算法day09 二叉树-CFANZ编程社区

class Node<V>{
    V  value;
    Node left;
    Node right;
}

一、用递归和非递归分别实现二叉树的前序，中序，后序遍历

非递归方式：

前序遍历根左右

0）利用stack后进先出的特点

要输出根左右的顺序，将元素右边先放入栈中元素左边后放入栈中，实现先弹出左边元素再弹出右边元素。

1) 入栈顺序：

①入栈，弹出；弹出的①视为根节点

每次while循环只看这一颗小树：

③入栈，②入栈；

第二次while循环，弹出的②视为根节点：

⑤入栈， ④入栈

第三次while循环，弹出的④视为根节点：

没有元素入栈

第四次while循环，弹出的⑤视为根节点：

没有元素入栈

第五次while循环，弹出的③视为根节点：

⑦入栈， ⑥入栈

. . . . . .

2）代码实现

import java.util.Stack;

public class Main {
    public static void main(String[] args) {
        TreeNode root = new TreeNode(1);
        root.left = new TreeNode(2);
        root.left.left = new TreeNode(4);
        root.left.right = new TreeNode(5);
        
        root.right = new TreeNode(3);
        root.right.left = new TreeNode(6);
        root.right.right = new TreeNode(7);

        System.out.println("Inorder Traversal:");
        InorderTraversal.inorderTraversal(root); 
    }
}

class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}

class InorderTraversal {
    public static void inorderTraversal(TreeNode root) {
        Stack<TreeNode> stack = new Stack<>();
        TreeNode current = root;
        stack.push(current);

        while ( !stack.isEmpty()) {
            // while (current != null) {
            //     stack.push(current);
            //     current = current.left;
            // }
            // current = stack.pop();
            // System.out.print(current.val + " ");
            // current = current.right;
             current  =  stack.pop();
             System.out.print(current.val+ " ");
             
             if(current.right!=null){
                 stack.push(current.right);
             }
             
                if(current.left!=null){
                 stack.push(current.left);
             }
            
        }
    }
}

中序遍历左根右

实现左根右的输出，从根节点①加入栈开始，再将所有左节点元素②、④依次加入到栈中

再根据栈的弹出找到最左边最先输出的树，

弹出④，再以④为根节点找④右子节点的元素，没有进入下次循环

每一次while循环只看根据栈的弹出的这一颗树

弹出②，这时根节点为②，找右子节点⑤

接着while循环以⑤为根节点

将从根节点⑤加入栈开始，如果⑤有左右节点的话，再将所有左节点元素加入到栈

. . . . . .

实质上发现while循环还是递归的另一种形式。

import java.util.Stack;

public class Main {
    public static void main(String[] args) {
        TreeNode root = new TreeNode(1);
        root.left = new TreeNode(2);
        root.left.left = new TreeNode(4);
        root.left.right = new TreeNode(5);
        
        root.right = new TreeNode(3);
        root.right.left = new TreeNode(6);
        root.right.right = new TreeNode(7);

        System.out.println("Inorder Traversal:");
        InorderTraversal.inorderTraversal(root); // Output should be 4 2 5 1 6 3 7
    }
}

class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}

class InorderTraversal {
    public static void inorderTraversal(TreeNode root) {
        Stack<TreeNode> stack = new Stack<>();
        TreeNode current = root;
        

        while (current!=null || !stack.isEmpty()) {
            while (current != null) {
                stack.push(current);
                current = current.left;
            }
            current = stack.pop();
            System.out.print(current.val + " ");
            current = current.right;
            
        }
    }
}

后序遍历左右根

再前序遍历的基础上，每次弹栈出的元素放入到新栈中，就能实现将根左右转换为右左根的顺序。

实现左右根的顺序，只需要将原来的根左右变为根右左。

import java.util.Stack;

public class Main {
    public static void main(String[] args) {
        TreeNode root = new TreeNode(1);
        root.left = new TreeNode(2);
        root.left.left = new TreeNode(4);
        root.left.right = new TreeNode(5);
        
        root.right = new TreeNode(3);
        root.right.left = new TreeNode(6);
        root.right.right = new TreeNode(7);

        System.out.println("Inorder Traversal:");
        InorderTraversal.inorderTraversal(root); 
    }
}

class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}

class InorderTraversal {
    public static void inorderTraversal(TreeNode root) {
        Stack<TreeNode> stack = new Stack<>();
        Stack<TreeNode> stack2 = new Stack<>();
        TreeNode current = root;
        stack.push(current);

        while ( !stack.isEmpty()) {
            // while (current != null) {
            //     stack.push(current);
            //     current = current.left;
            // }
            // current = stack.pop();
            // System.out.print(current.val + " ");
            // current = current.right;
             current  =  stack.pop();
             stack2.push(current);
            //  System.out.print(current.val+ " ");
             
             if(current.left!=null){
                 stack.push(current.left);
             }
             
                if(current.right!=null){
                 stack.push(current.right);
             }
            
        }
        while(!stack2.isEmpty()){
             System.out.print(stack2.pop().val);
        }
    }
}