Question

I have these two find algorithm which look the same to me. Can anyone help me out why they are actually different?

Find ( x ) :
    if x.parent = x then 
        return x
    else 
        return Find ( x.parent )

vs

Find ( x ) :
    if x.parent = x then 
        return x
    else 
        x.parent <- Find(x.parent)
        return x.parent 

I interpret the first one as

 int i = 0;    
 return i++;

while the second one as

int i = 0;
int tmp = i++;
return tmp

which are exactly the same to me.

Answer 1

This looks like Disjoint-set data structure.

Now to the question:

For the sake of clarity first version is FindA, second is FindB.

Suppose you have structure:

 0
 |
 1
 |
 2
 |
...
 n

First call to FindA(n) will return 0 in O(n), second call will return 0 in O(n) and so on.

If you call FindB(n) it will return 0 in O(n), but will also modify structure:

    0
 / /|\
1 2...n 

Now second call to FindB(n) will return 0 in O(1). More over FindB(k) will return 0 in O(1).