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

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

Options:

  1. It merges two sets based on their size
  2. It keeps track of the height of trees to minimize depth
  3. It sorts the elements in each set
  4. It finds the maximum element in a set

Correct Answer: It keeps track of the height of trees to minimize depth

Solution: 

The \'Union by Rank\' optimization keeps track of the height of trees to minimize depth, ensuring that the smaller tree is always added under the root of the larger tree.

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

Practice Questions

Q1
In the context of Disjoint Set Union, what does the 'Union by Rank' optimization do?
  1. It merges two sets based on their size
  2. It keeps track of the height of trees to minimize depth
  3. It sorts the elements in each set
  4. It finds the maximum element in a set

Questions & Step-by-Step Solutions

In the context of Disjoint Set Union, what does the 'Union by Rank' optimization do?
Correct Answer: Union by Rank optimization helps in keeping the tree flat by attaching smaller trees under larger trees.
  • Step 1: Understand that Disjoint Set Union (DSU) uses trees to represent sets.
  • Step 2: Each tree has a root, and the height of the tree is called its 'rank'.
  • Step 3: When we want to combine two sets (or trees), we need to connect their roots.
  • Step 4: 'Union by Rank' means we always attach the shorter tree under the root of the taller tree.
  • Step 5: This keeps the overall height of the trees smaller, making future operations faster.
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