Question

In linear probing hashing, if clustering is not a problem, We will
assume a very large table and that each probe is independent of the
previous probes. These assumptions are satisfied by a random collision
resolution strategy. First, we derive the expected number of probes in
an unsuccessful search. This is just the expected number of probes
until we find an empty cell. Since the fraction of empty cells is (1 –
(N/M)), where N is number of elements and M is hash table size. the
number of cells we expect to probe is 1/(1 – (N/M)). The number of
probes for a successful search is equal to the number of probes
required when the particular element was inserted.

My question is how do we got number of cells we expect to proble is 1/(1-(N/M)) in above text.

Thanks!

Answer 1

Probing works roughly like this: you have probability p for success, and you keep trying until you succeed.
This means that you’re dealing with the geometric probability distribution, so the expected number of attempts until you succeed is 1/p.

In this case, p=1-(N/M), so the expected number of attempts is 1/(1-(N/M)).