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。
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
版权声明:本文为博主原创文章,未经博主允许不得转载。个人github代码空间:https://github.com/gannyee
原文地址:http://blog.csdn.net/github_27609763/article/details/47705623