Write a pseudocode to calculate the factorial of a number (Hint: Factorial of 5, written as 5! = 5×4×3×2×1).

Exercise · Q15

Q. Write a pseudocode to calculate the factorial of a number (Hint: Factorial of 5, written as 5! = 5\times4\times3\times2\times1).

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Concept understanding — Iteration With Condition

Iteration With Condition

Imagine you're searching for a lost key in a dark room. You don't know how many steps you'll need — you just keep moving your hand along the floor until you feel the metal. You're repeating the same action (searching), but you stop only when a specific condition is met (you touch the key).

That's iteration with a condition. It's the idea of repeating a process not a fixed number of times, but while something remains true, or until something becomes true.

The Intuition

Most everyday loops are conditional. You don't say "I will stir the tea exactly 47 times." You say "I will stir the tea until the sugar dissolves." The number of stirs depends on when the condition (sugar dissolved) is satisfied.

In programming and mathematics, this is far more natural than a fixed-count loop. You often don't know in advance how many repetitions you'll need — you only know the rule that should keep you going, or the rule that should stop you.

The Precise Statement

An iteration with condition is a control structure that repeatedly executes a block of statements as long as a given Boolean condition evaluates to true. The condition is checked before (or after) each execution of the block.

The two standard forms are:

1. While loop (entry-controlled)

while (condition):
    statement(s)

The condition is tested first. If it's true, the block runs; then the condition is tested again. If it's false from the start, the block never runs.

2. Do-while loop (exit-controlled)

do:
    statement(s)
while (condition)

The block runs once unconditionally, then the condition is tested. If true, it repeats; if false, it stops. This guarantees at least one execution.

Watch out

A common mistake is writing a condition that never becomes false — an infinite loop. For example, while (x > 0) where x is never decreased. The program will run forever (or crash). Always ensure the body of the loop changes something that affects the condition.

A Concrete Example

Suppose you want to find the smallest power of 2 greater than 1000. You don't know the answer in advance — you need to keep doubling until you cross the threshold.

n = 1
while (n <= 1000):
    n = n * 2

Trace it:

Start: n = 1. Is 1 <= 1000? Yes → n = 2
n = 2. Is 2 <= 1000? Yes → n = 4 …

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Multiply a running product by every integer from 1 up to the number:

FACTORIAL
    INPUT num
    SET fact = 1, i = 1
    WHILE i <= num
        fact = fact * i
        i = i + 1
    END WHILE
    PRINT fact
END

Trace for num = 5: fact goes 1 → 1 → 2 → 6 → 24 → 120.

num = int(input()); fact = 1
for i in range(1, num + 1):
    fact = fact * i …

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Keep a running product fact starting at 1 and multiply it by every counter value from 1 to num — for 5 the product grows 1, 2, 6, 24, 120.

The idea (accumulation by multiplication). Factorial is repeated multiplication: 5! = 5×4×3×2×1. Just as a running sum starts at 0, a running product must start at 1 (the multiplicative identity); a counter-controlled loop then folds each integer into the product.

Pseudocode

FACTORIAL_ALGO
Step 1: INPUT num
Step 2: SET fact = 1
Step 3: SET i = 1
Step 4: WHILE i <= num, REPEAT Steps 5-6
Step 5:     fact = fact * i
Step 6:     i = i + 1
Step 7: PRINT "Factorial =", fact
END

Python verification

num = int(input("Enter a number: "))
fact = 1
for i in range(1, num + 1):
    fact = fact * i
print("Factorial =", fact)

Dry run for num = 5

Pass	i	fact = fact × i
1	1	1 × 1 = 1
2	2	1 × 2 = 2
3	3	2 × 3 = 6
4	4	6 × 4 = 24
5	5	24 × 5 = 120

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Q.Write a pseudocode to calculate the factorial of a number (Hint: Factorial of 5, written as 5! = 5×4×3×2×1).

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