understanding fundamentals of recursive functions

Question

I can't seem to fully understand the fundamentals off recursive functions. We have this code:

function myself (n) {
if (n <= 1) {
    return 1;
}
return n * myself(n-1);
}
myself(5);

I get that 5 would be multiplied by 4 equals to 20 and then 20 multiplied by 3 and so on but what I don't quite get is how can 'n' be two different numbers in one function.

`n` is local to an invocation of the function, not to the function itself. — Tobias, Nov 06 '16 at 19:19
Possible duplicate of https://stackoverflow.com/questions/500431/what-is-the-scope-of-variables-in-javascript — Madara's Ghost, Nov 06 '16 at 19:22
I think it goes like this https://sketch.io/render/sk-12d201670252aff23415d719d49cebbf.jpeg — Nenad Vracar, Nov 06 '16 at 19:39

score 6 · Accepted Answer · answered Nov 06 '16 at 19:41

6

how can 'n' be two different numbers in one function

Variable scope exists for a function invocation, not a function definition.

Each call to myself gets an n variable of its very own, which is unrelated to the previously existing ns.

answered Nov 06 '16 at 19:41

Quentin

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Was typing dozens of lines about the virtual machine's call stack when I read your answer. Could not agree more with @TomerW. – Tobias Nov 06 '16 at 19:48
Thanks for the answer, helped a lot. – Benas Lengvinas Nov 06 '16 at 20:06
@Quentin so i thought that i got it but i didn't :D so when myself(n-1) finishes the 'function myself (n // is it 4 now?). And when n is multiplied by n-1 where does the result go? I guess i don't fully understand the scope either.... – Benas Lengvinas Nov 06 '16 at 21:04
"when myself(n-1) finishes the 'function myself (n // is it 4 now?)." — Which `n`? As I said, there are multiple `n`s – Quentin Nov 07 '16 at 09:26
"And when n is multiplied by n-1 where does the result go?" — That never happens. `n - 1` is the argument to a function call, it is the return value of that function call which is multiplied by `n`. As for where it goes, there is a `return` statement on the left hand side, so it is returned to wherever it was called from. – Quentin Nov 07 '16 at 09:27

score 2 · Answer 2 · answered Nov 06 '16 at 19:36

n is a local variable. Your example would execute as follows.

myself(5) 
return 5 * myself(4)
return 5 * (return 4 * myself(3))
return 5 * (return 4 * (return 3 * myself(2)))
return 5 * (return 4 * (return 3 * (return 2 * myself(1))))
return 5 * (return 4 * (return 3 * (return 2 * return 1)))
return 5 * (return 4 * (return 3 * (return 2 * 1)))
return 5 * (return 4 * (return 3 * 2))
return 5 * (return 4 * 6)
return 5 * 24
return 120

n contains a reference to the number parameter at each invocation.

understanding fundamentals of recursive functions

2 Answers2