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.
Highlights
In a perfect binary tree, whose definition is seen at page 877 in Paul’s dictionary (Paul E Black,2004) and as illustrated in figure 1, an internal node might have a father, a grandfather or even ancestors of higher generations, as described by certain entries in the handbooks edited by Rosen K (Rosen K, 2000) and by Dinesh P M & Sartaj Sahni (Dinesh 2004)
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 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
Summary
In a perfect binary tree, whose definition is seen at page 877 in Paul’s dictionary (Paul E Black,2004) and as illustrated in figure 1, an internal node might have a father, a grandfather or even ancestors of higher generations, as described by certain entries in the handbooks edited by Rosen K (Rosen K, 2000) and by Dinesh P M & Sartaj Sahni (Dinesh 2004). In a perfect binary tree, whose definition is seen at page 877 in Paul’s dictionary (Paul E Black,2004) and as illustrated, an internal node might have a father, a grandfather or even ancestors of higher generations, as described by certain entries in the handbooks edited by Rosen K (Rosen K, 2000) and by Dinesh P M & Sartaj Sahni (Dinesh 2004). On a level of a perfect binary tree, it is known that, a node must have a brother that shares a father with it; it has cousins that share grandfather or ancestors of higher generations. Literatures of studying on the ancestors or descendants of a node in a tree can be frequently found in library. A recent study comes across a problem of finding the symmetric brothers (or cousins) for a given node. Since there is no referable literature, this article solves the problem
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