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By Mehlhorn K., Sanders P.

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The worst case execution time of checkFreeList should be independent of the batch size. Hint: In addition to freeList use a small array of free items. 15 Design a list data type that allows sublists to be moved between lists in constant time and allows constant time access to size whenever sublist operations have not been used since the last access to the list size. When sublist operations have been used size is only recomputed when needed. 16 Explain how the operations remove, insertAfter, and concat have to be modified to keep track of the length of a List.

There are mk−1 ways to choose the ai with i = j. Since the total number of possible choices for a is mk , we get prob(ha (x) = ha (y)) = mk−1 1 = . mk m Is it a serious restriction that we need prime table sizes? On the first glance, yes. We cannot burden users with the requirement to specify prime numbers for m. When we adaptively grow or shrink an array, it is also not obvious how to get prime numbers for the new value of m. But there is a simple way out. Number theory tells us that there is a prime number just around the corner [41].

1 analyzes hashing with chaining using rather 1 Strictly speaking, we have to add additional terms to the execution time for moving elements and for evaluating the hash function. To simplify notation, we assume in this chapter that all this takes constant time. The execution time in the more detailed model can be recovered by adding the time for one hash function evaluation and for a constant number of element moves to insert and remove. Hash Tables 61 optimistic assumptions about the properties of the hash function.

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