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In these trees, each node contains one of the input points. Since the division of the plane is decided by the order of point-insertion, the tree's height is sensitive to and dependent on insertion order. Inserting in a "bad" order can lead to a tree of height linear in the number of input points (at which point it becomes a linked-list).
Height - Length of the path from the root to the deepest node in the tree. A (rooted) tree with only one node (the root) has a height of zero. In the example diagram, the tree has height of 2. Sibling - Nodes that share the same parent node. A node p is an ancestor of a node q if it exists on the path from q to the root. The node q is then ...
The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such ...
Each node of a ternary search tree stores a single character, an object (or a pointer to an object depending on implementation), and pointers to its three children conventionally named equal kid, lo kid and hi kid, which can also be referred respectively as middle (child), lower (child) and higher (child). [1]
The simplest way to find a level ancestor of a node is to climb up the tree towards the root of the tree. On the path to the root of the tree, every ancestor of a node can be visited and therefore reported. In this case, the tree does not need to be preprocessed and the time to answer a query is O(h), where "h" is the height of the tree. This ...
For all nodes, the left subtree's key must be less than the node's key, and the right subtree's key must be greater than the node's key. These subtrees must all qualify as binary search trees. The worst-case time complexity for searching a binary search tree is the height of the tree, which can be as small as O(log n) for a tree with n elements.
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In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.