Factorial (Python)

Factorial example:

 

 def r_factorial(n):
    if n==1:
        return n
    else:
        t=r_factorial(n-1)
        t=t*n
    return t
    
print(r_factorial(5)) 

Why once t=1 the function continue?

The reason the recursion continues after reaching n == 1 is because of how recursive function calls work. Let's break it down step by step.

Understanding Recursive Execution:

Each recursive call pauses execution until the next recursive call returns a value. The recursion only stops when it reaches the base case, which is n == 1. At that point, the function starts returning values back up the recursive stack.

Step-by-Step Breakdown:

When you call recur_factorial(5), the function calls itself repeatedly, decreasing n each time:

1. r_factorial(5): Calls r_factorial(4), waiting for its result.

2. r_factorial(4): Calls r_factorial(3), waiting for its result.

3. r_factorial(3): Calls r_factorial(2), waiting for its result.

4. r_factorial(2): Calls r_factorial(1), waiting for its result.

5. r_factorial(1): Base case reached → returns 1.

Now, as each function returns, it resumes execution from where it left off:

6. r_factorial(2): t = 1 * 2 = 2, returns 2.

7. r_factorial(3): t = 2 * 3 = 6, returns 6.

8. r_factorial(4): t = 6 * 4 = 24, returns 24.

9. r_factorial(5): t = 24 * 5 = 120, returns 120.

Why the Loop "Keeps Working":

The function doesn't loop in the traditional sense (like a for or while loop). Instead, it stacks function calls.

Each function call pauses execution until the smaller subproblem is solved.

Once n == 1 is reached, the function starts returning values back up.

This is a fundamental principle of recursion: solve the smallest problem first, then use that result to solve the larger problems.

Example from the Python course:

https://www.youtube.com/watch?v=fW_OS3LGB9Q&t=869s