|
| 1 | +# [Symmetric Tree][title] |
| 2 | + |
| 3 | +## Description |
| 4 | + |
| 5 | +Given a binary tree, check whether it is a mirror of itself (ie, symmetric around its center). |
| 6 | + |
| 7 | +For example, this binary tree `[1,2,2,3,4,4,3]` is symmetric: |
| 8 | + |
| 9 | +``` |
| 10 | + 1 |
| 11 | + / \ |
| 12 | + 2 2 |
| 13 | + / \ / \ |
| 14 | +3 4 4 3 |
| 15 | +
|
| 16 | +``` |
| 17 | + |
| 18 | +But the following `[1,2,2,null,3,null,3]` is not: |
| 19 | + |
| 20 | +``` |
| 21 | + 1 |
| 22 | + / \ |
| 23 | + 2 2 |
| 24 | + \ \ |
| 25 | + 3 3 |
| 26 | +
|
| 27 | +``` |
| 28 | + |
| 29 | +**Note:** |
| 30 | +Bonus points if you could solve it both recursively and iteratively. |
| 31 | + |
| 32 | +**Tags:** Tree, Depth-first Search, Breadth-first Search |
| 33 | + |
| 34 | + |
| 35 | +## 思路0 |
| 36 | + |
| 37 | +题意是判断一棵二叉树是否左右对称,首先想到的是深搜,比较根结点的左右两棵子树是否对称,如果左右子树的值相同,那么再分别对左子树的左节点和右子树的右节点,左子树的右节点和右子树的左节点做比较即可。 |
| 38 | + |
| 39 | +``` java |
| 40 | +/** |
| 41 | + * Definition for a binary tree node. |
| 42 | + * public class TreeNode { |
| 43 | + * int val; |
| 44 | + * TreeNode left; |
| 45 | + * TreeNode right; |
| 46 | + * TreeNode(int x) { val = x; } |
| 47 | + * } |
| 48 | + */ |
| 49 | +class Solution { |
| 50 | + public boolean isSymmetric(TreeNode root) { |
| 51 | + return root == null || isSymmetricHelper(root.left, root.right); |
| 52 | + } |
| 53 | + |
| 54 | + public boolean isSymmetricHelper(TreeNode left, TreeNode right) { |
| 55 | + if (left == null || right == null) return left == right; |
| 56 | + if (left.val != right.val) return false; |
| 57 | + return isSymmetricHelper(left.left, right.right) && isSymmetricHelper(left.right, right.left); |
| 58 | + } |
| 59 | +} |
| 60 | +``` |
| 61 | + |
| 62 | +## 思路1 |
| 63 | + |
| 64 | +第二种思路就是宽搜了,宽搜肯定要用到队列,Java中可用`LinkedList`替代,也是要做到左子树的左节点和右子树的右节点,左子树的右节点和右子树的左节点做比较即可。 |
| 65 | + |
| 66 | +``` java |
| 67 | +/** |
| 68 | + * Definition for a binary tree node. |
| 69 | + * public class TreeNode { |
| 70 | + * int val; |
| 71 | + * TreeNode left; |
| 72 | + * TreeNode right; |
| 73 | + * TreeNode(int x) { val = x; } |
| 74 | + * } |
| 75 | + */ |
| 76 | +class Solution { |
| 77 | + public boolean isSymmetric(TreeNode root) { |
| 78 | + if (root == null) return true; |
| 79 | + LinkedList<TreeNode> q = new LinkedList<>(); |
| 80 | + q.add(root.left); |
| 81 | + q.add(root.right); |
| 82 | + TreeNode left, right; |
| 83 | + while (q.size() > 1) { |
| 84 | + left = q.pop(); |
| 85 | + right = q.pop(); |
| 86 | + if (left == null && right == null) continue; |
| 87 | + if (left == null || right == null) return false; |
| 88 | + if (left.val != right.val) return false; |
| 89 | + q.add(left.left); |
| 90 | + q.add(right.right); |
| 91 | + q.add(left.right); |
| 92 | + q.add(right.left); |
| 93 | + } |
| 94 | + return true; |
| 95 | + } |
| 96 | +} |
| 97 | +``` |
| 98 | + |
| 99 | +## 结语 |
| 100 | + |
| 101 | +如果你同我一样热爱数据结构、算法、LeetCode,可以关注我GitHub上的LeetCode题解:[awesome-java-leetcode][ajl] |
| 102 | + |
| 103 | + |
| 104 | + |
| 105 | +[title]: https://leetcode.com/problems/symmetric-tree |
| 106 | +[ajl]: https://github.com/Blankj/awesome-java-leetcode |
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