Question

I am writing a generic hash map in C++ which uses chaining to deal with collisions.

Say if I have a hash map with 11 buckets, and I insert 8 items. The hash function will distribute it as follows:

bucket[0] = empty
bucket[1] = 2 elements
bucket[2] = empty
bucket[3] = 1 element
bucket[4] = 1 element
bucket[5] = 3 elements
bucket[6] = empty
bucket[7] = 1 element
bucket[8] = empty
bucket[9] = empty
bucket[10] = empty

Calculating the spread over the buckets is 5/8 = 0.625.
But how do I calculate the spread taking the depth of the buckets into account?

I want to know this because:
Say if I added 20 elements, and every bucket has 1 element and the last bucket has 11 elements.

then the spread would be 1 if i calculate it the easy way, but this is obviously not correct! (the table resizes to avoid this of course, but I want to be able to show the spread) I want to use this information to be able to tune hash functions.

Thanks in advance!

Answer 1

If you’re only using this to tune the hash functions themselves, you could compute a genuine measure of statistical dispersion, such as the Gini coefficient. On the other hand, if you’re trying to make this a feature of the hash-map itself, I would recommend against it – computing a complicated benchmark as part of the ‘is resize necessary’ logic has its own performance costs; something naïve is probably better.