a) Imagine a hash table implementation where collisions are resolved by chaining but all the data…

a)
Imagine a hash table implementation where collisions are resolved
by chaining but all the data stays within the slots of the original table. All
entries not containing key–value pairs are marked with a Boolean flag and
linked together into a free list.

(i) Give clear
explanations on how to implement the set (key, value) method in expected
constant time, highlighting notable points and using high-level pseudocode
where appropriate. Make use of doubly-linked lists if necessary.

(ii) Assume the hash table has 5 slots, is
initially empty and uses the hash function h(x) = x mod 5. Draw five diagrams
of the hash table k representing the initially empty state and then the table
after the insertion of each of the following key–value pairs: (2, A), (2, C),
(12, T), (5, Z). In the final diagram, draw all the fields and pointers of all
the entries.

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