In a Disjoint Set Union, what is the effect of union by rank?

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Question: In a Disjoint Set Union, what is the effect of union by rank?

Options:

Correct Answer: It keeps the tree flat by attaching smaller trees under larger trees

Solution:

Union by rank keeps the tree flat by attaching smaller trees under larger trees, optimizing the union operation.

In a Disjoint Set Union, what is the effect of union by rank?

In a Disjoint Set Union, what is the effect of union by rank?

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 'union' operation. This operation combines two subsets into one.
Step 3: Know what 'rank' means. Rank is a way to measure the 'height' or 'depth' of a tree in the DSU.
Step 4: Realize that when we union two trees, we want to keep the overall structure flat to make future operations faster.
Step 5: Union by rank means we always attach the smaller tree (lower rank) under the larger tree (higher rank).
Step 6: This keeps the trees shorter and flatter, which helps in speeding up future union and find operations.

Union by Rank – A technique in Disjoint Set Union that optimizes the union operation by attaching the tree with a smaller rank under the tree with a larger rank, thereby keeping the overall structure flatter.