than 0. If so, return an error message.
3. Initialization:
   • Set a variable factorial to 1 to hold the result of the multiplication.
4. Looping through Integers:
   • Use a FOR loop to iterate from 1 to n.
   • In each iteration, multiply the current value of factorial by i, accumulating the product.
5. Return the Result: After the loop finishes, return the computed factorial.

Example Calculation

For n = 6:

• Loop iterations will be:
  • factorial = 1 * 1 (i = 1)
  • factorial = 1 * 2 (i = 2)
  • factorial = 2 * 3 (i = 3)
  • factorial = 6 * 4 (i = 4)
  • factorial = 24 * 5 (i = 5)
  • factorial = 120 * 6 (i = 6)

Final output: 720

This pseudo code provides a clear and structured approach to calculating the factorial of a non-negative integer, facilitating understanding and implementation in any programming language.