Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
In this problem we assume that h: U → {0, 1, . . . , m − 1} is a good hash function, that is, every key k has the same probability 1/m to map to any place in the table T of length m. (i) What is the probability that three pairwise distinct elements u1, u2, u3 ∈ U are mapped by the function h to the same place in the table (that is, h(u1) = h(u2) = h(u3))? (ii) We insert three elements into an empty hash table T using the hash function h. If collision is solved by chaining, what is the probability that T[0] and T[1] are empty?

In this problem we assume that h: U → {0, 1, . . . , m − 1} is a good hash function, that is, every key k has the same probability 1/m to map to any place in the table T of length m. (i) What is the probability that three pairwise distinct elements u1, u2, u3 ∈ U are mapped by the function h to the same place in the table (that is, h(u1) = h(u2) = h(u3))? (ii) We insert three elements into an empty hash table T using the hash function h. If collision is solved by chaining, what is the probability that T[0] and T[1] are empty?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
See similar textbooks
icon
Related questions
Question

Problem 2: In this problem we assume that h: U → {0, 1, . . . , m − 1} is a good hash
function, that is, every key k has the same probability 1/m to map to any place in the table
T of length m.
(i) What is the probability that three pairwise distinct elements u1, u2, u3 ∈ U are
mapped by the function h to the same place in the table (that is, h(u1) = h(u2) =
h(u3))?
(ii) We insert three elements into an empty hash table T using the hash function h. If
collision is solved by chaining, what is the probability that T[0] and T[1] are empty?

Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS