Hi, I need some help with this algorithms and data structures problem set.

Suppose hashing is used to store and retrieve a set of identifiers in a hash table. Assume that the hash function F is F(X) = first character of X, and that linear probing is used to handle collision.

A) Is this a good hashing function? Explain the advantages and disadvantages of this hash function.

B) Write an algorithm to list all the identifiers in the hash table in lexicographic (alphabetical) order.

C) If we need to locate frequently all the identifiers in the table between two identifiers (for example, list all identifiers between SAM and TIM, would hashing be a good search method to use?

If your answer is yes, suggest a good hash function and a collision resolution technique, and carefully explain the reasons for your choices.

If your answer is no, suggest an alternative method, explaining why this method is superior to hashing.