一种二叉树性质5的证明方法  

A Method to Proof the Fifth Property of Binary Tree

作　　者：沈华[1] 

机构地区：[1]湖北工业大学计算机学院网络工程系,武汉430068

出　　处：《电脑编程技巧与维护》2013年第14期24-25,39,共3页Computer Programming Skills & Maintenance

基　　金：国家自然科学基金青年基金项目资助(项目编号:41204112)

摘　　要：二叉树的性质5说明完全二叉树中结点之间的关系可以通过对结点编号的简单算术运算得到,这意味着可以用线性结构表示这种非线性结构。为了明确和深入理解为什么完全二叉树结点之间的关系可以隐藏在线性的结点编号中,提出了一种简明的二叉树性质5的证明方法,并将证明思路应用于完全三叉树和完全m叉树,得到一个关于结点编号表示结点之间关系的一般性结论。The fifth nature of binary tree illustrates that the relationships between nodes can be achieved by the simple nodes＂ ID arithmetic operations, which means the nonlinear structure can be represented by using a linear structure. In order to clarity and in-depth understand the reasons why the relationships between the nodes of complete binary tree can be hidden in the linear IDs of nodes, this paper presents a simple method to proof the fifth nature of binary tree. A general conclusion about the way using nodes＇ ID to represent the relationship between the nodes can be gotten by applying the proof idea to the complete triple tree and complete m-ary tree.

关 键 词：数据结构 二叉树 完全二叉树 完全三叉树 完全m叉树 

分 类 号：TP311.12[自动化与计算机技术—计算机软件与理论]