Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

Describe how to use a map to implement the dictionary ADT, assuming that the
user may attempt to insert entries with the same key.
C-9.2
Suppose we are given two ordered search tables S and T, each with n entries
(with S and T being implemented with arrays). Describe an O(log 2 n)-time
algorithm for finding the kth smallest key in the union of the keys from S and T
(assuming no duplicates).
C-9.3
Give an O(logn)-time solution for the previous problem.
C-9.4
Design a variation of binary search for performing operation findAll(k) in a
dictionary implemented with an ordered search table, and show that it runs in
time O(logn + s), where n is the number of elements in the dictionary and s is
the size of the iterator returned.
C-9.5
Describe the changes that must be made in the pseudo-code descriptions of the
fundamental dictionary methods when we implement a dictionary with a hash
table such that collisions are handled via separate chaining, but we add the
space optimization that if a bucket stores just a single entry, then we simply
have the bucket reference that entry directly.
C-9.6
The hash table dictionary implementation requires that we find a prime number
between a number M and a number 2M. Implement a method for finding such a
prime by using the sieve algorithm. In this algorithm, we allocate a 2M cell
Boolean array A, such that cell i is associated with the integer i. We then
initialize the array cells to all be "true" and we "mark off all the cells that are
multiples of 2, 3, 5, 7, and so on. This process can stop after it reaches a number
larger than . (Hint: Consider a bootstrapping method for finding the
primes up to .)
C-9.7
Describe how to perform a removal from a hash table that uses linear probing to
resolve collisions where we do not use a special marker to represent deleted
elements. That is, we must rearrange the contents so that it appears that the
removed entry was never inserted in the first place.
577