Analytic Formulas to Calculate Symmetric Brothers of a Node in a Perfect Binary Tree
Abstract
The paper puts forward and solves the problem of calculating the symmetric brother nodes of a given node in a perfect binary tree. By analyzing the relationships between a node and its ancestors, the position at which a node lies in term of the subtree rooted by an ancestor is expressed with a mathematical formula and consequently the mathematical formula to express its symmetric nodes is derived out. The formulas enable an easy calculation of a node and its symmetric nodes in the perfect binary tree.