Pseudo Code for Calculating Factorial Using REPEAT-UNTIL Loop

Overview

This section outlines the logic for computing the factorial of a non-negative integer using a REPEAT-UNTIL loop. The factorial of a non-negative integer n is the product of all positive integers less than or equal to n, denoted as n!.

Input

• A non-negative integer n.

Output

• The factorial value of n.

Assumptions

• The input integer n is a non-negative integer (0 or greater).

Pseudo Code

BEGIN
    // Initialize variables
    DECLARE integer n
    DECLARE integer factorial
    DECLARE integer counter

    // Prompt user for input
    OUTPUT "Enter a non-negative integer: "
    INPUT n

    // Initialize factorial to 1 (since 0! = 1)
    factorial = 1

    // Initialize counter to 1 (starting point for multiplication)
    counter = 1

    // REPEAT-UNTIL loop to calculate factorial
    REPEAT
        // Update factorial by multiplying with counter
        factorial = factorial * counter

        // Increment the counter
        counter = counter + 1
    UNTIL counter > n  // Repeat until counter exceeds n

    // Output result
    OUTPUT "The factorial of ", n, " is: ", factorial
END

Explanation of the Logic

1. Initialization:

   • Set factorial to 1, as the product identity for multiplication.
   • Set counter to 1, to begin the multiplication sequence.

2. User Input:

   • Prompt the user to input a non-negative integer n.

3. Loop Structure:

   • The REPEAT-UNTIL loop continues to execute until counter exceeds n.
   • Within the loop:
     • Update the factorial by multiplying it with the current counter.
     • Increment counter by 1.

4. Final Output:

   • Once the loop completes, the program outputs the factorial of n.

Conclusion

This pseudo code succinctly captures the essence of calculating the factorial using a REPEAT-UNTIL loop. It provides a clear, step-by-step breakdown of the logic required to achieve the task. Adjustments can be made to handle edge cases or to improve user interaction as needed.