Recursion in C, understand recursion example

Question

i am having trouble understanding this example. I cant figure out what actually happens after a certain point.

Here is the code, the result is supposed to be 4.

Answer 1

You can reason about this problem by substituting and simplifying.

You start off calling recursion(9), lets substitute 9 for i and reduce

recursion(9)
->  9 > 1 ? 9 - recursion(9/2) : 3
->  true ? 9 - recursion(4) : 3
->  9  - recursion(4)

now you do recursion(4), to simplify this you can repeat the process...

recursion(4)
->  4 > 1 ? 4 - recursion(4/2) : 3
->  true  ? 4 - recursion(2) : 3
-> 4 - recursion(2)

recursion(2)
-> 2 > 1 ? 2 - recursion(2/2) : 3
-> true ? 2 - recursion(1) : 3
-> 2 - recursion(1)

recursion(1)
-> 1 > 1 ? ... : 3
-> false ? ... : 3
-> 3

Here you got a final result, so substitute it back in to recursion(1)

2 - 3 -> -1

and recursion(2)

4 - -1 -> 5

and recursion(4)

9 - 5 -> 4