(f) A hash table with 6 buckets is initially empty and the hash function is h(k) = k%6. What is the state of the hash table after inserting 3, 6, 1, 12, 7 assuming linear probing?
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- Explain how hash table works in detail. Taking this as an example, the keyword sequence (54, 46, 7, 78, 12, 94, 25, 19) is stored in a hash table with length of 10. The hash function H (key) = key% 10,chain adressed method is used to solve the conflict. Please draw the hash tableExplain how a hash table with linear probing collision handling works internally. Illustrate by showing a hash table containing the numbers 3, 11, 16, 22, with 7 hash buckets. (Assume that we just use the numbers themselves as hash values, i.e., our hash function for integers is hashCode(x) = x.)A 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.
- Draw a hash table given these numbers and hashing function, build each of the hashing options, and decide if it is efficient, and what function or size might be a better match. Explain why it is efficient or what changes you would make for it to be efficient. a. Scenario 1 a. Hashing function: k mod 4 b. Linear Probing c. Array from 0 to 3 d. Values: 19, 7, 12, 11 b. Scenario 2 a. Hashing function: k mod 10 b. Quadratic Probing c. Array from 0 to 9 d. Values: 20 39 23 56 34 29 55 13 c. Scenario 3 a. Hashing function: first three digits of a phone number b. Overflow chaining c. File with base address of 0 and ends at 999 d. Values: 3135552314, 7343455523, 3134445555, 3134441234, 7342346555, e. 5555342232, 4072984555, 2692185552 d. Scenario 4 a. Hashing function: k mod 100 b. Internal Chaining c. Array 0 to 99 d. Values: 314 325 623 2234 425 1234 2132 2361 1245 123 436 742(b) Using the quadratic probe sequence from part (a), write the pseudo-code for an algorithm called HashInsert(T, k) that takes as input a hash table T[0,..., 12] and a key k to be inserted into the table. Your algorithm must insert the item k into the table, using the probe sequence h(k, i) and return true if the insertion is successful, and false otherwise. *You do not have to check for duplicates (you can assume when inserting k that it is not already in the table). You can assume that the table was initially empty and only inserts were carried out, no deletions(e) Assume a hash table with 6 buckets is initially empty. What are the contents of the hash table after insertion of the numbers 1, 18, 11, 4, 14 using the hash function h(k) = k%6?
- 3. For the input 30, 20, 56, 75, 31, 19 and hash function h(K) = K mod 11 a. apply closed-hashing. b. find the average number of key comparisons in a successful search in this table. c. find the worst case number of key comparisons in a successful search in this table.2. Suppose you have the following hash table, implemented using linear probing. The hash function we are using is the identity function, h(x) = x. 0 9 1 A B с D E 18 2 3 4 S 12 3 14 7 8 a) In which order could the elements have been added to the hash table? There are several correct answers, and you should give all of them. Assume that the hash table has never been resized, and no elements have been deleted yet. 12, 14, 3, 9, 4, 18, 21 12, 9, 18, 3, 14, 21,4 12, 3, 14, 18, 4, 9, 21 9, 12, 14, 3, 4, 21, 18 9, 14, 4, 18, 12, 3, 21 6 4 215. a) What is collision in hashing? b) Insert the values 19, 37, 25, 44, 59, 32, 35 and 73, into a hash table of size 12 using the hash function h(i) = i %12. Assuming that the collisions are resolved using linear probing, what are the contents of the hash table?
- The following should be taken into account while creating a fully working open hash table:8. Insert the following keys one-by-one into an initially empty hash table of size 7. Use the hash function h(x) = x mod 7 Show the result for {10, 1, 18, 15, 26, 11, 19} (a) a separate chaining hash table (do not rehash if the load factor becomes too large). (b) a table with linear probing, i.e. using the probing function f(i) = i. For parts (c) and (d), it is possible that you will not be able to insert some of the keys into the table. If you find such a key, rehash the table into a new table of size 11. You need to modify the hash function h(x) accordingly to adjust for the new table size. You do not have to change g(x) for part (d). Do not rehash earlier for any of the tables (even if the load factor becomes too large). (c) a table with quadratic probing, i.e. using the probing function f(i) = i² (d) a table that uses double hashing with a secondary hash function, i.e. f(i) = i* g(x), where the secondary hash function is g(x) = 5 - (x mod 5).Design a hash function for representing the state of a tic-tac-toe board.(It would—for strategy reasons—be useful to have mirror images of a board beconsidered equal.)