【二叉树】Leetcode 101. 对称二叉树【简单】

对称二叉树

给你一个二叉树的根节点 root ，检查它是否轴对称。

示例1：
在这里插入图片描述

输入：root = [1,2,2,3,4,4,3]
输出：true

解题思路

判断一棵二叉树是否是轴对称的，可以通过递归方式进行判断。

1、定义一个递归函数isMirror，用于判断两个节点是否是镜像对称的。
2、判断当前节点的左子树和右子树是否是镜像对称的。
3、如果左子树和右子树都为空，返回true。
4、如果左子树和右子树其中一个为空，返回false。
5、如果左子树的值等于右子树的值，
并且左子树的左子树与右子树的右子树镜像对称，
左子树的右子树与右子树的左子树镜像对称，
则返回true，否则返回false。

Java实现

public class SymmetricTree {static class TreeNode {int val;TreeNode left;TreeNode right;TreeNode(int val) {this.val = val;}}public boolean isSymmetric(TreeNode root) {if (root == null) {return true; // 空树是对称的}return isMirror(root.left, root.right);}private boolean isMirror(TreeNode left, TreeNode right) {// 如果两个节点都为空，是对称的if (left == null && right == null) {return true;}// 如果其中一个节点为空，另一个不为空，不对称if (left == null || right == null) {return false;}// 递归比较左子树的左节点和右子树的右节点，以及左子树的右节点和右子树的左节点return (left.val == right.val) && isMirror(left.left, right.right) && isMirror(left.right, right.left);}// 测试实例public static void main(String[] args) {// 构造对称的二叉树:    1//                   / \//                  2   2//                 / \ / \//                3  4 4  3TreeNode symmetricTree = new TreeNode(1);symmetricTree.left = new TreeNode(2);symmetricTree.right = new TreeNode(2);symmetricTree.left.left = new TreeNode(3);symmetricTree.left.right = new TreeNode(4);symmetricTree.right.left = new TreeNode(4);symmetricTree.right.right = new TreeNode(3);// 创建 SymmetricTreeChecker 实例SymmetricTree checker = new SymmetricTree();// 检查对称的二叉树boolean isSymmetric = checker.isSymmetric(symmetricTree);System.out.println("是否是对称二叉树: " + isSymmetric);// 构造非对称的二叉树:      1//                      / \//                     2   2//                      \   \//                       3    3TreeNode asymmetricTree = new TreeNode(1);asymmetricTree.left = new TreeNode(2);asymmetricTree.right = new TreeNode(2);asymmetricTree.left.right = new TreeNode(3);asymmetricTree.right.right = new TreeNode(3);// 检查非对称的二叉树boolean isAsymmetric = checker.isSymmetric(asymmetricTree);System.out.println("是否是对称二叉树: " + isAsymmetric);}
}