Implementation of the Binary Coding Scheme and the Tree Traversal Algorithms to Test for Ancestor- Descendant Relationships in K-ary Trees

This paper discusses the implementation of the binary coding scheme and its comparison with the post-order, preorder and in-order traversal techniques to test for ancestor-descendant relationships in k-ary trees (a tree in which any leaf node has up to k children). The approach used is assigning a unique binary code to each node in a tree. The value of the binary code for a node is the concatenation of the code for its parent node (referred to as prefix) and the unique binary representation of the immediate children of the parent node (referred to as suffix). For any two nodes I and J, if the binary code of node I forms the prefix of the code of node J, then node I is the ancestor for node J; otherwise not. This method to test ancestor-descendant relationships has a time complexity of O(1), whereas the tree-traversals incur a complexity of O(n).