What are the lesser known but useful data structures?

There are some data structures around that are really useful but are unknown to most programmers. Which ones are they?

Everybody knows about linked lists, binary trees, and hashes, but what about Skip lists and Bloom filters for example. I would like to know more data structures that are not so common, but are worth knowing because they rely on great ideas and enrich a programmer's tool box.

PS: I am also interested in techniques like Dancing links which make clever use of properties of a common data structure.

EDIT: Please try to include links to pages describing the data structures in more detail. Also, try to add a couple of words on why a data structure is cool (as Jonas Kölker already pointed out). Also, try to provide one data-structure per answer. This will allow the better data structures to float to the top based on their votes alone.


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.