6.11 - Summary of Union-Find Implementation
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Practice Questions
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What does the 'find' operation do in Union-Find?
💡 Hint: Think about what you are trying to retrieve regarding an element's membership.
True or False: Every element in a Union-Find structure starts in its own component.
💡 Hint: Consider the initial setup of the disjoint sets.
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Interactive Quizzes
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What does the 'find' operation accomplish in a Union-Find structure?
💡 Hint: Think about its purpose in relation to set membership.
Amortized analysis helps in determining the average time per operation across multiple operations.
💡 Hint: Ponder on the consequences of averaging time over many executions.
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Challenge Problems
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Given a set of seven elements with the following union operations: (1, 2), (2, 3), (4, 5), (5, 6), (1, 5). Determine the final components formed.
💡 Hint: Draw the connections graphically to visualize the unions.
Design an optimized Union-Find wherein path compression significantly reduces overall time. Discuss how many find operations can be consistently reduced in time.
💡 Hint: Consider how many steps the tree can collapse into after repeated finds.
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