Who invented binary search trees

O log N Complexities? The Solution What about Linked List? What about Hash Table? The Solution 4. Visualization BST Vertex Attributes BST Property 5.

BST Operations Static vs Dynamic Data Structure 6. Search v FindMin and FindMax O h Time Complexity 7. Successor v Predecessor v O h Time Complexity 8. Inorder Traversal O N Time Complexity Preorder and Postorder Traversal 9. Insert v O h Time Complexity Mini Quiz Remove v - Three Possible Cases Remove v - Case 1 Remove v - Case 2 Remove v - Case 3 Remove v - Case 3 Discussion The Answer Create BST Intermezzo Try Exploration Mode Balanced BST AVL Tree Extra BST Attribute: height v Formal Definition of height v Derivation of the Lower Bound The Combined Bound Step 1: Maintaining height v Efficiently Proof - 1 Proof - 2 Proof - 3 Proof - 4 Step 3: Maintain Invariant Introducing Tree Rotation Non-trivial O 1 Tree Rotation Pseudo-code Four Rebalancing Cases Insert v in AVL Tree Remove v in AVL Tree AVL Tree Summary Extras Online Quiz Online Judge Exercises Status Panel Codetrace Panel Media Control Return to 'Exploration Mode'.

X Esc. This special requirement of Table ADT will be made clearer in the next few slides. Yes No Submit Discussion: Why? Hint: Go back to the previous 4 slides ago. We will now introduce BST data structure. See the visualization of an example BST above! If v does not exist, we can report Or in another word, find the k -th smallest element in the BST.

Because of the BST properties, we can find the Successor of an integer v assume that we already know where integer v is located from earlier call of Search v as follows: If v has a right subtree, the minimum integer in the right subtree of v must be the successor of v.

Try Successor 23 should be If v does not have a right subtree, we need to traverse the ancestor s of v until we find 'a right turn' to vertex w or alternatively, until we find the first vertex w that is greater than vertex v. Once we find vertex w , we will see that vertex v is the maximum element in the left subtree of w. Try Successor 7 should be If v is the maximum integer in the BST, v does not have a successor.

Try Successor 71 should be none. Discussion: Why? K-d trees for semidynamic point sets. Distance browsing in spatial databases. Cache-oblivious data structures for orthogonal range searching. Highly Influenced. View 4 excerpts, cites methods. Index structures are frequently used to reduce search times in large databases. With index structures like the B-Tree search time grows only logarithmic with the size of a database for several types … Expand.

View 1 excerpt, cites background. View 2 excerpts, cites methods. Adding range restriction capability to dynamic data structures. Rank Selection in Multidimensional Data. View 2 excerpts, cites background.

An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. Time Bounds for Selection. More Filters. Splay Trees are usually considered forms of lexicographically ordered binary search trees [1, 2]. The motivation of this paper comes from the fact that the search trees have multiples drawbacks.

Inorder traversal of splay trees. On preorder splaying in binary search trees abstract and references only.

View 1 excerpt, cites background. Sequential access in splay trees takes linear time. View 2 excerpts, cites background and methods. Abstract Splay trees, a form of self-adjusting binary tree, were introduced by Sleator and Tarjan in the early s. Their main use is to store ordered lists. The idea is to keep the trees … Expand. Highly Influenced. View 2 excerpts, cites methods and background. Competitive Online Search Trees on Trees. Self-Adjusting k-ary Search Trees.