二叉树的遍历（递归与非递归）

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一、创建成员内部类Node

1.因为要频繁使用Node内的数据，所以创建Node成员内部类，Node记录的是树的基本结构，value值，rchild右子树，lchild左子树。构造方法让value初始化。、
代码如下（示例）：

class Node {
		private int val;
		private Node rchild;
		private Node lchild;
		public Node(int val) {
			this.val = val;
		}

二、添加树节点

利用Node的基本结构去创建数节点，构建树的整体框架

代码如下（示例）：

boolean insert(int val) {//添加树节点
		Node node = new Node(val);
		if (root == null) {
			root = node;
			return true;
		} else {
			Node cur = root;
			while (true) {
				Node newNode = new Node(val);
				if (cur.val > val) {
					if (cur.lchild == null) {
						cur.lchild = newNode;
						return true;
					}
					cur = cur.lchild;
				} else if (cur.val < val) {
					if (cur.rchild == null) {
						cur.rchild = newNode;
						return true;
					}
					cur = cur.rchild;
				} else {
					return false;
				}
			}
		}
	}

三、使用递归实现先.中.后序遍历

1.先序：

	static void preOrder(Node node) {
		if (node == null)
			return;
		System.out.print(node.val);
		preOrder(node.lchild);
		preOrder(node.rchild);
	}

2.中序：

static void inOrder(Node node) {
		if (node == null)
			return;
		inOrder(node.lchild);
		System.out.print(node.val);
		inOrder(node.rchild);
	}

3.后序

static void postOrder(Node node) {
		if (node == null)
			return;
		postOrder(node.lchild);
		postOrder(node.rchild);
		System.out.print(node.val);
	}

四、使用栈实现先.中.后序遍历

1.先序：

static void preorder(Node node) {
		if (node == null)
			return;
		Stack<Node> stack = new Stack<>();
		Node cur = root;
		while (cur != null || !stack.isEmpty()) {
			while (cur != null) {
				System.out.print(cur.val);//输出根
				stack.push(cur);//进栈
				cur = cur.lchild;//遍历左子树
			}
			cur = stack.pop();
			cur = cur.rchild;
		}
	}

2.中序

static void inorder(Node node) {
		if (node == null)
			return;
		Stack<Node> stack = new Stack<StackTree.Node>();
		Node cur = root;
		while (cur != null || !stack.isEmpty()) {
			while (cur != null) {
				stack.push(cur);
				cur = cur.lchild;
			}
			cur = stack.pop();
			System.out.print(cur.val);
			cur = cur.rchild;
		}
	
	}

3.后序

static void postorder(Node node) {
		if (root == null)
			return;
		Stack<Node> stack = new Stack<StackTree.Node>();
		Node cur = root;
		Node t=null;//标识是否已经出栈
		while (cur != null || !stack.isEmpty()) {
			while (cur != null) {
				stack.push(cur);
				cur = cur.lchild;
			}//cur.left==null
			cur=stack.peek();//取栈顶元素
			if(cur.rchild==null||t==cur.rchild) {//右子树为空或者右子树已经处理过
				t=stack.pop();//出栈，标识是否已经处理过
				System.out.print(t.val);
				cur=null;
			}else {
				cur=cur.rchild;
			}
 
		}
 
	}

static void postorder1(Node node) {
		if(root==null) return ;
		Stack<Node> stack = new Stack<StackTree.Node>();
		Stack<Node> stack1 = new Stack<StackTree.Node>();
		Node cur = root;
		while(cur!=null||!stack.isEmpty()) {
			while(cur!=null) {
				stack1.push(cur);
				stack.push(cur);
				cur = cur.rchild;
			}
			cur = stack.pop();
			cur = cur.lchild;
		}
		int n = stack1.size();
		for (int i = 0; i < n; i++) {
			System.out.print(stack1.pop().val);
			
		}
	}

五、main方法实现

public static void main(String[] args) {
		StackTree tree = new StackTree();
		int[] a = { 2, 5, 1, 3, 9, 8, 7, 4, 6 };
		for (int i = 0; i < a.length; i++) {
			tree.insert(a[i]);
		}
		preOrder(root);//先序——递归
		System.out.println();
		preorder(root);//先序——栈
		System.out.println();
		inOrder(root);//中序——递归
		System.out.println();
		inorder(root);//中序——栈
		System.out.println();
		postOrder(root);//后序——递归
		System.out.println();
		postorder(root);//后序——单栈标记法
		System.out.println();
		postorder1(root);//后序——双栈标记法
	}

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