剑指Offer——二叉树
前言
数据结构通常是编程面试中考察的重点。在参加面试之前，应聘者需要熟练掌握链表、树、栈、队列和哈希表等数据结构，以及它们的操作。本片博文主要讲解二叉树操作的相关知识，主要包括二叉树的建立、遍历方法的循环和递归写法。
二叉树是树形结构的一个重要类型。许多实际问题抽象出来的数据结构往往是二叉树的形式，即使是一般的树也能简单地转换为二叉树，而且二叉树的存储结构及其算法都较为简单，因此二叉树显得特别重要。
二叉树的java实现
首先创建一棵二叉树如下图，然后对这颗二叉树进行遍历操作（遍历操作的实现分为递归实现和非递归实现），同时还提供一些方法如获取双亲结点、获取左孩子、右孩子等。
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package cn.edu.ujn.nk;
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import java.util.Stack;
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/**
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* 二叉树的链式存储
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* @author WWX
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*/
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public class BinaryTree {
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private TreeNode root=null;
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public BinaryTree(){
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root=new TreeNode(1,"rootNode(A)");
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}
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/**
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* 创建一棵二叉树
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* <pre>
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* A
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* B C
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* D E F
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* </pre>
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* @param root
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* @author WWX
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*/
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public void createBinTree(TreeNode root){
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TreeNode newNodeB = new TreeNode(2,"B");
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TreeNode newNodeC = new TreeNode(3,"C");
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TreeNode newNodeD = new TreeNode(4,"D");
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TreeNode newNodeE = new TreeNode(5,"E");
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TreeNode newNodeF = new TreeNode(6,"F");
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root.leftChild=newNodeB;
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root.rightChild=newNodeC;
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root.leftChild.leftChild=newNodeD;
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root.leftChild.rightChild=newNodeE;
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root.rightChild.rightChild=newNodeF;
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}
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public boolean isEmpty(){
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return root==null;
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}
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//树的高度
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public int height(){
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return height(root);
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}
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//节点个数
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public int size(){
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return size(root);
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}
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private int height(TreeNode subTree){
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if(subTree == null)
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return 0; // 递归结束：空树高度为0
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else{
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int i = height(subTree.leftChild);
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int j = height(subTree.rightChild);
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return (i < j) ? (j + 1) : (i + 1);
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}
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}
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private int size(TreeNode subTree){
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if(subTree == null){
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return 0;
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}else{
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return 1 + size(subTree.leftChild) + size(subTree.rightChild);
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}
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}
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//返回双亲结点
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public TreeNode parent(TreeNode element){
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return (root == null|| root == element) ? null : parent(root, element);
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}
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public TreeNode parent(TreeNode subTree,TreeNode element){
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if(subTree == null)
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return null;
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if(subTree.leftChild == element || subTree.rightChild == element)
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//返回父结点地址
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return subTree;
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TreeNode p;
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// 先在左子树中找，如果左子树中没有找到，才到右子树去找
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if((p = parent(subTree.leftChild, element)) != null)
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//递归在左子树中搜索
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return p;
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else
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//递归在右子树中搜索
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return parent(subTree.rightChild, element);
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}
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public TreeNode getLeftChildNode(TreeNode element){
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return (element != null) ? element.leftChild : null;
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}
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public TreeNode getRightChildNode(TreeNode element){
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return (element != null) ? element.rightChild : null;
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}
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public TreeNode getRoot(){
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return root;
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}
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//在释放某个结点时，该结点的左右子树都已经释放，
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//所以应该采用后续遍历，当访问某个结点时将该结点的存储空间释放
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public void destroy(TreeNode subTree){
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//删除根为subTree的子树
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if(subTree!=null){
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//删除左子树
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destroy(subTree.leftChild);
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//删除右子树
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destroy(subTree.rightChild);
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//删除根结点
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subTree=null;
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}
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}
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public void traverse(TreeNode subTree){
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System.out.println("key:"+subTree.key+"--name:"+subTree.data);;
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traverse(subTree.leftChild);
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traverse(subTree.rightChild);
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}
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//前序遍历
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public void preOrder(TreeNode subTree){
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if(subTree!=null){
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visted(subTree);
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preOrder(subTree.leftChild);
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preOrder(subTree.rightChild);
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}
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}
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//中序遍历
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public void inOrder(TreeNode subTree){
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if(subTree!=null){
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inOrder(subTree.leftChild);
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visted(subTree);
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inOrder(subTree.rightChild);
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}
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}
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//后续遍历
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public void postOrder(TreeNode subTree) {
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if (subTree != null) {
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postOrder(subTree.leftChild);
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postOrder(subTree.rightChild);
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visted(subTree);
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}
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}
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//前序遍历的非递归实现
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public void nonRecPreOrder(TreeNode p){
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Stack<TreeNode> stack=new Stack<TreeNode>();
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TreeNode node=p;
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while(node!=null||stack.size()>0){
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while(node!=null){
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visted(node);
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stack.push(node);
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node=node.leftChild;
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}
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while(stack.size()>0){
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node=stack.pop();
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node=node.rightChild;
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}
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}
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}
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//中序遍历的非递归实现
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public void nonRecInOrder(TreeNode p){
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Stack<TreeNode> stack =new Stack<BinaryTree.TreeNode>();
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TreeNode node =p;
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while(node!=null||stack.size()>0){
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//存在左子树
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while(node!=null){
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stack.push(node);
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node=node.leftChild;
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}
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//栈非空
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if(stack.size()>0){
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node=stack.pop();
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visted(node);
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node=node.rightChild;
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}
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}
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}
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//后序遍历的非递归实现
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public void noRecPostOrder(TreeNode p){
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Stack<TreeNode> stack=new Stack<BinaryTree.TreeNode>();
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TreeNode node =p;
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while(p!=null){
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//左子树入栈
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for(;p.leftChild!=null;p=p.leftChild){
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stack.push(p);
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}
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//当前结点无右子树或右子树已经输出
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while(p!=null&&(p.rightChild==null||p.rightChild==node)){
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visted(p);
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//纪录上一个已输出结点
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node =p;
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if(stack.empty())
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return;
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p=stack.pop();
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}
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//处理右子树
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stack.push(p);
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p=p.rightChild;
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}
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}
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public void visted(TreeNode subTree){
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subTree.isVisted=true;
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System.out.println("key:"+subTree.key+"--name:"+subTree.data);;
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}
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/**
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* 二叉树的节点数据结构
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* @author WWX
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*/
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private class TreeNode{
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private int key = 0;
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private String data = null;
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private boolean isVisted = false;
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private TreeNode leftChild = null;
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private TreeNode rightChild = null;
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public TreeNode(){}
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/**
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* @param key 层序编码
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* @param data 数据域
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*/
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public TreeNode(int key,String data){
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this.key = key;
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this.data = data;
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this.leftChild = null;
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this.rightChild = null;
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}
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}
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//测试
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public static void main(String[] args) {
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BinaryTree bt = new BinaryTree();
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bt.createBinTree(bt.root);
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System.out.println("the size of the tree is " + bt.size());
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System.out.println("the height of the tree is " + bt.height());
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System.out.println("***递归实现****(前序遍历)[ABDECF]遍历*****************");
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bt.preOrder(bt.root);
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System.out.println("***递归实现****(中序遍历)[DBEACF]遍历*****************");
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bt.inOrder(bt.root);
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System.out.println("***递归实现****(后序遍历)[DEBFCA]遍历*****************");
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bt.postOrder(bt.root);
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System.out.println("***非递归实现****(前序遍历)[ABDECF]遍历*****************");
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bt.nonRecPreOrder(bt.root);
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System.out.println("***非递归实现****(中序遍历)[DBEACF]遍历*****************");
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bt.nonRecInOrder(bt.root);
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System.out.println("***非递归实现****(后序遍历)[DEBFCA]遍历*****************");
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bt.noRecPostOrder(bt.root);
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}
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}
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文章来源: shq5785.blog.csdn.net，作者：No Silver Bullet，版权归原作者所有，如需转载，请联系作者。
原文链接：shq5785.blog.csdn.net/article/details/52143212