Given a non-negative integer n, compute n! (n factorial). Input: one integer…

Concept

For a non-negative integer n, the factorial n! is the product of all positive integers from 1 through n. By definition, 0! = 1.

An iterative algorithm maintains a running product. Starting from 1 is essential because 1 is the multiplicative identity, so it does not change the product.

Application

1. Read n and initialize result = 1.

2. For each integer i from 2 through n, update result = result × i.

3. Print result. If n is 0 or 1, the loop performs no multiplication and the initialized value 1 is printed.

Trace for n = 5 (result starts at 1):

1. i = 2: result = 1 × 2 = 2

2. i = 3: result = 2 × 3 = 6

3. i = 4: result = 6 × 4 = 24

4. i = 5: result = 24 × 5 = 120

The algorithm uses O(n) time and O(1) extra space.

Cross-check

For n = 4, the same process gives 1 × 2 × 3 × 4 = 24, matching the sample output. For n = 0, it returns 1, matching the definition of 0!.