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k-level skip list

Due: March 1
Points: 2

(Note: you should probably start by doing Problem 41.)

What if a skip list were restricted to k levels, for some constant k? What would be the optimum way of storing n items in a skip-list of height k, and what would the resulting cost of search, insert, and delete be?

Describe the data structure construction (briefly). Give a big-O bound in terms of n and k. Then show how this relates to the usual skip list with expected height $$k = \lg n$$.