All algorithms are in pseudocode

Hash tables 3.1 (5p) For the input 30; 53; 58; 35; 93; 54; 25; 43; 31; 45 and hash function h(k) = k mod 19, construct the open hash table. 3.2 (5p) Find the largest number of key comparisons in a successful search in this table. Find the average number of key comparisons in a successful search in this table. 3.3 (5p) Find the probability of all n keys being hashed to the same cell of a hash table of size m if the hash function distributes keys evenly among all the cells of the table. 3.4 (5p) Explain how to use hashing to check whether all elements of a list are distinct. What is the time eciency of this application? Compare its with that of the brute-force solution and to the pre-sorting solution ( rst sort array then traverse to nd if all elements are distinct).