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With given nodes, the minimum possible tree height is = (+) with which the tree is a balanced full tree or perfect tree. With a given height h {\displaystyle h} , the number of nodes can't exceed the 2 h + 1 − 1 {\displaystyle 2^{h+1}-1} as the number of nodes in a perfect tree.
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.
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 ...
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 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 ...
Unlike red–black trees, red nodes on an AA tree can only be added as a right subchild. In other words, no red node can be a left sub-child. This results in the simulation of a 2–3 tree instead of a 2–3–4 tree , which greatly simplifies the maintenance operations.
In the case of a perfect binary tree of height h, there are 2 h+1 −1 nodes and 2 h+1 Null pointers as children (2 for each of the 2 h leaves), so short-circuiting cuts the number of function calls in half in the worst case.
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.