In a Disjoint Set Union, what does the 'Union by Rank' technique help to achieve

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Question: In a Disjoint Set Union, what does the \'Union by Rank\' technique help to achieve?

Options:

Correct Answer: Reduced height of trees

Solution:

The \'Union by Rank\' technique helps to achieve reduced height of trees, which in turn optimizes the \'Find\' operation.

In a Disjoint Set Union, what does the 'Union by Rank' technique help to achieve?

In a Disjoint Set Union, what does the 'Union by Rank' technique help to achieve?

Step 1: Understand what a Disjoint Set Union (DSU) is. It is a data structure that keeps track of a partition of a set into disjoint (non-overlapping) subsets.
Step 2: Learn about the 'Find' operation. This operation helps to determine which subset a particular element belongs to.
Step 3: Recognize that in DSU, subsets are often represented as trees. Each element points to a parent, and the root of the tree represents the subset.
Step 4: Understand that if trees are too tall, the 'Find' operation can take longer because you may have to traverse many levels to find the root.
Step 5: Introduce the 'Union by Rank' technique. This technique helps to keep the trees short by always attaching the smaller tree under the root of the larger tree when merging two subsets.
Step 6: Realize that by keeping the trees shorter, the 'Find' operation becomes faster, as there are fewer levels to traverse.

Union by Rank – A technique used in Disjoint Set Union to keep the tree flat by attaching the smaller tree under the root of the larger tree, thus reducing the overall height.
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 which subset a particular element is in, often used to check if two elements are in the same subset.