Assume a Hash table has 7 slots and the hash function h(k) = k mod 7...
Assume a Hash table has 7 slots and the hash function h(k) = k mod 7 is used. The keys 14, 3, 11, 6, 10, 4, 20, and 17 are inserted in the table with collision resolution by chaining. Assume that the keys arrive in the order shown.
(a) Show the hash table obtained after inserting all 8 keys. [Show only the final table]
(b) Under the assumption that each key is searched with probability 1/8, calculate expected number of steps a successful search takes.
(c) Under the assumption of simple uniform hashing, calculate expected number of steps an unsuccessful search takes. [Note, now the probability is not 1/8 for unsuccessful search.]
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Assume a Hash table has 7 slots and the hash function h(k) = k
mod 7...
5. Hashing (a) Consider a hash table with separate chaining of size M = 5 and...
5. Hashing (a) Consider a hash table with separate chaining of size M = 5 and the hash function h(x) = x mod 5. i. (1) Pick 8 random numbers in the range of 10 to 99 and write the numbers in the picked sequence. Marks will only be given for proper random numbers (e.g., 11, 12, 13, 14 ... or 10, 20, 30, 40, .. are not acceptable random sequences). ii. (2) Draw a sketch of the hash table...
(g - 6 pts) Construct a hash table of the given array using a hash function H(K) = K mod 5. (h - ...
(g - 6 pts) Construct a hash table of the given array using a hash function H(K) = K mod 5. (h - 6 pts) For the hash table of (g), determine the average number of comparisons for a successful search and the worst case number of comparisons for an unsuccessful search. (i - 9 pts) Consider the elements of the array assigned to you are known only one at a time. Construct a sequence of priority queues (as max...
Exercise 3 (5 points). Suppose we have a hash table of m = 9 slots, and...
Exercise 3 (5 points). Suppose we have a hash table of m = 9 slots, and we resolve collisions by chaining. Demonstrate what happens when we insert the keys 5, 28, 19, 15, 20, 33, 12, 17, 10. Use the division-method hash function h (k) = k mod 9.
Assume that you have a ten-slot closed hash table (the slots are numbered 0 through 9)....
Assume that you have a ten-slot closed hash table (the slots are numbered 0 through 9). Show the final hash table that would result if you used the hash function h(k) = k mod 10 and pseudo-random probing. The list of numbers to be inserted in order are: 6, 15, 24, 19, 25, 44 The permutation of offsets to be used by the pseudo-random probing will be: 2, 5, 1, 8, 4, 9, 3, 6, 7
3. Given input (89, 18, 49, 58, 69), h)k(mod 10) g) Iymod 8), and a hash function f(k) h(k) +j-g(...
3. Given input (89, 18, 49, 58, 69), h)k(mod 10) g) Iymod 8), and a hash function f(k) h(k) +j-g(k) (mod 10), show the resulting hash table. Solve collisions with double hashing.
3. Given input (89, 18, 49, 58, 69), h)k(mod 10) g) Iymod 8), and a hash function f(k) h(k) +j-g(k) (mod 10), show the resulting hash table. Solve collisions with double hashing.
10. Submission In this question you will work with a hash table that uses double hashing. The hash table is size 11, the primary hash function is h(K)-K mod 11, and the secondary hash function is hp(...
10. Submission In this question you will work with a hash table that uses double hashing. The hash table is size 11, the primary hash function is h(K)-K mod 11, and the secondary hash function is hp(K)-(K mod9) +1 Take an empty hash table. Take your student number and split it into 4 2-digit integers. Insert each of these 2-digit numbers in the order in which they appear in your student number into the empty heap. Then insert the values...
1) What’s the (worst-case) running time of Hash Table Search for collision resolution by chaining? Express...
1) What’s the (worst-case) running time of Hash Table Search for collision resolution by chaining? Express your answer in asymptotic notation. Use the standard notation where n is number of keys and m is number of slots. 2) What’s the (worst-case) running time of Hash Table Search for collision resolution by open-addressing? Express your answer in asymptotic notation. Use the standard notation where n is number of keys and m is number of slots. 3)What simple change in BucketSort can...
3. (20 points) In open addressing with double hashing, we have h(k,i) hi(k)+ih2(k) mod m, where h...
3. (20 points) In open addressing with double hashing, we have h(k,i) hi(k)+ih2(k) mod m, where hi(k) and h2(k) is an auxiliary functions. In class we saw that h2(k) and m should not have any common divisors (other than 1). Explain what can go wrong if h2(k) and m have a common divisor. In particular, consider following scenario: m- 16, h(k) k mod (m/8) and h2(k)-m/2 and the keys are ranged from 0 to 15. Using this hash function, can...
3. Assume that you have a seven-slot hash table (the slots are numbered 0 through 6)....
3. Assume that you have a seven-slot hash table (the slots are numbered 0 through 6). Show the final hash table that would result if you used the following approach to put 7, 13, 10,6 into the hash (4 points each) the hash function h(k)-k mod 7 and linear probing function the hash function h(k)-k mod 7 and quadratic probing (a) (b)
Suppose we use the hash function h(x) = x mod 7 (i.e. h(x) is the remainder...
Suppose we use the hash function h(x) = x mod 7 (i.e. h(x) is the remainder of the division of x by 7) to hash into a table with 7 slots (the slots are numbered 0, 1,…, 6) the following numbers: 32, 57, 43, 20, 28, 67, 41, 62, 91, 54. We use chaining to handle collisions. Which slot contains the longest chain?
5. Hashing (a) Consider a hash table with separate chaining of size M = 5 and the hash function h(x) = x mod 5. i. (1) Pick 8 random numbers in the range of 10 to 99 and write the numbers in the picked sequence. Marks will only be given for proper random numbers (e.g., 11, 12, 13, 14 ... or 10, 20, 30, 40, .. are not acceptable random sequences). ii. (2) Draw a sketch of the hash table...
Exercise 3 (5 points). Suppose we have a hash table of m = 9 slots, and we resolve collisions by chaining. Demonstrate what happens when we insert the keys 5, 28, 19, 15, 20, 33, 12, 17, 10. Use the division-method hash function h (k) = k mod 9.
3. Given input (89, 18, 49, 58, 69), h)k(mod 10) g) Iymod 8), and a hash function f(k) h(k) +j-g(k) (mod 10), show the resulting hash table. Solve collisions with double hashing.
3. Given input (89, 18, 49, 58, 69), h)k(mod 10) g) Iymod 8), and a hash function f(k) h(k) +j-g(k) (mod 10), show the resulting hash table. Solve collisions with double hashing.
10. Submission In this question you will work with a hash table that uses double hashing. The hash table is size 11, the primary hash function is h(K)-K mod 11, and the secondary hash function is hp(K)-(K mod9) +1 Take an empty hash table. Take your student number and split it into 4 2-digit integers. Insert each of these 2-digit numbers in the order in which they appear in your student number into the empty heap. Then insert the values...
3. (20 points) In open addressing with double hashing, we have h(k,i) hi(k)+ih2(k) mod m, where hi(k) and h2(k) is an auxiliary functions. In class we saw that h2(k) and m should not have any common divisors (other than 1). Explain what can go wrong if h2(k) and m have a common divisor. In particular, consider following scenario: m- 16, h(k) k mod (m/8) and h2(k)-m/2 and the keys are ranged from 0 to 15. Using this hash function, can...
3. Assume that you have a seven-slot hash table (the slots are numbered 0 through 6). Show the final hash table that would result if you used the following approach to put 7, 13, 10,6 into the hash (4 points each) the hash function h(k)-k mod 7 and linear probing function the hash function h(k)-k mod 7 and quadratic probing (a) (b)
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