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What are the applications of binary trees?

What are binary trees? Why are they useful? Why do some STL containers use them for storing elements? Why is the time required to search a tree O(log n)?

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    Also see [What are the applications of binary trees?](http://stackoverflow.com/questions/2130416/what-are-the-applications-of-binary-trees). – Jesse Good Jul 26 '12 at 20:41

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