什么时候AVL树比哈希表更好？

Question

更具体地说，如果使用AVL树而不是哈希表，是否有任何操作可以更有效地执行？

Answer 1

I generally prefer AVL trees to hash tables. I know that the expected-time O(1) complexity of hash tables beats the guaranteed-time O(log n) complexity of AVL trees, but in practice constant factors make the two data structures generally competitive, and there are no niggling worries about some unexpected data that evokes bad behavior. Also, I often find that sometime during the maintenance life of a program, in a situation not foreseen when the initial choice of a hash table seemed right, that I need the data in sorted order, so I end up rewriting the program to use an AVL tree instead of a hash table; do that enough times, and you learn that you may as well just start with AVL trees.

If your keys are strings, ternary search tries offer a reasonable alternative to AVL trees or hash tables.

Answer 2

An obvious difference, of course, is that with AVL trees (and other balanced trees), you can have persistency : you can insert/remove an element from the tree in O(log N) space-and-time and end up with not just the new tree, but also get to keep the old tree.

With a hash-table, you generally cannot do that in less than O(N) time-and-space.

Another important difference is the operations needed on the keys: AVL tress need a <= comparison between keys, whereas hash-tables need an = comparison as well as a hash function.