Question

design hash table

Suppose you need to design a hash table. The keys themselves are (pointers to) C-style zero-terminating strings, so the string "foobar" occupies seven bytes. You are interested in minimizing the space used while keeping search time within reasonable bounds. You expect to store 1000 names with (on average) 7 letters each. If, for example, you choose separate chaining with 2000 buckets, the space required will be 24000 bytes: 8000 = (2000 buckets times 4 bytes per bucket for a pointer) +8000 = (1000 items 8 bytes per item for two pointers: one pointer to the starting address of the string, and another to the next item in the chain) +8000 = (1000 items times 8 bytes per string) (a) Another option is to use open addressing with double hashing. You want the expected number of probes for an unsuccessful search to be at most 3. Determine how many buckets the table should have, and calculate the total number of bytes required for the whole structure. (b) You might also try coalesced chaining. The expected number of probes for an unsuccessful search is given by the formula [Gonnet and Baeza-Yates, Handbook of Algorithms and Data Structures in Pascal and C, p. 79]. U_lambda {lambda + e^-lambda if lambda lessthanorequalto 0.63 1/2(e^2lambda-1.26 - lambda + 2) if lambda Greaterthanorequalto 0.63 Again, determine the appropriate number of buckets if you want the expected number of probes for an unsuccessful search to be at most 3, then analyze the total space required. (This formula assumes that the cellar occupies 14% of the total space.)