Advantages of Binary Search Trees over Hash Tables

Question

What are the advantages of binary search trees over hash tables?

Hash tables can look up any element in Theta(1) time and it is just as easy to add an element....but

Answer 1

In addition to all the other good comments:

Hash tables in general have better cache behavior requiring less memory reads compared to a binary tree. For a hash table you normally only incur a single read before you have access to a reference holding your data. The binary tree, if it is a balanced variant, requires something in the order of k * lg(n) memory reads for some constant k.

On the other hand, if an enemy knows your hash-function the enemy can enforce your hash table to make collisions, greatly hampering its performance. The workaround is to choose the hash-function randomly from a family, but a BST does not have this disadvantage. Also, when the hash table pressure grows too much, you often tend to enlargen and reallocate the hash table which may be an expensive operation. The BST has simpler behavior here and does not tend to suddenly allocate a lot of data and do a rehashing operation.

Trees tend to be the ultimate average data structure. They can act as lists, can easily be split for parallel operation, have fast removal, insertion and lookup on the order of O(lg n). They do nothing particularly well, but they don't have any excessively bad behavior either.

Finally, BSTs are much easier to implement in (pure) functional languages compared to hash-tables and they do not require destructive updates to be implemented (the persistence argument by Pascal above).