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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Question
Chapter 11, Problem 3P
(a)
Program Plan Intro
To show the given search scheme is an instance of the general “quadratic probing” scheme by exhibiting the appropriate constants c1 and c2 for equation 11.5
(b)
Program Plan Intro
To prove that the given scheme examines every slot of the table in the worst case.
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Suppose you have a hash table of size N = 64, and you are using quadratic probing. The keys in
your hash are 4-digit integers (0000 through 9999) and your hash function is h(k) = (the sum of
the digits in k).
Assuming keys are uniformly random over the range 0000 to 9999, is this a good hash function?
(Answer true for yes, false for no).
True
False
Given a hash table of size 9 with hash function x%9.
Write the element order of the linear probe hash table when these keys are inserted in
the given order.
1,20,11,28,25,9,18
Answer is just a sequence of elements in the same format. Use hypen - to indicate
empty space.
For example a table like below must be written as in the following:
11
28
9,28,-,11,1,-,-
Cevap:
Kalan Süre 1:37:31
Suppose you have a hash table of size N = 64, and you are using quadratic probing with c1 = 1 and
c2 = 1. The keys in your hash are 4-digit integers (0000 through 9999) and your hash function is
h(k) = (the sum of the digits in k). What are the first 4 values in the search sequence (starting
with the home position) for a record with key k=1948?
Blank # 1
Blank # 2
Blank # 3
Blank # 4
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- A hash function f defined as f(key)=key mod 7 with linear probing is used to insert the keys 37,38,72,48,98,11,56 into a table indexed from 0 to 6, what will be the location of key 11.arrow_forwardA hashing algorithm is using the hash function h(K) = K mod 997. At a given point in the operation, 500 of the table entries already have at least one key stored. a) The algorithm now receives a new key, K1. What is the probabiltity that we DO NOT have a collision? Work: Final numerical Result: P(no collision for k1) = _______ b) Good news, there was no collision for k1! next, another new key,k2 is received. what is the probability that we DO have a collision? Work: final numerical result: P(collision for k2) =arrow_forwardThe Java hash function for Strings computes a hash code based on a fixed maximum number of characters of the string. Given that Strings have no meaningful upper bound in length, describe how an effective, constant-time hashing algorithm can be constructed. (Hint: If you were to pick, say, eight characters to represent a string of length l, which would you choose?)arrow_forward
- The hash function h(k)= [(m(kA mod 1)] for A = 2-³ is used to insert the keys 61, 62, 63, 64, and 65 into a hash table of size m = 1000. The order of the hash codes in the table are given by a. 625, 125, 0, 750, 875 b. 625, 750, 625, 125, 0 c. 625,125, 0, 875, 750 d. 625, 750, 875, 0, 125 e. 625, 750, 125, 875, 0arrow_forwardA hash-map has been constructed with quadratic-hashing. The hashing function is h(k;) = (3 * k; + 7) mod 17 and the table length is N = 17. How many cells will be probed by the call of insert(2) 1 4 5 6 7 8 10 11 12 13 14 15 16 26 89 11 35 70 59 Note: First row contains the indices and the second row contains the items.arrow_forwardA hash function h defined as h[k]=k mod 10, with linear probing is used to store the following keys 44,45,79,55,91,18,63 and 11. What will be location of the last record?arrow_forward
- security pr As we mentioned in class, a universal hash function is a function UH(K, M) that takes a key K, a message M and produces a fixed length digest. The universal hash is defined to be "secure" if for any two messages M₁ and M2, if K is selected uniformly at random, then the probability that UH(K, M₁) UH(K, M₂) is approximately zero. == Suppose that H is a secure hash function. Is UH(K, M) = H(K||M) a secure universal hash function? Either prove the answer is "yes" using the security properties of H (which can be assumed), or show how the security of UH could be violated. VOarrow_forwardA hash code is generated by the Java hash function for Strings based on a string's highest allowed character count. Explain how a powerful, constant-time hashing algorithm can be created given that Strings have no useful maximum length. Which eight characters, say, would you select to represent a string of length l if you had to?arrow_forwardLottery with Hash commitments. We have 3 parties in a lottery where one of them will be the winner. Assume X chooses 58906, Y chooses 79654702, and Z chooses 2578012. Each computes the SHA-256 hash of their chosen number. They publish their hashes first; then they publish their random numbers; the winner is the one: (H(X) XOR H(Y) XOR H(Z) mod 3. X is the winner if the final value is 0; Y is the winner if it is 1; and Z is the winner if it is 2. Compute the steps and show each step; and show the final winner.arrow_forward
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