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@ -151,7 +151,7 @@ So every time we run this function, it will re-connect every vertex on the path
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### Quiz Time
Can you write the iterative version of the above $FIND(X)$ function with path compression?
Can you write the iterative version of the above $\text{FIND}(X)$ function with path compression?
Answer:
```
@ -204,7 +204,7 @@ int Find(x)
$Union(X,Y)$ operation first of all finds root element of both the disjoint sets containing X and Y respectively. Then it connects the root element of one of the disjoint set to the another.
Well, how do we decide which root will connet to which? If we do it randomly then it may increase the tree height up to O(N), which means that the next $Find(x)$ operation will take O(N) time. Can we do better?
Well, how do we decide which root will connet to which? If we do it randomly then it may increase the tree height up to $O(N)$, which means that the next $Find(x)$ operation will take $O(N)$ time. Can we do better?
Yes, we have two standard techniques: **By size and By rank**.