Limit for quadratic probing a hash table

Question

I was doing a program to compare the average and maximum accesses required for linear probing, quadratic probing and separate chaining in hash table.

I had done the element insertion part for 3 cases. While finding the element from hash table, I need to have a limit for ending the searching. In the case of separate chaining, I can stop when next pointer is null. For linear probing, I can stop when probed the whole table (ie size of table). What should I use as limit in quadratic probing? Will table size do?

My quadratic probing function is like this

newKey = (key + i*i) % size;

where i varies from 0 to infinity. Please help me..

Answer 1

For such problems analyse the growth of i in two pieces:

First Interval : i goes from 0 to size-1

In this case, I haven't got the solution for now. Hopefully will update.

Second Interval : i goes from size to infinity

In this case i can be expressed as i = size + k, then

newKey = (key + i*i) % size 
       = (key + (size+k)*(size+k)) % size
       = (key + size*size + 2*k*size + k*k) % size
       = (key + k*k) % size

So it's sure that we will start probing previously probed cells, after i reaches to size. So you only need to consider the situation where i goes from 0 to size-1. Because rest is only the same story again and again.

What the story tells up to now: A simple analysis showed me that I need to probe at most size times because beyond size times I started probing the same cells.