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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. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:
A labeled binary tree of size 9 (the number of nodes in the tree) and height 3 (the height of a tree defined as the number of edges or links from the top-most or root node to the farthest leaf node), with a root node whose value is 1. The above tree is unbalanced and not sorted.
For an m-ary tree with height h, the upper bound for the maximum number of leaves is . The height h of an m-ary tree does not include the root node, with a tree containing only a root node having a height of 0. The height of a tree is equal to the maximum depth D of any node in the tree.
1. The height of a node in a rooted tree is the number of edges in a longest path, going away from the root (i.e. its nodes have strictly increasing depth), that starts at that node and ends at a leaf. 2. The height of a rooted tree is the height of its root. That is, the height of a tree is the number of edges in a longest possible path, going ...
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 ...
The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (a tree with no vertices, if such are allowed) has depth and height −1. A k-ary tree (for nonnegative integers k) is a rooted tree in which each vertex has at most k children.
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 ...
For each t ∈ T, the order type of {s ∈ T : s < t} is called the height of t, denoted ht(t, T). The height of T itself is the least ordinal greater than the height of each element of T. A root of a tree T is an element of height 0. Frequently trees are assumed to have only one root.