If two elements belong to different sets in a Disjoint Set Union, what will the

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Question: If two elements belong to different sets in a Disjoint Set Union, what will the \'Find\' operation return for each element?

Options:

Correct Answer: Different roots

Solution:

If two elements belong to different sets, the \'Find\' operation will return different roots for each element.

If two elements belong to different sets in a Disjoint Set Union, what will the 'Find' operation return for each element?

If two elements belong to different sets in a Disjoint Set Union, what will the 'Find' operation return for each element?

Step 1: Understand what a Disjoint Set Union (DSU) is. It is a data structure that keeps track of a collection of disjoint (non-overlapping) sets.
Step 2: Know that each set in a DSU has a unique representative element called the 'root'.
Step 3: When you perform the 'Find' operation on an element, it returns the root of the set that the element belongs to.
Step 4: If two elements are in different sets, they will have different roots because they belong to separate groups.
Step 5: Therefore, when you perform the 'Find' operation on each of these two elements, you will get different results (different roots).

Disjoint Set Union (DSU) – A data structure that keeps track of a partition of a set into disjoint subsets, allowing for efficient union and find operations.
Find Operation – An operation that determines the root or representative of the set containing a particular element.
Different Sets – Refers to elements that are in separate subsets within the disjoint set structure.