Understanding Time complexity of recursive functions

Hi, in this video i will show how to analyse Time Complexity of a function with multiple recursion calls.

[ParthPaTeL-wmkt]

Really straight to the point, likedd it.

[Alptugaydin]

It was very clear to understand. Thank you..

[elhouarizohier]

thank you, this was extreamly helpfult and straight to the point

[dhruvsaraswat]

Should we express the depth of the tree as 'N', or as a function of 'n' ( the size of the input ) ?
Lets say that instead of "f( n - 1 ) + f( n - 1 )", the recursive call was "f( n / 2 ) + f( n / 2 )", in this case the depth would change, and as a result, the Time Complexity would also change.

[roomswilldo]

Wouldn't it by 2^n-1? Because f(2) gives 2 outputs, f(3), gives 4 outputs (2^2), f(4) gives 8 outputs (2^3), and so on.

[Vikasslytherine]

What if in the recursive call, n reduces by 2, 3... instead of 1? I guess the depth would be reduced.

[thepresistence]

I followed your procedure but I am getting some wrong answer:

code:
def factorial(n):
if n < 0: # O(1)
return -1 # O(1)
elif n == 0: # O(n)
return 1 # O(n)
else:
return n * factorial(n-1) # O(n)

print(factorial(3))

## O( branches ^ depth)
* Here the function calls 3 times, So = O(N 3)

But the real answer is O(N) only Why?