What are the lesser known but useful data structures?

Question

Tries, also known as prefix-trees or crit-bit trees, have existed for over 40 years but are still relatively unknown. A very cool use of tries is described in "TRASH - A dynamic LC-trie and hash data structure", which combines a trie with a hash function.

Bloom filter: Bit array of m bits, initially all set to 0.

To add an item you run it through k hash functions that will give you k indices in the array which you then set to 1.

To check if an item is in the set, compute the k indices and check if they are all set to 1.

Of course, this gives some probability of false-positives (according to wikipedia it's about 0.61^(m/n) where n is the number of inserted items). False-negatives are not possible.

Removing an item is impossible, but you can implement counting bloom filter, represented by array of ints and increment/decrement.

Rope: It's a string that allows for cheap prepends, substrings, middle insertions and appends. I've really only had use for it once, but no other structure would have sufficed. Regular strings and arrays prepends were just far too expensive for what we needed to do, and reversing everthing was out of the question.

Skip lists are pretty neat.

Wikipedia
A skip list is a probabilistic data structure, based on multiple parallel, sorted linked lists, with efficiency comparable to a binary search tree (order log n average time for most operations).

They can be used as an alternative to balanced trees (using probalistic balancing rather than strict enforcement of balancing). They are easy to implement and faster than say, a red-black tree. I think they should be in every good programmers toolchest.

If you want to get an in-depth introduction to skip-lists here is a link to a video of MIT's Introduction to Algorithms lecture on them.

Also, here is a Java applet demonstrating Skip Lists visually.

Spatial Indices, in particular R-trees and KD-trees, store spatial data efficiently. They are good for geographical map coordinate data and VLSI place and route algorithms, and sometimes for nearest-neighbor search.

Bit Arrays store individual bits compactly and allow fast bit operations.

Zippers - derivatives of data structures that modify the structure to have a natural notion of 'cursor' -- current location. These are really useful as they guarantee indicies cannot be out of bound -- used, e.g. in the xmonad window manager to track which window has focused.

Amazingly, you can derive them by applying techniques from calculus to the type of the original data structure!