Java实现二叉树的前序、中序、后序、层序遍历（非递归方法）

时间：2021-05-12 11:23:16

在上一篇博客中，实现了Java中二叉树的四种遍历方式的递归实现，接下来，在此实现Java中非递归实现二叉树的前序、中序、后序、层序遍历，在非递归实现中，借助了栈来帮助实现遍历。前序和中序比较类似，也简单一些，但是后序遍历需要两个栈来进行辅助，稍微复杂一些，层序遍历中借助了一个队列来进行实现。

Java实现二叉树的前序、中序、后序、层序遍历（非递归方法）

  同样是那棵二叉树

  • 前序遍历：4 2 1 3 6 5 7 8 10

  • 中序遍历：1 2 3 4 5 6 7 8 10

  • 后序遍历：1 3 2 5 10 8 7 6 4

  • 层序遍历：4 2 6 1 3 5 7 8 10

import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;

public class Tree<AnyType extends Comparable<? super AnyType>>
{
private static class BinaryNode<AnyType>
{
BinaryNode(AnyType theElement)
        {
this(theElement, null, null);
        }

BinaryNode(AnyType theElement, BinaryNode<AnyType> lt, BinaryNode<AnyType> rt)
        {
            element = theElement;
            left = lt;
            right = rt;
        }

        AnyType element;
        BinaryNode<AnyType> left;
        BinaryNode<AnyType> right;
    }

private BinaryNode<AnyType> root;

public void insert(AnyType x)
{
        root = insert(x, root);
    }

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

private BinaryNode<AnyType> insert(AnyType x, BinaryNode<AnyType> t)
{
if(t == null)
        {
return new BinaryNode<>(x, null, null);
        }

int compareResult = x.compareTo(t.element);

if(compareResult < 0)
        {
            t.left = insert(x, t.left);
        }
else if(compareResult > 0)
        {
            t.right = insert(x, t.right);
        }
else
        {
            ;
        }

return t;
    }

/**
 * 前序遍历
 * 递归
 */
public void preOrder(BinaryNode<AnyType> Node)
{
if (Node != null)
        {
            System.out.print(Node.element + " ");
preOrder(Node.left);
preOrder(Node.right);
        }
    }

/**
 * 中序遍历
 * 递归
 */
public void midOrder(BinaryNode<AnyType> Node)
{
if (Node != null)
        {
midOrder(Node.left);
            System.out.print(Node.element + " ");
midOrder(Node.right);
        }
    }

/**
 * 后序遍历
 * 递归
 */
public void posOrder(BinaryNode<AnyType> Node)
{
if (Node != null)
        {
posOrder(Node.left);
posOrder(Node.right);
            System.out.print(Node.element + " ");
        }
    }

/*
 * 层序遍历
 * 递归
 */
public void levelOrder(BinaryNode<AnyType> Node) {
if (Node == null) {
return;
        }

int depth = depth(Node);

for (int i = 1; i <= depth; i++) {
levelOrder(Node, i);
        }
    }

private void levelOrder(BinaryNode<AnyType> Node, int level) {
if (Node == null || level < 1) {
return;
        }

if (level == 1) {
            System.out.print(Node.element + " ");
return;
        }

// 左子树
levelOrder(Node.left, level - 1);

// 右子树
levelOrder(Node.right, level - 1);
    }

public int depth(BinaryNode<AnyType> Node) {
if (Node == null) {
return 0;
        }

int l = depth(Node.left);
int r = depth(Node.right);
if (l > r) {
return l + 1;
        } else {
return r + 1;
        }
    }

/**
 * 前序遍历
 * 非递归
 */
public void preOrder1(BinaryNode<AnyType> Node)
{
        Stack<BinaryNode> stack = new Stack<>();
while(Node != null || !stack.empty())
        {
while(Node != null)
            {
                System.out.print(Node.element + " ");
                stack.push(Node);
                Node = Node.left;
            }
if(!stack.empty())
            {
                Node = stack.pop();
                Node = Node.right;
            }
        }
    }

/**
 * 中序遍历
 * 非递归
 */
public void midOrder1(BinaryNode<AnyType> Node)
{
        Stack<BinaryNode> stack = new Stack<>();
while(Node != null || !stack.empty())
        {
while (Node != null)
            {
                stack.push(Node);
                Node = Node.left;
            }
if(!stack.empty())
            {
                Node = stack.pop();
                System.out.print(Node.element + " ");
                Node = Node.right;
            }
        }
    }

/**
 * 后序遍历
 * 非递归
 */
public void posOrder1(BinaryNode<AnyType> Node)
{
        Stack<BinaryNode> stack1 = new Stack<>();
        Stack<Integer> stack2 = new Stack<>();
int i = 1;
while(Node != null || !stack1.empty())
        {
while (Node != null)
            {
                stack1.push(Node);
                stack2.push(0);
                Node = Node.left;
            }

while(!stack1.empty() && stack2.peek() == i)
            {
                stack2.pop();
                System.out.print(stack1.pop().element + " ");
            }

if(!stack1.empty())
            {
                stack2.pop();
                stack2.push(1);
                Node = stack1.peek();
                Node = Node.right;
            }
        }
    }

/*
 * 层序遍历
 * 非递归
 */
public void levelOrder1(BinaryNode<AnyType> Node) {
if (Node == null) {
return;
        }

        BinaryNode<AnyType> binaryNode;
        Queue<BinaryNode> queue = new LinkedList<>();
        queue.add(Node);

while (queue.size() != 0) {
            binaryNode = queue.poll();

            System.out.print(binaryNode.element + " ");

if (binaryNode.left != null) {
                queue.offer(binaryNode.left);
            }
if (binaryNode.right != null) {
                queue.offer(binaryNode.right);
            }
        }
    }

public static void main( String[] args )
{
int[] input = {4, 2, 6, 1, 3, 5, 7, 8, 10};
        Tree<Integer> tree = new Tree<>();
for(int i = 0; i < input.length; i++)
        {
            tree.insert(input[i]);
        }
        System.out.print("递归前序遍历 ：");
        tree.preOrder(tree.root);
        System.out.print("\n非递归前序遍历：");
        tree.preOrder1(tree.root);
        System.out.print("\n递归中序遍历 ：");
        tree.midOrder(tree.root);
        System.out.print("\n非递归中序遍历 ：");
        tree.midOrder1(tree.root);
        System.out.print("\n递归后序遍历 ：");
        tree.posOrder(tree.root);
        System.out.print("\n非递归后序遍历 ：");
        tree.posOrder1(tree.root);
        System.out.print("\n递归层序遍历：");
        tree.levelOrder(tree.root);
        System.out.print("\n非递归层序遍历 ：");
        tree.levelOrder1(tree.root);
    }
}

  在以上代码中，preOrder1、midOrder1、posOrder1、levelOrder1四个函数，分别代表了非递归实现的二叉树前序、中序、后序、层序遍历遍历。

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