Hashing a tuple of maximum-valued integers

Question

I'm considering a hash function for a tuple of and maximum-valued integers for example (3 ,2, 5 ) -- where each element of the tuple has some maximum value N.

My plan is to treat the elements of the tuple as the digits of a number in base N, so that in the trivial case of N = 10 the tuple(3 ,2, 5 ) hashes to 325, or 213 if N = 8.

(1) Is this hashing technique flawed and (2) If not, does it have a name, and (3) Are there better ways to hash a tuple of integers.

It will work fine, if the maximum value of each number does not exceed N-1. In fact, it will work more than fine; there will be zero collisions. — Robert Harvey, Jun 08 '16 at 00:00
@Oxinabox I'm not sure. The tuples are intersection points from geometry. I'm hashing to assign ids to these points. — Olumide, Jun 08 '16 at 00:20
What you're doing is encoding, not hashing since it's possible to decode the result into the original form. (assuming the absence of integer overflow) — CodesInChaos, Jun 08 '16 at 10:18

score 3 · Accepted Answer · answered Jun 08 '16 at 09:34

While this will work and in some situations will give good results, there are two dangers with this approach:

considering a tuple with M values where reach has maximum N, your calculation of the hash value will overflow if M*N > your integer type limit. If you have either large N or M this is an issue that you can rectify by using a smaller multiplier. This will, however, perform worse for smaller N and M, so you should pick your approach depending on how likely overflow is.
if you are using the hash codes for storage in a hash table, note that your hash code will be taken modulo the size of the table. This means that if your N is a factor of the table size and your individual values are not evenly distributed, you are more likely to see collisions. Ensuring your multiplier is coprime with the table size is the best approach; the easy ways of doing this are to either pick a prime table size, or a prime multiplier I in your hash function. As most modern hah table implementations automatically choose sizes that are not typically prime, you should usually use primes in your hash function. One approach would be to have a list of primes and pick the smallest >= N. I think this would solve this issue.

You're right about the overflow. But what do you mean by multiplier? — Olumide, Jun 08 '16 at 10:27
Worse: if N to the power of M exceeds the type limit, there will be an overflow. — Martin Kochanski, Jun 08 '16 at 11:27

Hashing a tuple of maximum-valued integers

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