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...
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.
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.
(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...
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...
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...
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?
design hash table Suppose you need to design a hash table. The keys themselves are (pointers...
design hash table
Suppose you need to design a hash table. The keys themselves are (pointers to) C-style zero-terminating strings, so the string "foobar" occupies seven bytes. You are interested in minimizing the space used while keeping search time within reasonable bounds. You expect to store 1000 names with (on average) 7 letters each. If, for example, you choose separate chaining with 2000 buckets, the space required will be 24000 bytes: 8000 = (2000 buckets times 4 bytes per bucket...
1. Suppose that a hash table contains hash_size = 13 entries indexed from 0 through 12...
1. Suppose that a hash table contains hash_size = 13 entries indexed from 0 through 12 and that the following keys are to be mapped into the table: 24 34 33 55 46 38 37 The hash function determines the hash address by first summing all digits of a key (in ordinary decimal representation) and then applying % hash_size. Answer the following questions. Assume that double hashing g(k) = 7 – (k mod 7) is used. Present the hash table...
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.
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...
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. 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)
design hash table
Suppose you need to design a hash table. The keys themselves are (pointers to) C-style zero-terminating strings, so the string "foobar" occupies seven bytes. You are interested in minimizing the space used while keeping search time within reasonable bounds. You expect to store 1000 names with (on average) 7 letters each. If, for example, you choose separate chaining with 2000 buckets, the space required will be 24000 bytes: 8000 = (2000 buckets times 4 bytes per bucket...
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