Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Problem Hashing (a) Consider a hash table of size M = 5. If items with keys k = 17, 3, 22 are inserted in this order, draw the resulting hash table(s) if we resolve collisions using: 1. Chaining, with h(k) = k mod 5 %3D 2. Linear Probing, with h(k) = k mod 5 %3D 3. Cuckoo Hashing, with ho(k) = k mod 5, h1(k) = [k/5]. Note: both tables have M = 5, so there are a total of 10 cells in the data structure. %3D 4. Double Hashing, with ho(k) 1+y5 = k mod 5, h1(k) = 1 + [4(kø – [kø])], where (b) Which of h1(k) = k mod 5, h2(k) = [k/5], and h3(k) = 5 – (k mod 5) are suitable hash functions for a hash table T = [0, . ,4] of size 5, with keys k E N? %3D .... (c) (i) Suppose we are using an open-addressed hash table of size M to store n items, where n < M/2, with an ideal random hash function. For any i, let X; denote the number of probes required for the ith insertion into the table. Prove that Pr[X; > k] < 1/2* for all i and k. (ii) Prove that Pr[X; > 2 log n] < 1/n². (iii) Let X 2 log n] < 1/n. = max; X; be the length of the longest probe sequence. Prove that Pr[X >

Problem Hashing (a) Consider a hash table of size M = 5. If items with keys k = 17, 3, 22 are inserted in this order, draw the resulting hash table(s) if we resolve collisions using: 1. Chaining, with h(k) = k mod 5 %3D 2. Linear Probing, with h(k) = k mod 5 %3D 3. Cuckoo Hashing, with ho(k) = k mod 5, h1(k) = [k/5]. Note: both tables have M = 5, so there are a total of 10 cells in the data structure. %3D 4. Double Hashing, with ho(k) 1+y5 = k mod 5, h1(k) = 1 + [4(kø – [kø])], where (b) Which of h1(k) = k mod 5, h2(k) = [k/5], and h3(k) = 5 – (k mod 5) are suitable hash functions for a hash table T = [0, . ,4] of size 5, with keys k E N? %3D .... (c) (i) Suppose we are using an open-addressed hash table of size M to store n items, where n < M/2, with an ideal random hash function. For any i, let X; denote the number of probes required for the ith insertion into the table. Prove that Pr[X; > k] < 1/2* for all i and k. (ii) Prove that Pr[X; > 2 log n] < 1/n². (iii) Let X 2 log n] < 1/n. = max; X; be the length of the longest probe sequence. Prove that Pr[X >

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
100%

Don't Copy from other websites i will votes

Problem Hashing (a) Consider a hash table of size M = 5. If items with keys k = 17,3, 22 are inserted in this order, draw the resulting hash table(s) if we resolve collisions using: 1. Chaining, with h(k) = k mod 5 2. Linear Probing, with h(k) = k mod 5 3. Cuckoo Hashing, with ho(k) = k mod 5, h1(k) = [k/5]. Note: both tables have M = 5, so there are a total of 10 cells in the data structure. 4. Double Hashing, with ho(k) 1+y5 k mod 5, h1(k) = 1+ [4(kø – [kø])], where = k mod 5, h2(k) (b) Which of h1(k) hash functions for a hash table T = [0, . , 4] of size 5, with keys k E N? [k/5], and h3(k) = 5 – (k mod 5) are suitable %3D (c) (i) Suppose we are using an open-addressed hash table of size M to store n items, where n < M/2, with an ideal random hash function. For any i, let X; denote the number of probes required for the ith insertion into the table. Prove that Pr[X; > k] < 1/2k for all i and k. (ii) Prove that Pr[X; > 2 log n] < 1/n². (iii) Let X 2 log n] < 1/n. max; X; be the length of the longest probe sequence. Prove that Pr[X >
Transcribed Image Text:Problem Hashing (a) Consider a hash table of size M = 5. If items with keys k = 17,3, 22 are inserted in this order, draw the resulting hash table(s) if we resolve collisions using: 1. Chaining, with h(k) = k mod 5 2. Linear Probing, with h(k) = k mod 5 3. Cuckoo Hashing, with ho(k) = k mod 5, h1(k) = [k/5]. Note: both tables have M = 5, so there are a total of 10 cells in the data structure. 4. Double Hashing, with ho(k) 1+y5 k mod 5, h1(k) = 1+ [4(kø – [kø])], where = k mod 5, h2(k) (b) Which of h1(k) hash functions for a hash table T = [0, . , 4] of size 5, with keys k E N? [k/5], and h3(k) = 5 – (k mod 5) are suitable %3D (c) (i) Suppose we are using an open-addressed hash table of size M to store n items, where n < M/2, with an ideal random hash function. For any i, let X; denote the number of probes required for the ith insertion into the table. Prove that Pr[X; > k] < 1/2k for all i and k. (ii) Prove that Pr[X; > 2 log n] < 1/n². (iii) Let X 2 log n] < 1/n. max; X; be the length of the longest probe sequence. Prove that Pr[X >
Expert Solution
steps

Step by step

Solved in 2 steps with 4 images

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