A binary search tree requires a total order relationship among the keys. A hash table requires only an equivalence or identity relationship with a consistent hash function.
If a total order relationship is available, then a sorted array has lookup performance comparable to binary trees, worst-case insert performance in the order of hash tables, and less complexity and memory use than both.
The worst-case insertion complexity for a hash table can be left at O(1)/O(log K) (with K the number of elements with the same hash) if it's acceptable to increase the worst-case lookup complexity to O(K) or O(log K) if the elements can be sorted.
Invariants for both trees and hash tables are expensive to restore if the keys change, but less than O(n log N) for sorted arrays.
These are factors to take into account in deciding which implementation to use:
- Availability of a total order relationship.
- Availability of a good hashing function for the equivalence relationship.
- A-priory knowledge of the number of elements.
- Knowledge about the rate of insertions, deletions, and lookups.
- Relative complexity of the comparison and hashing functions.
