A New Algorithm to Represent a Given k-ary Tree into Its Equivalent Binary Tree Structure

Abstract

In this paper we have developed an algorithm that converts a given k-ary tree, for any k ≥ 3, to its equivalent binary tree structure. The binary tree is generated in O(n) time, for a k-ary tree with a total of n nodes. The algorithm is designed aiming at reducing the height of the constructed binary tree. The constructed tree does not contain any free links in the non-leaf nodes. That means the constructed tree is like a complete binary tree, where only leaves have no children, and nodes other than leaf nodes contain child (children) and some other valid information of the given k-ary tree.