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  1. PO
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    <p>Here are a few:</p> <ul> <li><p>Suffix tries. Useful for almost all kinds of string searching (<a href="http://en.wikipedia.org/wiki/Suffix_trie#Functionality" rel="nofollow noreferrer"><a href="http://en.wikipedia.org/wiki/Suffix_trie#Functionality" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Suffix_trie#Functionality</a></a>). See also suffix arrays; they're not quite as fast as suffix trees, but a whole lot smaller.</p></li> <li><p>Splay trees (as mentioned above). The reason they are cool is threefold:</p> <ul> <li>They are small: you only need the left and right pointers like you do in any binary tree (no node-color or size information needs to be stored)</li> <li>They are (comparatively) very easy to implement</li> <li>They offer optimal amortized complexity for a whole host of "measurement criteria" (log n lookup time being the one everybody knows). See <a href="http://en.wikipedia.org/wiki/Splay_tree#Performance_theorems" rel="nofollow noreferrer"><a href="http://en.wikipedia.org/wiki/Splay_tree#Performance_theorems" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Splay_tree#Performance_theorems</a></a></li> </ul></li> <li><p>Heap-ordered search trees: you store a bunch of (key, prio) pairs in a tree, such that it's a search tree with respect to the keys, and heap-ordered with respect to the priorities. One can show that such a tree has a unique shape (and it's not always fully packed up-and-to-the-left). With random priorities, it gives you expected O(log n) search time, IIRC.</p></li> <li><p>A niche one is adjacency lists for undirected planar graphs with O(1) neighbour queries. This is not so much a data structure as a particular way to organize an existing data structure. Here's how you do it: every planar graph has a node with degree at most 6. Pick such a node, put its neighbors in its neighbor list, remove it from the graph, and recurse until the graph is empty. When given a pair (u, v), look for u in v's neighbor list and for v in u's neighbor list. Both have size at most 6, so this is O(1).</p></li> </ul> <p>By the above algorithm, if u and v are neighbors, you won't have both u in v's list and v in u's list. If you need this, just add each node's missing neighbors to that node's neighbor list, but store how much of the neighbor list you need to look through for fast lookup.</p>
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    1. POWhat are the lesser known but useful data structures?
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    1. USJonas Kölker
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      1. VTUpMod
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    1. COYou couldn't just list one per answer, could ya? Makes it easier for the single, good data structures to float to the top.
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      1. USKingNestor
    2. COI could, but I'm still not /quite/ getting the hang of this weird wiki/forum hybrid. I'm not gonna edit right now (eat-sleep-rinse-repeat), and I'm probably gonna forget to do it later ;)
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      1. USJonas Kölker
    3. COThe Heap ordered search tree is called a treap. One trick you can do with these is change the priority of a node to push it to the bottom of the tree where its easier to delete.
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      1. USpaperhorse
 

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