Consider a hash table with m = 8 slots. a) Show the result of inserting numbers 9, 12, 2, 43, 31, 25 using a hash function h(k) = [m(kA mod 1)] for A = √3/2 with collision resolution by chaining. b) Show the results of inserting numbers 9, 12, 2, 43, 31, 25 using open addressing with auxiliary hash function h'(k) = [m(kA mod 1)] for A = √3/2 and linear probing. How many probes are needed in this open-addressing cache to determine that 38 isn't in the hash? Explain your answers

2. Give the use of a hash function, Draw the hash table that results using the hash function: hik)-k mod 13 to hash the keys 2. 7.4, 41, 15, 32. 25, 11, 30. Assuming collisions are handled by Quadratic probing. 3. Draw the hash table that results using the hash function: h(k)-k mod 13 to hash the keys 2,7,4, 41, 15, 32, 25. 11, 30. Assuming collisions are handled by Linear probing 4. Draw the hash table that results using the hash function: h(k)-kmod7 to hash the keys 76. 93. 40, 47, 10. 55. Assuming collisions are handied by Double hashing.

Consider Cuckoo hashing with a hash table H[0...10] and the two hash functions: h₁(x) = (x + 2) mod 11 h₂(x) = (4x + 1) mod 11. (When inserting, try h₁ first.) Consider the following sequence of operations: Insert(11) Insert(13) Insert(33) Insert(27) Insert(7) Insert(24) What element is at H[9]? 11 O) 13 33 27 7 24 Unknown since it results in a rehash.

Given a sequence of 5 keys < 53, 66, 32, 41, 88 > for searching task: a) Given the hash function H(k) = (3.k) mod 7, insert the keys above according to its original order (from left to right) into a hash table of 7 slots. Indicate the cases of collision. Clearly show the steps and calculation with a table. b) In case of any collisions found above in a) part, determine the new slot for each collided case using Linear Probing to solve the collision problem. Clearly show your answer for each identified case. No step of calculation required. o (Answer with “NO collision found”, in case there is no collisions found above) c) In case of any collisions found above in a) part, determine the new slot ONLY for the first collided case using Double-Hashing (with functions below) to solve the collision problem. Clearly show the steps of your calculation. d1 = H(k) = (3.k) mod 7 di = (di−1 + ((5·k) mod 6) + 1) mod 7 , i ≥ 2 o (Answer with “NO collision found”, in case there is no collisions…