In the context of Disjoint Set Union, what does the term 'union by rank' refer to?
Practice Questions
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Q1
In the context of Disjoint Set Union, what does the term 'union by rank' refer to?
Combining two sets based on their size
Combining two sets based on their depth
Finding the maximum element in a set
Sorting elements in a set
Union by rank refers to the strategy of combining two sets by attaching the smaller tree under the root of the larger tree, thus keeping the overall tree shallow.
Questions & Step-by-step Solutions
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Q
Q: In the context of Disjoint Set Union, what does the term 'union by rank' refer to?
Solution: Union by rank refers to the strategy of combining two sets by attaching the smaller tree under the root of the larger tree, thus keeping the overall tree shallow.
Steps: 6
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 way to measure the height or depth of these trees.
Step 4: When combining two sets (or trees), we want to keep the resulting tree as short as possible.
Step 5: 'Union by rank' means that when we merge two trees, we attach the shorter tree (the one with a smaller rank) under the root of the taller tree (the one with a larger rank).
Step 6: This strategy helps keep the overall structure of the trees shallow, which makes future operations faster.
