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

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

Options:

  1. To keep track of the number of elements in each set
  2. To minimize the height of the trees representing sets
  3. To ensure all elements are unique
  4. To sort the elements in each set

Correct Answer: To minimize the height of the trees representing sets

Solution: 

The purpose of union by rank in Disjoint Set Union is to minimize the height of the trees representing sets, which helps in optimizing the \'Find\' operation.

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

Practice Questions

Q1
In a Disjoint Set Union, what is the purpose of union by rank?
  1. To keep track of the number of elements in each set
  2. To minimize the height of the trees representing sets
  3. To ensure all elements are unique
  4. To sort the elements in each set

Questions & Step-by-Step Solutions

In a Disjoint Set Union, what is the purpose of union by rank?
  • 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: Each set in DSU can be represented as a tree, where each node points to its parent, and the root of the tree represents the set.
  • Step 3: The height of these trees can affect how quickly we can find the root of a set, which is done using the 'Find' operation.
  • Step 4: If we always attach the smaller tree under the root of the larger tree when merging two sets (this is called 'union by rank'), we keep the overall height of the trees smaller.
  • Step 5: A smaller height means that the 'Find' operation will take less time, making the DSU more efficient.
  • Union by Rank – A technique used in Disjoint Set Union to keep the tree representing the sets as flat as possible by attaching the smaller tree under the root of the larger tree.
  • Disjoint Set Union – A data structure that keeps track of a partition of a set into disjoint subsets and supports 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.
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