MATLAB recursive function [Factorials]

Question

The code works but I am confused. When n==1, I am assigning a=1, shouldn't that overwrite the value and return only 1?

format compact
fct(5)

---

function a = fct(n)
    if n==1
       a = 1; 
    else 
       a = n*fct(n-1);
    end
end

Answer 1

This is how I picture it... Below is a recursion/factorial diagram that shows the cascading effect of the recursive calls. At the deepest recursive call fct(1) is evaluated which is equal to 1 given by the first if statement. Each recursive call is therefore defined by a deeper recursive call. I typically like to decompose the recursive function until reaching its terminating case. I guess a way to phrase it is "a function within function" not so much of a loop.

Where, fct(1) → 1

---

format compact
fct(5)

function a = fct(n)
    if n == 1
       a = 1;
    else
       a = n*fct(n-1);
       fprintf("%d\n",a);
    end

end

Cumulative/Recursive Results:

2
6
24
120

ans =
   120

---

My Preferred Structuring:

format compact
fct(5)

function a = fct(n)
    if n > 1
       a = n*fct(n-1);
    else
       a = n;
    end
end