Hash table - implementing with Binary Search Tree

Question

From Cracking the Coding Interview, page 71:

Alternatively, we can implement hash table with a BST. We can then guarantee an O(log n) lookup ti

Answer 1

a O(logN) bound would be the worst case scenario in case of a tree.Lets look at it this way. We insert 45, 33, 55,66,22 and we would then have 45 as the root node,33 and 55 in level1,22 and 66 in level 2..

So, if you were to hash for value 45, it would still be a O(1) operation...Only when you look for nodes in level2 would it amount close to O(logN)....The tree could be a RB tree/AVL tree so that it does not degenerate into a linked list....You lose some tiem efficiency but make up for it in space efficiency..

One more advantage would be you don't need to bother about collisions then in hash table. http://www.cs.rit.edu/~ib/Classes/CS233_Spring08-09/Slides/Week9_Hashing.pdf

Basically, you would have a dynamic allocation of nodes and no space is wasted on unused buckets in hash table...Say, you were to use a static hash table witha pre-determined size(busckets), then, it would lead to a space inefficient implementation .