Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 11.2, Problem 6E
Program Plan Intro

To describe a procedure that selects a key at random from among the keys in hash table and returns it in expected time O(L.(1+1/α)) .

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Let S be the set consisting of all 10 digits and all upper- and lowercase letters. Let U be the set of all (ordered) strings consisting of exactly four elements from S. Construct an injective hash function h: U -> N with the smallest possible value of maxUh(u). Modify your hash function to give a simply uniform map h' to the set {0, ..., 30}. In other words, if U is a probability space with P(u) = P(u') for all u, u' in U, then the random variable h': U -> {0, ..., 30} should have a uniform distribution..
Regarding the Hash algorithm, which one(s) of the following is/are correct, check all that apply. Given a hash of a piece of information, it is hard to recover the original information itself. Given a piece of information, it is hard to find another piece of information that can generate the same hash. O It is theoretically possible, but practically infeasible, to find two pieces of information that generates the same hash. O Hash is unique to a piece of information, there are no any two piece of information that can generate the same hash unless these two pieces of information are identical.
Given a sorted array of n comparable items A, and a search value key, return the position (array index) of key in A if it is present, or -1 if it is not present. If key is present in A, your algorithm must run in order O(log k) time, where k is the location of key in A. Otherwise, if key is not present, your algorithm must run in O(log n) time.
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