c++ - unordered_map complexity

Question

I need to create a lookup function where a (X,Y) pair corresponds to a specific Z value. One major requirement for this is that I need to do it in as close to O(1) complexi

Answer 1

To have no collisions in a hashed data structure is incredibly difficult (if not impossible for a given hash function and any kind of data). It would also require a table size exactly equal to the number of keys. No, it does not need to be that strict. As long as the hash function distributes the values in a relatively uniform way, you will have O(1) lookup complexity.

Hash tables are generally just arrays with linked lists taking care of the collisions (this is the chaining method - there are other methods, but this is likely the most utilized way of dealing with collisions). Thus, to find if a value is contained within a bucket, it will have to (potentially) iterate over all the values in that bucket. So if the hash function gives you a uniform distribution, and there are N buckets, and a total of M values, there should be (on average) M/N values per bucket. As long as this value is not too large, this allows O(1) lookup.

So, as a bit of a long winded answer to your question, as long as the hashing function is reasonable, you will get O(1) lookup, with it having to iterate over (on average) O(M/N) keys to give you a "negative" result.