剑指Offer——二叉树

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。

package cn.edu.ujn.nk;

import java.util.Stack;

/**
 * 二叉树的链式存储
 * @author WWX
 */
public class BinaryTree {  

    private TreeNode root=null;  

    public BinaryTree(){
        root=new TreeNode(1,"rootNode(A)");
    }  

    /**
     * 创建一棵二叉树
     * <pre>
     *           A
     *     B          C
     *  D     E            F
     *  </pre>
     * @param root
     * @author WWX
     */
    public void createBinTree(TreeNode root){
        TreeNode newNodeB = new TreeNode(2,"B");
        TreeNode newNodeC = new TreeNode(3,"C");
        TreeNode newNodeD = new TreeNode(4,"D");
        TreeNode newNodeE = new TreeNode(5,"E");
        TreeNode newNodeF = new TreeNode(6,"F");
        root.leftChild=newNodeB;
        root.rightChild=newNodeC;
        root.leftChild.leftChild=newNodeD;
        root.leftChild.rightChild=newNodeE;
        root.rightChild.rightChild=newNodeF;
    }  

    public boolean isEmpty(){
        return root==null;
    }  

    //树的高度
    public int height(){
        return height(root);
    }  

    //节点个数
    public int size(){
        return size(root);
    }  

    private int height(TreeNode subTree){
        if(subTree == null)
            return 0;	// 递归结束：空树高度为0
        else{
            int i = height(subTree.leftChild);
            int j = height(subTree.rightChild);
            return (i < j) ? (j + 1) : (i + 1);
        }
    }

    private int size(TreeNode subTree){
        if(subTree == null){
            return 0;
        }else{
            return 1 + size(subTree.leftChild) + size(subTree.rightChild);
        }
    }  

    //返回双亲结点
    public TreeNode parent(TreeNode element){
        return (root == null|| root == element) ? null : parent(root, element);
    }

    public TreeNode parent(TreeNode subTree,TreeNode element){
        if(subTree == null)
            return null;
        if(subTree.leftChild == element || subTree.rightChild == element)
            //返回父结点地址
            return subTree;
        TreeNode p;
        // 先在左子树中找，如果左子树中没有找到，才到右子树去找
        if((p = parent(subTree.leftChild, element)) != null)
            //递归在左子树中搜索
            return p;
        else
            //递归在右子树中搜索
            return parent(subTree.rightChild, element);
    }  

    public TreeNode getLeftChildNode(TreeNode element){
        return (element != null) ? element.leftChild : null;
    }  

    public TreeNode getRightChildNode(TreeNode element){
        return (element != null) ? element.rightChild : null;
    }  

    public TreeNode getRoot(){
        return root;
    }  

    //在释放某个结点时，该结点的左右子树都已经释放，
    //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
    public void destroy(TreeNode subTree){
        //删除根为subTree的子树
        if(subTree!=null){
            //删除左子树
            destroy(subTree.leftChild);
            //删除右子树
            destroy(subTree.rightChild);
            //删除根结点
            subTree=null;
        }
    }  

    public void traverse(TreeNode subTree){
        System.out.println("key:"+subTree.key+"--name:"+subTree.data);;
        traverse(subTree.leftChild);
        traverse(subTree.rightChild);
    }  

    //前序遍历
    public void preOrder(TreeNode subTree){
        if(subTree!=null){
            visted(subTree);
            preOrder(subTree.leftChild);
            preOrder(subTree.rightChild);
        }
    }  

    //中序遍历
    public void inOrder(TreeNode subTree){
        if(subTree!=null){
            inOrder(subTree.leftChild);
            visted(subTree);
            inOrder(subTree.rightChild);
        }
    }  

    //后续遍历
    public void postOrder(TreeNode subTree) {
        if (subTree != null) {
            postOrder(subTree.leftChild);
            postOrder(subTree.rightChild);
            visted(subTree);
        }
    }  

    //前序遍历的非递归实现
    public void nonRecPreOrder(TreeNode p){
        Stack<TreeNode> stack=new Stack<TreeNode>();
        TreeNode node=p;
        while(node!=null||stack.size()>0){
            while(node!=null){
                visted(node);
                stack.push(node);
                node=node.leftChild;
            }
            while(stack.size()>0){
                node=stack.pop();
                node=node.rightChild;
            }
        }
    }  

    //中序遍历的非递归实现
    public void nonRecInOrder(TreeNode p){
        Stack<TreeNode> stack =new Stack<BinaryTree.TreeNode>();
        TreeNode node =p;
        while(node!=null||stack.size()>0){
            //存在左子树
            while(node!=null){
                stack.push(node);
                node=node.leftChild;
            }
            //栈非空
            if(stack.size()>0){
                node=stack.pop();
                visted(node);
                node=node.rightChild;
            }
        }
    }  

    //后序遍历的非递归实现
    public void noRecPostOrder(TreeNode p){
        Stack<TreeNode> stack=new Stack<BinaryTree.TreeNode>();
        TreeNode node =p;
        while(p!=null){
            //左子树入栈
            for(;p.leftChild!=null;p=p.leftChild){
                stack.push(p);
            }
            //当前结点无右子树或右子树已经输出
            while(p!=null&&(p.rightChild==null||p.rightChild==node)){
                visted(p);
                //纪录上一个已输出结点
                node =p;
                if(stack.empty())
                    return;
                p=stack.pop();
            }
            //处理右子树
            stack.push(p);
            p=p.rightChild;
        }
    }
    public void visted(TreeNode subTree){
        subTree.isVisted=true;
        System.out.println("key:"+subTree.key+"--name:"+subTree.data);;
    }  

    /**
     * 二叉树的节点数据结构
     * @author WWX
     */
    private class  TreeNode{
        private int key = 0;
        private String data = null;
        private boolean isVisted = false;
        private TreeNode leftChild = null;
        private TreeNode rightChild = null;  

        public TreeNode(){}  

        /**
         * @param key  层序编码
         * @param data 数据域
         */
        public TreeNode(int key,String data){
            this.key = key;
            this.data = data;
            this.leftChild = null;
            this.rightChild = null;
        }
    }  

    //测试
    public static void main(String[] args) {
        BinaryTree bt = new BinaryTree();
        bt.createBinTree(bt.root);
        System.out.println("the size of the tree is " + bt.size());
        System.out.println("the height of the tree is " + bt.height());  

        System.out.println("***递归实现****(前序遍历)[ABDECF]遍历*****************");
        bt.preOrder(bt.root);  

        System.out.println("***递归实现****(中序遍历)[DBEACF]遍历*****************");
        bt.inOrder(bt.root);  

        System.out.println("***递归实现****(后序遍历)[DEBFCA]遍历*****************");
        bt.postOrder(bt.root);  

        System.out.println("***非递归实现****(前序遍历)[ABDECF]遍历*****************");
        bt.nonRecPreOrder(bt.root);  

        System.out.println("***非递归实现****(中序遍历)[DBEACF]遍历*****************");
        bt.nonRecInOrder(bt.root);  

        System.out.println("***非递归实现****(后序遍历)[DEBFCA]遍历*****************");
        bt.noRecPostOrder(bt.root);
    }
}

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