3.- Prove that the bound 2/2d in Lemma 4.1 is the best possible bound by showing that, if x = 2-d-1 and y = 3x, then Pr[hash(x) = hash(y)] - = 2/22. (Hint look at the binary representations of zx and z3x and use the fact that z3x = zx + 2zx.) Lemma 4.1. Let x and y be any two values in {0,..., 2 -1} with x #y. Then Pr{hash(x) = hash(y)} ≤ 2/2d.
3.- Prove that the bound 2/2d in Lemma 4.1 is the best possible bound by showing that, if x = 2-d-1 and y = 3x, then Pr[hash(x) = hash(y)] - = 2/22. (Hint look at the binary representations of zx and z3x and use the fact that z3x = zx + 2zx.) Lemma 4.1. Let x and y be any two values in {0,..., 2 -1} with x #y. Then Pr{hash(x) = hash(y)} ≤ 2/2d.
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...
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Hello. Please answer the attached Hashing in Data Structures question correctly and follow all directions. Please give the solution for the problem. Do not copy the answers already given on Chegg or Bartleby. I just want your own personal answer.
*If you solve the problem by yourself and it is correct I will provide a thumbs up for you. Thank you.
![3.- Prove that the bound 2/2d in Lemma 4.1 is the best possible bound by showing that, if x = 2w-d-1 and y = 3x, then
Pr[hash(x) = hash(y)] = 2/2². (Hint look at the binary representations of zx and z3x and use the fact that z3x = zx + 2zx.)
Lemma 4.1. Let x and y be any two values in {0,..., 2w - 1} with x = y. Then
Pr{hash(x) = hash(y)} ≤ 2/2ª.
With Lemma 4.1, the performance of remove(x), and find(x) are easy
to analyze:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1223c4c6-4ebb-4911-bc0d-edb37c26385f%2Fa194c263-9bd3-4077-9f01-4c6f74233a73%2F46157ap_processed.png&w=3840&q=75)
Transcribed Image Text:3.- Prove that the bound 2/2d in Lemma 4.1 is the best possible bound by showing that, if x = 2w-d-1 and y = 3x, then
Pr[hash(x) = hash(y)] = 2/2². (Hint look at the binary representations of zx and z3x and use the fact that z3x = zx + 2zx.)
Lemma 4.1. Let x and y be any two values in {0,..., 2w - 1} with x = y. Then
Pr{hash(x) = hash(y)} ≤ 2/2ª.
With Lemma 4.1, the performance of remove(x), and find(x) are easy
to analyze:
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