By Mehlhorn K., Sanders P.
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Extra resources for Concise algorithmics, the basic toolbox
B,t , . . 14 findNext using sentinels is faster than an implementation that checks for the end of the list in each iteration. But how much faster? What speed difference do you predict for many searches in a small list with 100 elements, or for a large list with 10 000 000 elements respectively? Why is the relative speed difference dependent on the size of the list? Similarly, findNext should not return the handle of the SItem with the next fit but its predecessor. This way it remains possible to remove the element found.
5 explains how the k-th smallest from n elements can be found in time O (n). 6. 7 generalizes quicksort and mergesort to very good algorithms for sorting huge inputs that do not fit into internal memory. ) Assume you are a hotel manager who has to consider n advance bookings of rooms for the next season. Your hotel has k identical rooms. Bookings contain arrival date and departure date. You want to find 78 Sorting and Selection out whether there are enough rooms in your hotel to satisfy the demand.
1 for fully random hash functions. 3 If n elements are stored in a hash table with m entries using hashing with chaining, the expected execution time of remove or find is O (1 + cn/m) if we assume a hash function taken randomly from a c-universal family. Now it remains to find c-universal families of hash functions that are easy to compute. We explain a simple and quite practical 1-universal family in detail and give further examples in the exercises. 8 gives an family that is perhaps even easier to understand since it uses only simple bit operations.