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?
To keep track of the number of elements in each set
To minimize the height of the trees representing sets
To ensure all elements are unique
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.
