Ternary tree

In computer science, a ternary tree is a tree data structure in which each node has at most three child nodes, usually distinguished as "left", “mid” and "right". Nodes with children are parent nodes, and child nodes may contain references to their parents. Outside the tree, there is often a reference to the "root" node (the ancestor of all nodes), if it exists. Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left, mid or right child.

Ternary trees are used to implement Ternary search trees and Ternary heaps.

- 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 termed a descendant of p.

- A size of a node is the number of descendants it has including itself.

– Let ${\displaystyle h}$ be height of a ternary tree.

– Let ${\displaystyle M(h)}$ be the maximum number of nodes in a ternary tree of height h

– ${\displaystyle M(h)=1+3+9+\cdots +3^{h}=\sum _{i=0}^{h}3^{i}={\frac {3^{h+1}-1}{2}}}$

...
Wikipedia