Question

1) What’s the (worst-case) running time of Hash Table Search for collision resolution by chaining? Express your answer in asymptotic notation. Use the standard notation where n is number of keys and m is number of slots.

2) What’s the (worst-case) running time of Hash Table Search for collision resolution by open-addressing? Express your answer in asymptotic notation. Use the standard notation where n is number of keys and m is number of slots.

3)What simple change in BucketSort can improve its worst-case running time performance by a multiplicative factor of n/lgn?

Answer 1

(1)worst case : when all (n)keys get the same slot in Hash Table making a chain of length (n).Therefore in this case for searching a key we need to traverse the complete chain (in worst case).Hence worst case time complexity = O(n).

(2)worst case : when all the slot in Hash Table are filled by key .Therefore in this case for searching a key we need to traverse all the slots in open Hashing.Hence worst case time complexity = O(m).

(3)If we replace Insertion Sort by Merge Sort in Bucket sorting, and if i^th bucket has n_ⁱ elements, sorting i^th bucket would take n_i log n_i < n_i log n steps. Thus, sorting all buckets will take O(n log n) steps.It can improve its worst-case running time performance by a multiplicative factor of n/lgn