If two elements belong to the same set in a Disjoint Set Union, what will the 'F

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Question: If two elements belong to the same set in a Disjoint Set Union, what will the \'Find\' operation return for both elements?

Options:

Correct Answer: The same root

Solution:

If two elements belong to the same set in a Disjoint Set Union, the \'Find\' operation will return the same root for both elements.

If two elements belong to the same set in a Disjoint Set Union, what will the 'Find' operation return for both elements?

If two elements belong to the same set in a Disjoint Set Union, what will the 'Find' operation return for both elements?

Correct Answer: Same root for both elements

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 the same set, they share the same root.
Step 5: Therefore, when you perform the 'Find' operation on both elements, it will return the same root for both.

Disjoint Set Union (DSU) – A data structure that keeps track of a partition of a set into disjoint subsets, supporting union and find operations.
Find Operation – An operation that determines the root representative of the set containing a particular element.