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|space_worst= |search_avg= |search_worst= |insert_avg= |insert_worst= |delete_avg= |delete_worst= }} In computer science, binary search trees (BST), sometimes called ordered or sorted binary trees, are a particular type of containers: data structures that store "items" (such as numbers, names etc.) in memory. They allow fast lookup, addition and removal of items, and can be used to implement either dynamic sets of items, or lookup tables that allow finding an item by its ''key'' (e.g., finding the phone number of a person by name). Binary search trees keep their keys in sorted order, so that lookup and other operations can use the principle of binary search: when looking for a key in a tree (or a place to insert a new key), they traverse the tree from root to leaf, making comparisons to keys stored in the nodes of the tree and deciding, based on the comparison, to continue searching in the left or right subtrees. On average, this means that each comparison allows the operations to skip about half of the tree, so that each lookup, insertion or deletion takes time proportional to the logarithm of the number of items stored in the tree. This is much better than the linear time required to find items by key in an (unsorted) array, but slower than the corresponding operations on hash tables. Several variants of the binary search tree have been studied in computer science; this article deals primarily with the basic type, making references to more advanced types when appropriate. ==Definition== A binary search tree is a rooted binary tree, whose internal nodes each store a key (and optionally, an associated value) and each have two distinguished sub-trees, commonly denoted ''left'' and ''right''. The tree additionally satisfies the binary search tree property, which states that the key in each node must be greater than all keys stored in the left sub-tree, and smaller than all keys in right sub-tree. (The leaves (final nodes) of the tree contain no key and have no structure to distinguish them from one another. Leaves are commonly represented by a special or symbol, a pointer, etc.) Generally, the information represented by each node is a record rather than a single data element. However, for sequencing purposes, nodes are compared according to their keys rather than any part of their associated records. The major advantage of binary search trees over other data structures is that the related sorting algorithms and search algorithms such as in-order traversal can be very efficient; they are also easy to code. Binary search trees are a fundamental data structure used to construct more abstract data structures such as sets, multisets, and associative arrays. Some of their disadvantages are as follows: * The shape of the binary search tree totally depends on the order of insertions and deletions, and it can become degenerated. * When inserting or searching for an element in a binary search tree, the key of each visited node has to be compared with the key of the element to be inserted or found. * The keys in the binary search tree may be long and the run time may increase. * After a long intermixed sequence of random insertion and deletion, the expected height of the tree approaches square root of the number of keys, , which grows much faster than . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「binary search tree」の詳細全文を読む スポンサード リンク
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