Use an open-addressed hashing table of size m

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Reference no: EM13341137

1)Suppose that we use an open-addressed hashing table of size m to store n ? m / 2 items. Assuming uniform hashing, show that for i = 1, 2, ..., n, the probability is at most 2?k that the i-th
insertion requires strictly more than k probes.

(2) [10 points] Discuss the difficulties of deletion operation in hashing. Again use open-addressed hashing
instead of chaining. Give a deletion algorithm for linear probing.

(3) [10 points] In this assignment, you are going to find out the performance of (open-addressed) hashing by simulation. You should design a hash table of size approximately 200, a hash function of your own design (you are not allowed to use the ones in the notes nor those in the textbook), and test the hashing table at 10% increment of the load factor until 90% and then increase it by 1% until 95% or the algorithm failed somehow. The test should show the average "probes" required to insert a new element into the table. You will be given a list of words as the elements. If the word was already in the table, ignore it. Otherwise add it to the table. Use two strategies to resolve collisions: (1) linear probing, and (2) your own design. Produce a comparison of the two strategies to see if they are significantly different. Explain why if necessary. Assume the file name "q5.dat" for input data.

4) Show that the notion of a randomly chosen binary search tree on n keys, where each binary search tree of n keys is equally likely to be chosen, is different from the notion of a randomly built binary search tree given in this section. (Hint: List the possibilities when n D 3.)

5)What is the asymptotic performance of TREE-INSERT when used to insert n items with identical keys into an initially empty binary search tree?

Reference no: EM13341137

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