space complexity of multi-dimensional hash

Question

I would like to store an input of tab separated values where say C1, C2, C3 and C4 represent the columns of the data and there are N rows of data. If so, I could do lookups in the hash to see if some given values for C1,C2,C3,C4 exist. Someone suggested to me that, in the worst case, the space complexity of this was N⁴. I would like help formulating a clear explanation as to why that is not true.

Answer 1

The other person is thinking that if you try to store an N by N grid of points, there will be N⁴ points to store.

But if you have N points, then you're just storing a hash. And a hash with N data points typically takes O(N) space. (Technically it takes the size of the hash table plus the space for the data, but people usually dynamically size the hash table to be the same order of magnitude size as the data set.)