Lecture 34

Learning Outcomes

At the end of this lecture, you’ll be able to:

• Identify the operations of the Union-Find data structure.
• Trace the quick find implementation strategy for union-find.
• Trace the quick union implementation strategy for union-find.
• Differentiate the advantages/disadvantages of quick find vs. quick union.
• Trace the “quick union” implementation with union-by-size and path compression heuristics.
• Explain the runtime improvements gained by using the heuristics for union-find operations.
• Define the iterated logarithm (log-star) function.
• Identify the amortized runtime of union-find operations.
• Explain how to implement Kruskal’s algorithm efficiently using a union-find structure for detecting cycles, and identify the resulting run-times.