Problem 2. As you know, when implementing a hash table, we normally have hash collisions where multiple elements have the same hash value. Thus, we should try to choose such a hash function that will not result in too many collisions. Suppose you have an empty hash table of length 13 with hash function h(x)=x mod n Initially n was chosen to be equa l to 13. (a) How many collisions will be in the hash table for the following dataset 14,27, 40,53,66,79,92,105, 118,131,144? (b) Can you come up with another n for which the function h(x) - x mod n produces no collisions for this dataset without increasing the size of the hash table? If your answer is "yes", give the value of n and explain why there are no collisions If your answer 1s "no", explain why it is impossible to do (c) Propose a function different from h(x) -r mod n which produces no collisions for our dataset