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3 cards from this section. Quick, good the night before a test.
What are the two primary operations of the Union-Find data structure?
Think about what these operations do to a set.
What is the worst-case time complexity for the naive union operation?
Consider the number of elements you may have to visit in a union operation.
What does the find operation in the Union-Find structure do?
Think about the purpose of checking components.
True or False: The union by size technique merges the larger tree into the smaller tree.
Consider what it means for trees to be balanced.
Given a set of cities represented as nodes and roads as edges connecting them, explain how you would implement a Union-Find structure to detect cycles when planning a new road network.
Consider the implications of connecting components when checking for cycles.
Implement a Union-Find algorithm with path compression and union by size. Analyze its complexity over a series of operations.
Look at how merging impacts future operations and their costs.
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