树结构的自定义及基本算法（Java数据结构学习笔记）

数据结构可以归类两大类型：线性结构与非线性结构，本文的内容关于非线性结构：树的基本定义及相关算法。关于树的一些基本概念定义可参考：维基百科

树的ADT模型：

根据树的定义，每个节点的后代均构成一棵树树，称为子树。因此从数据类型来讲，树、子树、树节点是等同地位，可将其看作为一个节点，用通类：Tree表示。如下图所示：



图：Tree ADT模型示意图

可采用“父亲-儿子-兄弟”模型来表示树的ADT。如图所示，除数据项外，分别用三个引用表示指向该节点的父亲，儿子，兄弟。



图：“父亲-儿子-兄弟”模型的数据结构示意图

表：树ADT实现的操作



就对树的更新操作而言，不同的应用问题会要求树结构提供不同方法。这方面的差异太大，无法在树 ADT 中定义出通用的更新操作。在之后将结合各种应用问题，陆续给出一些具体的更新操作的实现。

树的java接口：

package com.tree;

/**
* Java Structure for Tree
* Construct interface Tree
* @author gannyee
*
*/
public interface Tree {
//Get size of tree which recent node as parent
public int getSize();

//Get height of recent node
public int getHeight();

//Get depth of recent node
public int getDepth();

//Get element of recent node
public Object getElement();

//Set element of recent node, return former element
public Object setElement(Object newElement);

//Get parent of recent node
public TreeLinkedList getParent();

//Get first child of recent node
public TreeLinkedList getFirstChild();

//Get biggest sibling of recent node
public TreeLinkedList getNextSibling();
}

Java代码：树节点模型实现

package com.tree;

import java.lang.reflect.Constructor;

public class TreeLinkedList implements Tree{
//Pointer point to parent
private TreeLinkedList parent;
//Element
private Object element;
//Pointer point to firstChild
private TreeLinkedList firstChild;
//Pointer point to nextSibling
private TreeLinkedList nextSibling;

//Constructor
public TreeLinkedList(){
this(null,null,null,null);
}

//Constructor with parameters
public TreeLinkedList(TreeLinkedList p, Object e,TreeLinkedList f,TreeLinkedList n){
this.parent = p;
this.element = e;
this.firstChild = f;
this.nextSibling = n;
}
//Get size of tree which recent node as parent
public int getSize(){
int size = 1; //Recent node also include own children
TreeLinkedList subTree = firstChild;//Start with first child
while(null != subTree){
size += subTree.getSize();
subTree = subTree.getNextSibling();//Get all descendants
}
return size;
}

//Get height of recent node
public int getHeight(){
int height = -1;//Recent node's(parent) height
TreeLinkedList subTree = firstChild;//Start with first child

while(null != subTree){
height = Math.max(height, subTree.getHeight());//Get the max height
subTree = subTree.getNextSibling();
}
return height + 1;//Get recent node height
}

//Get depth of recent node
public int getDepth(){
int depth = 0;
TreeLinkedList p = parent;//Start with parent
while(p != null){
depth ++;
p = p.getParent();//Get all parents of every node
}
return depth;
}

//Get element of recent node,if nothing return null
public Object getElement(){
return this.element;
}

//Set element of recent node,return former element
public Object setElement(Object newElement){
Object swap;
swap = this.element;
this.element = newElement;
return this.element;
}

//Get parent of recent node,if nothing return null
public TreeLinkedList getParent(){
return parent;
}

//Get first child of recent node,if nothing return null
public TreeLinkedList getFirstChild(){
return firstChild;
}

//Get biggest sibling of recent node,if nothing return null
public TreeLinkedList getNextSibling(){
return nextSibling;
}
}

测试代码：

package com.tree;

public class TreeTest {

/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub

TreeLinkedList a = new TreeLinkedList();
TreeLinkedList b = new TreeLinkedList();
TreeLinkedList c = new TreeLinkedList();
TreeLinkedList d = new TreeLinkedList();
TreeLinkedList e = new TreeLinkedList();
TreeLinkedList f = new TreeLinkedList();
TreeLinkedList g = new TreeLinkedList();

a = new TreeLinkedList(null,0,d,null);
b = new TreeLinkedList(a,1,d,c.getFirstChild());
c = new TreeLinkedList(a,2,null,null);
d = new TreeLinkedList(b,3,f,e.getFirstChild());
e = new TreeLinkedList(b,4,null,null);
f = new TreeLinkedList(d,5,null,g.getFirstChild());
g = new TreeLinkedList(d,6,null,null);

System.out.println(a.getDepth());
System.out.println(b.getDepth());
System.out.println(c.getDepth());
System.out.println(d.getDepth());
System.out.println(e.getDepth());
System.out.println(f.getDepth());

System.out.println(a.getHeight());
System.out.println(b.getHeight());
System.out.println(c.getHeight());
System.out.println(d.getHeight());
System.out.println(e.getHeight());
System.out.println(f.getHeight());
System.out.println(g.getHeight());

}

}

测试结果：

0
1
2
com.tree.TreeLinkedList@7c1c8c58
1
null
null

后续将给出关于树的遍历算法！

参考文献：数据结构与算法（ Java 描述）邓俊辉 著