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In the context of Disjoint Set Union, what does the 'Union by Rank' technique do

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Question: In the context of Disjoint Set Union, what does the \'Union by Rank\' technique do?

Options:

  1. It merges two sets based on their size
  2. It merges two sets based on their depth
  3. It keeps track of the number of elements in each set
  4. It optimizes the \'Find\' operation

Correct Answer: It merges two sets based on their depth

Solution: 

The \'Union by Rank\' technique merges two sets based on their depth, ensuring that the smaller tree is always added under the root of the larger tree to keep the overall tree shallow.

In the context of Disjoint Set Union, what does the 'Union by Rank' technique do

Practice Questions

Q1
In the context of Disjoint Set Union, what does the 'Union by Rank' technique do?
  1. It merges two sets based on their size
  2. It merges two sets based on their depth
  3. It keeps track of the number of elements in each set
  4. It optimizes the 'Find' operation

Questions & Step-by-Step Solutions

In the context of Disjoint Set Union, what does the 'Union by Rank' technique do?
  • Step 1: Understand that a Disjoint Set Union (DSU) is a data structure that keeps track of a collection of disjoint (non-overlapping) sets.
  • Step 2: Know that each set can be represented as a tree, where each tree has a root node.
  • Step 3: Recognize that 'rank' is a measure of the depth (or height) of a tree in the DSU.
  • Step 4: When merging two sets (or trees), 'Union by Rank' compares the ranks of the two trees.
  • Step 5: If one tree has a higher rank than the other, the smaller tree (lower rank) is attached under the root of the larger tree (higher rank).
  • Step 6: This process keeps the overall structure of the trees shallow, which helps in speeding up future operations.
  • Union by Rank – A technique in Disjoint Set Union that merges two sets by attaching the smaller tree under the root of the larger tree to maintain a shallow structure.
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