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Wiki binary search tree

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wiki binary search tree

In computer sciencea self-balancing or height-balanced binary search tree is any wiki -based binary search tree that automatically keeps binary height maximal number of levels below the root small in the face of arbitrary item insertions and deletions. Most operations on a binary search tree BST take time directly proportional to the height of the tree, so it is desirable to keep the height small. For example, tree the items are inserted in sorted key order, the tree degenerates into a linked list with n nodes. However, there are many situations such as online algorithms where this randomization is not viable. Self-balancing binary trees solve this problem by performing transformations on the tree such as tree rotations at key insertion times, in order to keep the height proportional to log n. Although a certain overhead is involved, it may be justified in the long run by wiki fast execution of later operations. In the asymptotic " Big-O " sense, a self-balancing BST structure containing n items allows the lookup, insertion, and removal of an item in O log n worst-case time, search ordered enumeration of all items in O n time. For some implementations these are per-operation time bounds, while for others they are amortized bounds over a sequence of operations. These times are asymptotically optimal among all data structures that manipulate the key only through comparisons. Self-balancing binary search trees can be used in a natural way to construct and maintain ordered lists, such as priority queues. They can wiki be used for associative arrays ; key-value pairs are simply inserted with an ordering based on the key alone. In this capacity, self-balancing BSTs have a number of advantages and disadvantages over their main competitor, hash tables. One advantage of self-balancing BSTs is that they allow fast indeed, asymptotically optimal enumeration of the items in key binarywhich hash tables do not provide. One disadvantage is that their lookup algorithms get more complicated when there may be multiple items with the same key. Self-balancing BSTs have better worst-case lookup performance than hash tables O log n compared to O nsearch have worse average-case performance O log n compared to O Self-balancing BSTs can be used to implement any algorithm that requires mutable ordered lists, to achieve optimal worst-case asymptotic performance. For example, if binary tree sort is implemented with a self-balanced BST, we have a very simple-to-describe yet search optimal O n log n sorting algorithm. Similarly, many algorithms in computational geometry exploit variations on binary BSTs to solve problems such as the line segment intersection problem and the tree location problem efficiently. For search performance, however, self-balanced BSTs may wiki less efficient than other solutions. Binary tree sort, in particular, is likely to be slower than merge sortquicksortor heapsortbecause of the tree-balancing overhead as well as cache access patterns. For example, one can record the number of nodes in each subtree having a certain property, allowing one to count the number of nodes in a certain key range with that property in O log n time. Addison-Wesley, ISBN Section Balanced Trees, tree. By using this site, binary agree to the Terms of Use and Privacy Policy. wiki binary search tree

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