In graph theory, a k-ary tree is a rooted tree in which each node has no more than k children. It is also sometimes known as a k-way tree, an N-ary tree, or an M-ary tree. A binary tree is the special case where k=2.
Types of k-ary trees 
- A full k-ary tree is a k-ary tree where within each level every node has either 0 or k children.
- A perfect k-ary tree is a full  k-ary tree in which all leaf nodes are at the same depth.
- A complete k-ary tree is a k-ary tree which is maximally space efficient. It must be completely filled on every level (meaning that each level has k children) except for the last level (which can have at most k children). However, if the last level is not complete, then all nodes of the tree must be "as far left as possible". 
Properties of k-ary trees 
- For a k-ary tree with height h, the upper bound for the maximum number of leaves is .
- The total number of nodes is , while the height h is
Note : A Tree containing only one node is taken to be of height 0 for this formula to be applicable.
Note : Formula applicable only for number_of_nodes = number of nodes in *complete* k-ary tree
- Storer, James A. (2001). An Introduction to Data Structures and Algorithms. Birkhäuser Boston. ISBN 3-7643-4253-6.
|This computer science article is a stub. You can help Wikipedia by expanding it.|