一 前言

树是一种逻辑结构，物理实现有连续存储方式（数组）和非连续的链表方式。最常见的是二叉树，连续存储就是按照层次遍历的方法，依次存入数组，但空的节点也必须存储，也就是说会造成空间的浪费 ，所以只适用于满二叉树和完全二叉树。

树的遍历方法 有两类，一类是深度遍历：

前序遍历：就是先遍历当前节点，再遍历左子树，最后遍历右子树   中左右  对于下图  80 55 32 60 90 96 98

中序遍历：对应的就是  左中右   32 55 60 80 90 96 98

后序遍历： 左右中       32 60 55 98 96 90 80

另一类是层次遍历 

就是按层访问  80  55 90 32 60 96 98

 

 对于第一类深度优先，是一个递归的过程，所以用递归的算法很容易。而非递归在于自己手动创建栈，实现递归过程。

二 代码实现

二叉树的遍历首先是要有一棵树，在漫画算法里有一个基于链表创建二叉树的例子。见代码：（另外要用数组描述二叉树，有两种方式，一是给出中序遍历和其它先（后）序遍历，或者就是带空节点的遍历方法 比如上图的遍历就是

{80, 55, 32, null, null, 60, null, null, 90, null, 96,null,98,null,null}

 下面的算法就是基于这样的链表实现二叉树的创建的

 

package tree;import java.util.*;public class MyTree {    int val;    MyTree left;    MyTree right;    MyTree() {    }    MyTree(int val) {        this.val = val;    }  //二叉树结构定义//根据链表创建二叉树    public static MyTree createTree(LinkedList
     
       list) {        if (list == null || list.size() == 0)            return null;        Integer data = list.removeFirst();        MyTree node = null;        if (data != null) {            node = new MyTree(data);            node.left = createTree(list);            node.right = createTree(list);        }        return node;    }//前序遍历的递归版本    public static void xianXu(MyTree tree) {        if (tree == null)            return;        System.out.print(tree.val + " ");        xianXu(tree.left);        xianXu(tree.right);    }//中序遍历的递归版本    public static void zhongXu(MyTree tree) {        if (tree == null)            return;        zhongXu(tree.left);        System.out.print(tree.val + " ");        zhongXu(tree.right);    }//后序遍历的递归版本    public static void houXu(MyTree tree) {        if (tree == null)            return;        houXu(tree.left);        houXu(tree.right);        System.out.print(tree.val + " ");    }//先序遍历的非递归版本    public static void xianXu1(MyTree tree) {        if (tree == null)            return;        Deque
      
        deque = new ArrayDeque<>();        MyTree node = null;        deque.push(tree);        while (!deque.isEmpty()) {            node = deque.pop();            System.out.print(node.val + " ");            if (node.right != null)                deque.push(node.right);            if (node.left != null)                deque.push(node.left);        }    }//中序遍历的非递归版本    public static void zhongXu1(MyTree tree) {        if (tree == null) {            return;        }        MyTree now = tree;        Deque
       
         deque = new ArrayDeque<>();        while (!deque.isEmpty() || now != null) {            while (now != null) {                deque.push(now);                now = now.left;            }            now = deque.pop();            System.out.print(now.val + " ");            now = now.right;        }    }//后序遍历的非递归版本    public static void houXu1(MyTree tree) {        if (tree == null)            return;        Deque
        
          deque = new ArrayDeque<>();        Deque
         
           deque1 = new ArrayDeque<>();        MyTree node = null;        deque.push(tree);        while (!deque.isEmpty()) {            node = deque.pop();            deque1.push(node.val);            if (node.left != null)                deque.push(node.left);            if (node.right != null)                deque.push(node.right);        }        while (!deque1.isEmpty())            System.out.print(deque1.pop() + " ");    }//层次遍历    public static void cengCi(MyTree tree) {        if (tree == null)            return;        Queue
          
            queue = new ArrayDeque<>(); MyTree now = null; queue.offer(tree); while (!queue.isEmpty()) { now = queue.poll(); System.out.print(now.val + " "); if (now.left != null) queue.offer(now.left); if (now.right != null) queue.offer(now.right); } }}
          
         
        
       
      
     

 

　　下面是测试代码：

public class TreeTest {    public static void main(String[] args) {        Integer[] arr = {80, 55, 32, null, null, 60, null, null, 90, null, 96,null,98,null,null};        MyTree tree=MyTree.createTree(new LinkedList<>(Arrays.asList(arr)));        MyTree.xianXu(tree);        System.out.println("前序递归");        MyTree.xianXu1(tree);        System.out.println("前序非递归");        MyTree.zhongXu(tree);        System.out.println("中序递归");        MyTree.zhongXu1(tree);        System.out.println("中序非递归");        MyTree.houXu(tree);        System.out.println("后序递归");        MyTree.houXu1(tree);        System.out.println("后序非递归");        MyTree.cengCi(tree);        System.out.println("层次遍历");    }}