二叉树
二叉树的抽象数据类型的接口定义
public interface BinaryTree
{
final String []mode={"preOrder","inOrder","postOrder","levelOrder"};
boolean createBTree(String gt);
boolean isEmpty();
void traverseBTree(String s);
Object findBTree(Object obj);
int depthBTree();
int countBTree();
void printBTree();
void clearBTree();
}二叉树的顺序存储结构是不合适的，链接存储结构通常被采用。首先是二叉树的结点的定义。
public class BTreeNode{
Object element;
BTreeNode left,right;
public BTreeNode(Object obj) {element=obj;left=right=null;}
public BTreeNode(Object obj,BTreeNode lt,BTreeNode rt)
{
element=obj;left=lt;right=rt;
}
}具体实现
public class LinkBinaryTree implements BinaryTree
{
protected BTreeNode root;
public LinkBinaryTree(){
root=null;
}
public LinkBinaryTree(BTreeNode rt){
root=rt;
}
private void preOrder(BTreeNode rt)
{
if(rt!=null){
System.out.print(rt.element+" ");
preOrder(rt.left);
preOrder(rt.right);
}
}
private void inOrder(BTreeNode rt)
{
if(rt!=null){
inOrder(rt.left);
System.out.print(rt.element+" ");
inOrder(rt.right);
}
}
private void postOrder(BTreeNode rt)
{
if(rt!=null){
postOrder(rt.left);
postOrder(rt.right);
System.out.print(rt.element+" ");
}
}
private void levelOrder(BTreeNode rt)
{
Queue que=new SequenceQueue();
BTreeNode p=null;
que.enter(rt);
while(!que.isEmpty()){
p=(BTreeNode)que.leave();
System.out.print(p.element+" ");
if(p.left!=null) que.enter(p.left);
if(p.right!=null) que.enter(p.right);
}
}
private Object findBTree(BTreeNode rt)
{
}
private int depthBTree(BTreeNode rt)
{
}
private int countBTree(BTreeNode rt)
{
}
private void printBTree(BTreeNode rt)
{
}
public boolean createBTree(String gt)
{
Stack sck=new SequenceStack();
root=null;
BTreeNode p=null;
int k=1;
char []a=str.toCharArray();
for(int i=0;i<a.length;i++)
{
switch(a[i]){
case ‘ ‘:
break;
case ‘(‘:
sck.push(p);k=1;
break;
case ‘)‘:
if(sck.isEmpty()){
System.out.println("二叉树广义表字符串错，返回假！");
return false;
}
sck.pop(); break;
case ‘,‘:
k=2;break;
default:
if((a[i]>=‘a‘&&a[i]<=‘z‘)||(a[i]>=‘A‘&&a[i]<=‘Z‘)){
p=new BTreeNode(a[i]);
if(root==null) root=p;
else{
if(k==1) ((BTreeNode)sck.peek()).left=p;
else ((BTreeNode)sck.peek()).right=p;
}
}
else{
System.out.println("二叉树广义表中存在非法字符，返回假！");
return false;
}
}
}
if(sck.isEmpty()) return true;else return false;
}
public boolean isEmpty(){
return root==null;
}
public void traverseBTree(String s)
{
if(s.equals(mode[0])) preOrder(root);
else if(s.equals(mode[1])) inOrder(root);
else if(s.equals(mode[2])) postOrder(root);
else if(s.equals(mode[3])) levelOrder(root);
System.out.println();
}
public Object findBTree(Object obj){
return findBTree(root,obj);
}
private Object findBTree(BTreeNode rt,Object x)
{
if(rt==null) return null;
else{
if(rt.element.equals(x))
{
return rt.element;
}
else{
Object y;
y=findBTree(rt.left,x); if(y!=null) return y;
y=findBTree(rt.right,x); if(y!=null) return y;
return null;
}
}
}
public int depthBTree(){
return depthBTree(root);
}
private int depthBTree(BTreeNode rt)
{
if(rt==null)
return 0;
else{
int dep1=depthBTree(rt.left);
int dep2=depthBTree(rt.right);
if(dep1>dep2)
return dep1+1;
else
return dep2+2;
}
}
public int countBTree(){
return countBTree(root);
}
private int countBTree(BTreeNode rt)
{
if(rt==null) return 0;
else return countBTree(rt.left)+countBTree(rt.right);
}
public void printBTree(){
printBTree(root);
System.out.println();
}
private void printBTree(BTreeNode rt)
{
if(rt!=null){
System.out.print(rt.element);
if(rt.left!=null||rt.right!=null){
System.out.print(‘(‘);
printBTree(rt.left);
if(rt.right!=null)
System.out.print(‘,‘);
printBTree(rt.right);
System.out.print(‘)‘);
}
}
}
public void clearBTree(){root=null;}
}客户端实现代码如下：
public class Example
{
public static void main(String[] args)
{
BinaryTree nt=new LinkBinaryTree();
String s="a(b(c),d(e(f,g),h(,i)))";
boolean yn=bt.createBTree(s);
if(!yn){
System.out.println("表示二叉树的字符串s有误，退出运行！");
System.exit(1);
}
System.out.println("二叉树的广义表形式：");bt.printBTree();
System.out.println("前序："); bt.traverseBTree("preOrder");
System.out.println("中序："); bt.traverseBTree("inOrder");
System.out.println("后序："); bt.traverseBTree("postOrder");
System.out.println("按层："); bt.traverseBTree("levelOrder");
System.out.println("深度："+bt.depthBTree());
System.out.println("结点数："+bt.countBTree());
System.out.println("查找结点："+bt.findBTree(‘g‘)+bt.findBTree(‘G‘));
bt.clearBTree();
}
}普通树的存储结构和运算
普通树的接口如下：
public interface GeneralTree{
final String []mode={"preOrder","postOrder","levelOrder"};
boolean createBTree(String gt);
void traverseBTree(String s);
int degree();
Object findGTree(Object obj);
int depthGTree();
int countGTree();
void printGTree();
boolean isEmpty();
void clearGTree();
}普通树的链接存储结构
结点定义：
public class GTreeNode{
Obejct element;
GTreeNode[] next;
public GTreeNode(Object obj){
element=obj;
next=new GTreeNode[k];
for(int i=0;i<k;i++) next[i]=null;
}
public GTreeNode(Object obj,GTreeNode[] nt){
element=obj;
next=new GTreeNode[k];
for(int i=0;i<k;i++) next[i]=nt[i];
}
}树的链接存储类
public class LinkGeneralTree implements GeneralTree
{
public class GTreeNode{
Obejct element;
GTreeNode[] next;
public GTreeNode(Object obj){
element=obj;
next=new GTreeNode[k];
for(int i=0;i<k;i++) next[i]=null;
}
public GTreeNode(Object obj,GTreeNode[] nt){
element=obj;
next=new GTreeNode[k];
for(int i=0;i<k;i++) next[i]=nt[i];
}
}
protected final int k;
protected GTreeNode root;
public LinkGeneralTree(int kk){
k=kk;
root=null;
}
public int degree() {return k;}
private void preOrder(GTreeNode gt) {
if(gt!=null){
System.out.print(gt.element+" ");
for(int i=0;i<k;i++)
preOrder(gt.next[i]);
}
}
private void postOrder(GTreeNode gt) {
if(gt!=null){
for(int i=0;i<k;i++)
postOrder(gt.next[i]);
System.out.print(gt.element+" ");
}
}
private void levelOrder(GTreeNode gt) {
Queue que=new SequenceQueue();
GTreeNode p=null;
que.enter(gt);
while(!que.isEmpty()){
p=(GTreeNode)que.leave();
System.out.print(p.element+" ");
for(int i=0;i<k;i++)
if(p.next[i]!=null) que.enter(p.next[i]);
}
}
private Object findGTree(GTreeNode gt,Object x) {
if(gt==null) return null;
else if(gt.element.equals(x))
return gt.element;
else{
Object y;
for(int i=0;i<k;i++)
if((y=findGTree(gt.next[i],x))!=null) return y;
return null;
}
}
private int depthGTree(GTreeNode gt) {
if(gt==null)
return 0;
else{
int max=0;
for(int i=0;i<k;i++){
int dep=depthGTree(gt.next[i]);
if(dep>max) max=dep;
}
return max+1;
}
}
private int countGTree(GTreeNode gt) {
if(gt==null) return 0;
else{
int c=0;
for(int i=0;i<k;i++) c+=countGTree(gt.next[i]);
return c+1;
}
}
private void printGTree(GTreeNode gt) {
if(gt!=null){
System.out.print(gt.element);
int i,j=-1;
for(i=0;i<k;i++)
if(gt.next[i]!=null) j=i;
if(j>=0){
System.out.print(‘(‘);
printGTree(gt.next[0]);
for(i=1;i<=j;i++){
System.out.print(‘,‘);
printGTree(gt.next[i]);
}
System.out.print(‘)‘);
}
}
}
public boolean createGTree(String str) {
Stack sck=new SequenceStack();
Stack ord=new SequenceStack();
root=null;
GTreeNode p=null;
char []a=str.toCharArray();
for(int i=0;i<a.length;i++)
{
switch(a[i]){
case ‘ ‘:
break;
case ‘(‘:
sck.push(p);
ord.push(0);
break;
case ‘)‘:
if(sck.isEmpty()){
System.out.println("普通树广义表字符串错，返回假！");
return false;
}
sck.pop();ord.pop();
break;
case ‘,‘:
int x=(Integer)ord.pop();
ord.push(x+1);break;
default:
if((a[i]>=‘a‘&&a[i]<=‘z‘)||(a[i]>=‘A‘&&a[i]<=‘Z‘))
{
p=new GTreeNode(a[i]);
if(root==null) root=p;
else{
((GTreeNode)sck.peek()).next[(Integer)ord.peek()]=p;
}
}
else{
System.out.println("普通树广义表中存在非法字符，返回假！");
return false;
}
}
}
if(sck.isEmpty()) return true;else return false;
}
public boolean isEmpty(){
return root==null;
}
public void clearGTree() {root=null;}
public void traverseGTree(String s)
{
if(s.equals(mode[0])) preOrder(root);
else if(s.equals(mode[1])) postOrder(root);
else if(s.equals(mode[2])) levelOrder(root);
System.out.println();
}
public Object findGTree(Object obj){
return findGTree(root,obj);
}
public int depthGTree(){
return depthGTree(root);
}
public int countGTree(){
return countGTree(root);
}
public void printGTree(){
printGTree(root);
System.out.println();
}
}调试普通树的客户端代码如下
public class Example{
public static void main(String[] args){
GeneralTree gt=new LinkGeneralTree(3);
String s="A(B(D,E(,H,I),F),,C(,,G))";
boolean yn=gt.createGTree(s);
if(!yn){
System.out.println("表示普通树的字符串s有误，退出运行！");
System.exit(1);
}
System.out.print("树的广义形式：");gt.printGTree();
System.out.println("树的度数："+gt.degree());
System.out.print("前序遍历：");gt.traverseGTree("preOrder");
System.out.print("后序遍历：");gt.traverseGTree("postOrder");
System.out.print("按层遍历：");gt.traverseGTree("levelOrder");
System.out.println("树的深度："+gt.depthGTree());
System.out.println("总结点数："+gt.countGTree());
System.out.println("查找结点："+(Character)gt.findGTree(‘d‘)+" "+(Character)gt.findGTree(‘H‘));
gt.clearGTree();
}
}本文出自 “仙路千叠惊尘梦” 博客，请务必保留此出处http://secondscript.blog.51cto.com/9370042/1617190
原文地址：http://secondscript.blog.51cto.com/9370042/1617190
