How to do different cases of Union Find?

Question

Here is the question: enter image description here

I understand that the absolute parents are 1, 3, 0, and 8, respectively, but I'm not sure how to do union here. Could someone help me understand how to do this?

• codeR: Just blindly follow the procedures given for the $Union$ and $Find$ operations.
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Answer 1

To take the first question, (i).

When you want to perform union(8, 9) you do r1 = find(8) and r2 = find(9), and then you let either r1 point to r2 or vice versa.

In this case, they have the same rank, and as it says, you should break even by spring by index, hence 8 should point to 0.