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701 lines
21 KiB
Markdown
701 lines
21 KiB
Markdown
<p align="center">
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<a href="https://programmercarl.com/other/xunlianying.html" target="_blank">
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<img src="../pics/训练营.png" width="1000"/>
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</a>
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<p align="center"><strong><a href="https://mp.weixin.qq.com/s/tqCxrMEU-ajQumL1i8im9A">参与本项目</a>,贡献其他语言版本的代码,拥抱开源,让更多学习算法的小伙伴们收益!</strong></p>
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# 二叉树的迭代遍历
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《代码随想录》算法视频公开课:
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* [写出二叉树的非递归遍历很难么?(前序和后序)](https://www.bilibili.com/video/BV15f4y1W7i2)
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* [写出二叉树的非递归遍历很难么?(中序))](https://www.bilibili.com/video/BV1Zf4y1a77g)
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相信结合视频在看本篇题解,更有助于大家对本题的理解。
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> 听说还可以用非递归的方式
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看完本篇大家可以使用迭代法,再重新解决如下三道leetcode上的题目:
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* [144.二叉树的前序遍历](https://leetcode.cn/problems/binary-tree-preorder-traversal/)
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* [94.二叉树的中序遍历](https://leetcode.cn/problems/binary-tree-inorder-traversal/)
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* [145.二叉树的后序遍历](https://leetcode.cn/problems/binary-tree-postorder-traversal/)
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为什么可以用迭代法(非递归的方式)来实现二叉树的前后中序遍历呢?
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我们在[栈与队列:匹配问题都是栈的强项](https://programmercarl.com/1047.删除字符串中的所有相邻重复项.html)中提到了,**递归的实现就是:每一次递归调用都会把函数的局部变量、参数值和返回地址等压入调用栈中**,然后递归返回的时候,从栈顶弹出上一次递归的各项参数,所以这就是递归为什么可以返回上一层位置的原因。
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此时大家应该知道我们用栈也可以是实现二叉树的前后中序遍历了。
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## 前序遍历(迭代法)
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我们先看一下前序遍历。
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前序遍历是中左右,每次先处理的是中间节点,那么先将根节点放入栈中,然后将右孩子加入栈,再加入左孩子。
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为什么要先加入 右孩子,再加入左孩子呢? 因为这样出栈的时候才是中左右的顺序。
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动画如下:
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不难写出如下代码: (**注意代码中空节点不入栈**)
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```CPP
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class Solution {
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public:
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vector<int> preorderTraversal(TreeNode* root) {
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stack<TreeNode*> st;
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vector<int> result;
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if (root == NULL) return result;
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st.push(root);
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while (!st.empty()) {
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TreeNode* node = st.top(); // 中
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st.pop();
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result.push_back(node->val);
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if (node->right) st.push(node->right); // 右(空节点不入栈)
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if (node->left) st.push(node->left); // 左(空节点不入栈)
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}
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return result;
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}
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};
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```
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此时会发现貌似使用迭代法写出前序遍历并不难,确实不难。
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**此时是不是想改一点前序遍历代码顺序就把中序遍历搞出来了?**
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其实还真不行!
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但接下来,**再用迭代法写中序遍历的时候,会发现套路又不一样了,目前的前序遍历的逻辑无法直接应用到中序遍历上。**
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## 中序遍历(迭代法)
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为了解释清楚,我说明一下 刚刚在迭代的过程中,其实我们有两个操作:
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1. **处理:将元素放进result数组中**
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2. **访问:遍历节点**
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分析一下为什么刚刚写的前序遍历的代码,不能和中序遍历通用呢,因为前序遍历的顺序是中左右,先访问的元素是中间节点,要处理的元素也是中间节点,所以刚刚才能写出相对简洁的代码,**因为要访问的元素和要处理的元素顺序是一致的,都是中间节点。**
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那么再看看中序遍历,中序遍历是左中右,先访问的是二叉树顶部的节点,然后一层一层向下访问,直到到达树左面的最底部,再开始处理节点(也就是在把节点的数值放进result数组中),这就造成了**处理顺序和访问顺序是不一致的。**
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那么**在使用迭代法写中序遍历,就需要借用指针的遍历来帮助访问节点,栈则用来处理节点上的元素。**
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动画如下:
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**中序遍历,可以写出如下代码:**
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```CPP
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class Solution {
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public:
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vector<int> inorderTraversal(TreeNode* root) {
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vector<int> result;
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stack<TreeNode*> st;
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TreeNode* cur = root;
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while (cur != NULL || !st.empty()) {
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if (cur != NULL) { // 指针来访问节点,访问到最底层
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st.push(cur); // 将访问的节点放进栈
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cur = cur->left; // 左
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} else {
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cur = st.top(); // 从栈里弹出的数据,就是要处理的数据(放进result数组里的数据)
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st.pop();
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result.push_back(cur->val); // 中
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cur = cur->right; // 右
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}
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}
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return result;
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}
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};
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```
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## 后序遍历(迭代法)
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再来看后序遍历,先序遍历是中左右,后续遍历是左右中,那么我们只需要调整一下先序遍历的代码顺序,就变成中右左的遍历顺序,然后在反转result数组,输出的结果顺序就是左右中了,如下图:
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**所以后序遍历只需要前序遍历的代码稍作修改就可以了,代码如下:**
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```CPP
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class Solution {
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public:
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vector<int> postorderTraversal(TreeNode* root) {
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stack<TreeNode*> st;
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vector<int> result;
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if (root == NULL) return result;
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st.push(root);
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while (!st.empty()) {
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TreeNode* node = st.top();
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st.pop();
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result.push_back(node->val);
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if (node->left) st.push(node->left); // 相对于前序遍历,这更改一下入栈顺序 (空节点不入栈)
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if (node->right) st.push(node->right); // 空节点不入栈
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}
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reverse(result.begin(), result.end()); // 将结果反转之后就是左右中的顺序了
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return result;
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}
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};
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```
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# 总结
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此时我们用迭代法写出了二叉树的前后中序遍历,大家可以看出前序和中序是完全两种代码风格,并不像递归写法那样代码稍做调整,就可以实现前后中序。
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**这是因为前序遍历中访问节点(遍历节点)和处理节点(将元素放进result数组中)可以同步处理,但是中序就无法做到同步!**
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上面这句话,可能一些同学不太理解,建议自己亲手用迭代法,先写出来前序,再试试能不能写出中序,就能理解了。
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**那么问题又来了,难道 二叉树前后中序遍历的迭代法实现,就不能风格统一么(即前序遍历 改变代码顺序就可以实现中序 和 后序)?**
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当然可以,这种写法,还不是很好理解,我们将在下一篇文章里重点讲解,敬请期待!
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# 其他语言版本
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Java:
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```java
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// 前序遍历顺序:中-左-右,入栈顺序:中-右-左
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class Solution {
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public List<Integer> preorderTraversal(TreeNode root) {
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List<Integer> result = new ArrayList<>();
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if (root == null){
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return result;
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}
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Stack<TreeNode> stack = new Stack<>();
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stack.push(root);
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while (!stack.isEmpty()){
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TreeNode node = stack.pop();
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result.add(node.val);
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if (node.right != null){
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stack.push(node.right);
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}
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if (node.left != null){
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stack.push(node.left);
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}
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}
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return result;
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}
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}
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// 中序遍历顺序: 左-中-右 入栈顺序: 左-右
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class Solution {
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public List<Integer> inorderTraversal(TreeNode root) {
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List<Integer> result = new ArrayList<>();
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if (root == null){
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return result;
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}
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Stack<TreeNode> stack = new Stack<>();
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TreeNode cur = root;
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while (cur != null || !stack.isEmpty()){
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if (cur != null){
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stack.push(cur);
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cur = cur.left;
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}else{
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cur = stack.pop();
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result.add(cur.val);
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cur = cur.right;
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}
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}
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return result;
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}
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}
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// 后序遍历顺序 左-右-中 入栈顺序:中-左-右 出栈顺序:中-右-左, 最后翻转结果
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class Solution {
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public List<Integer> postorderTraversal(TreeNode root) {
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List<Integer> result = new ArrayList<>();
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if (root == null){
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return result;
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}
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Stack<TreeNode> stack = new Stack<>();
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stack.push(root);
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while (!stack.isEmpty()){
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TreeNode node = stack.pop();
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result.add(node.val);
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if (node.left != null){
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stack.push(node.left);
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}
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if (node.right != null){
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stack.push(node.right);
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}
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}
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Collections.reverse(result);
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return result;
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}
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}
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```
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Python:
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```python
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# 前序遍历-迭代-LC144_二叉树的前序遍历
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class Solution:
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def preorderTraversal(self, root: TreeNode) -> List[int]:
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# 根结点为空则返回空列表
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if not root:
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return []
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stack = [root]
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result = []
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while stack:
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node = stack.pop()
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# 中结点先处理
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result.append(node.val)
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# 右孩子先入栈
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if node.right:
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stack.append(node.right)
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# 左孩子后入栈
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if node.left:
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stack.append(node.left)
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return result
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# 中序遍历-迭代-LC94_二叉树的中序遍历
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class Solution:
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def inorderTraversal(self, root: TreeNode) -> List[int]:
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if not root:
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return []
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stack = [] # 不能提前将root结点加入stack中
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result = []
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cur = root
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while cur or stack:
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# 先迭代访问最底层的左子树结点
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if cur:
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stack.append(cur)
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cur = cur.left
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# 到达最左结点后处理栈顶结点
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else:
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cur = stack.pop()
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result.append(cur.val)
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# 取栈顶元素右结点
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cur = cur.right
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return result
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# 后序遍历-迭代-LC145_二叉树的后序遍历
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class Solution:
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def postorderTraversal(self, root: TreeNode) -> List[int]:
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if not root:
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return []
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stack = [root]
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result = []
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while stack:
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node = stack.pop()
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# 中结点先处理
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result.append(node.val)
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# 左孩子先入栈
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if node.left:
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stack.append(node.left)
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# 右孩子后入栈
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if node.right:
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stack.append(node.right)
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# 将最终的数组翻转
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return result[::-1]
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```
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Go:
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> 迭代法前序遍历
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```go
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func preorderTraversal(root *TreeNode) []int {
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ans := []int{}
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if root == nil {
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return ans
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}
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st := list.New()
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st.PushBack(root)
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for st.Len() > 0 {
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node := st.Remove(st.Back()).(*TreeNode)
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ans = append(ans, node.Val)
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if node.Right != nil {
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st.PushBack(node.Right)
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}
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if node.Left != nil {
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st.PushBack(node.Left)
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}
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}
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return ans
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}
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```
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> 迭代法后序遍历
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```go
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func postorderTraversal(root *TreeNode) []int {
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ans := []int{}
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if root == nil {
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return ans
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}
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st := list.New()
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st.PushBack(root)
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for st.Len() > 0 {
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node := st.Remove(st.Back()).(*TreeNode)
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ans = append(ans, node.Val)
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if node.Left != nil {
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st.PushBack(node.Left)
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}
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if node.Right != nil {
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st.PushBack(node.Right)
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}
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}
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reverse(ans)
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return ans
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}
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func reverse(a []int) {
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l, r := 0, len(a) - 1
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for l < r {
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a[l], a[r] = a[r], a[l]
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l, r = l+1, r-1
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}
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}
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```
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> 迭代法中序遍历
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```go
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func inorderTraversal(root *TreeNode) []int {
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ans := []int{}
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if root == nil {
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return ans
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}
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st := list.New()
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cur := root
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for cur != nil || st.Len() > 0 {
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if cur != nil {
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st.PushBack(cur)
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cur = cur.Left
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} else {
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cur = st.Remove(st.Back()).(*TreeNode)
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ans = append(ans, cur.Val)
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cur = cur.Right
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}
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}
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return ans
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}
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```
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javaScript:
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```js
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前序遍历:
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// 入栈 右 -> 左
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// 出栈 中 -> 左 -> 右
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var preorderTraversal = function(root, res = []) {
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if(!root) return res;
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const stack = [root];
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let cur = null;
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while(stack.length) {
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cur = stack.pop();
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res.push(cur.val);
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cur.right && stack.push(cur.right);
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cur.left && stack.push(cur.left);
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}
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return res;
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};
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中序遍历:
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// 入栈 左 -> 右
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// 出栈 左 -> 中 -> 右
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var inorderTraversal = function(root, res = []) {
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const stack = [];
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let cur = root;
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while(stack.length || cur) {
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if(cur) {
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stack.push(cur);
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// 左
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cur = cur.left;
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} else {
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// --> 弹出 中
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cur = stack.pop();
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res.push(cur.val);
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// 右
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cur = cur.right;
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}
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};
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return res;
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};
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后序遍历:
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// 入栈 左 -> 右
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// 出栈 中 -> 右 -> 左 结果翻转
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var postorderTraversal = function(root, res = []) {
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if (!root) return res;
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const stack = [root];
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let cur = null;
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do {
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cur = stack.pop();
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res.push(cur.val);
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cur.left && stack.push(cur.left);
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cur.right && stack.push(cur.right);
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} while(stack.length);
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return res.reverse();
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};
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```
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TypeScript:
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```typescript
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// 前序遍历(迭代法)
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function preorderTraversal(root: TreeNode | null): number[] {
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if (root === null) return [];
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let res: number[] = [];
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let helperStack: TreeNode[] = [];
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let curNode: TreeNode = root;
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helperStack.push(curNode);
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while (helperStack.length > 0) {
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curNode = helperStack.pop()!;
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res.push(curNode.val);
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if (curNode.right !== null) helperStack.push(curNode.right);
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if (curNode.left !== null) helperStack.push(curNode.left);
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||
}
|
||
return res;
|
||
};
|
||
|
||
// 中序遍历(迭代法)
|
||
function inorderTraversal(root: TreeNode | null): number[] {
|
||
let helperStack: TreeNode[] = [];
|
||
let res: number[] = [];
|
||
if (root === null) return res;
|
||
let curNode: TreeNode | null = root;
|
||
while (curNode !== null || helperStack.length > 0) {
|
||
if (curNode !== null) {
|
||
helperStack.push(curNode);
|
||
curNode = curNode.left;
|
||
} else {
|
||
curNode = helperStack.pop()!;
|
||
res.push(curNode.val);
|
||
curNode = curNode.right;
|
||
}
|
||
}
|
||
return res;
|
||
};
|
||
|
||
// 后序遍历(迭代法)
|
||
function postorderTraversal(root: TreeNode | null): number[] {
|
||
let helperStack: TreeNode[] = [];
|
||
let res: number[] = [];
|
||
let curNode: TreeNode;
|
||
if (root === null) return res;
|
||
helperStack.push(root);
|
||
while (helperStack.length > 0) {
|
||
curNode = helperStack.pop()!;
|
||
res.push(curNode.val);
|
||
if (curNode.left !== null) helperStack.push(curNode.left);
|
||
if (curNode.right !== null) helperStack.push(curNode.right);
|
||
}
|
||
return res.reverse();
|
||
};
|
||
```
|
||
|
||
Swift:
|
||
|
||
```swift
|
||
// 前序遍历迭代法
|
||
func preorderTraversal(_ root: TreeNode?) -> [Int] {
|
||
var result = [Int]()
|
||
guard let root = root else { return result }
|
||
var stack = [root]
|
||
while !stack.isEmpty {
|
||
let current = stack.removeLast()
|
||
// 先右后左,这样出栈的时候才是左右顺序
|
||
if let node = current.right { // 右
|
||
stack.append(node)
|
||
}
|
||
if let node = current.left { // 左
|
||
stack.append(node)
|
||
}
|
||
result.append(current.val) // 中
|
||
}
|
||
return result
|
||
}
|
||
|
||
// 后序遍历迭代法
|
||
func postorderTraversal(_ root: TreeNode?) -> [Int] {
|
||
var result = [Int]()
|
||
guard let root = root else { return result }
|
||
var stack = [root]
|
||
while !stack.isEmpty {
|
||
let current = stack.removeLast()
|
||
// 与前序相反,即中右左,最后结果还需反转才是后序
|
||
if let node = current.left { // 左
|
||
stack.append(node)
|
||
}
|
||
if let node = current.right { // 右
|
||
stack.append(node)
|
||
}
|
||
result.append(current.val) // 中
|
||
}
|
||
return result.reversed()
|
||
}
|
||
|
||
// 中序遍历迭代法
|
||
func inorderTraversal(_ root: TreeNode?) -> [Int] {
|
||
var result = [Int]()
|
||
var stack = [TreeNode]()
|
||
var current: TreeNode! = root
|
||
while current != nil || !stack.isEmpty {
|
||
if current != nil { // 先访问到最左叶子
|
||
stack.append(current)
|
||
current = current.left // 左
|
||
} else {
|
||
current = stack.removeLast()
|
||
result.append(current.val) // 中
|
||
current = current.right // 右
|
||
}
|
||
}
|
||
return result
|
||
}
|
||
```
|
||
Scala:
|
||
```scala
|
||
// 前序遍历(迭代法)
|
||
object Solution {
|
||
import scala.collection.mutable
|
||
def preorderTraversal(root: TreeNode): List[Int] = {
|
||
val res = mutable.ListBuffer[Int]()
|
||
if (root == null) return res.toList
|
||
// 声明一个栈,泛型为TreeNode
|
||
val stack = mutable.Stack[TreeNode]()
|
||
stack.push(root) // 先把根节点压入栈
|
||
while (!stack.isEmpty) {
|
||
var curNode = stack.pop()
|
||
res.append(curNode.value) // 先把这个值压入栈
|
||
// 如果当前节点的左右节点不为空,则入栈,先放右节点,再放左节点
|
||
if (curNode.right != null) stack.push(curNode.right)
|
||
if (curNode.left != null) stack.push(curNode.left)
|
||
}
|
||
res.toList
|
||
}
|
||
}
|
||
|
||
// 中序遍历(迭代法)
|
||
object Solution {
|
||
import scala.collection.mutable
|
||
def inorderTraversal(root: TreeNode): List[Int] = {
|
||
val res = mutable.ArrayBuffer[Int]()
|
||
if (root == null) return res.toList
|
||
val stack = mutable.Stack[TreeNode]()
|
||
var curNode = root
|
||
// 将左节点都入栈,当遍历到最左(到空)的时候,再弹出栈顶元素,加入res
|
||
// 再把栈顶元素的右节点加进来,继续下一轮遍历
|
||
while (curNode != null || !stack.isEmpty) {
|
||
if (curNode != null) {
|
||
stack.push(curNode)
|
||
curNode = curNode.left
|
||
} else {
|
||
curNode = stack.pop()
|
||
res.append(curNode.value)
|
||
curNode = curNode.right
|
||
}
|
||
}
|
||
res.toList
|
||
}
|
||
}
|
||
|
||
// 后序遍历(迭代法)
|
||
object Solution {
|
||
import scala.collection.mutable
|
||
def postorderTraversal(root: TreeNode): List[Int] = {
|
||
val res = mutable.ListBuffer[Int]()
|
||
if (root == null) return res.toList
|
||
val stack = mutable.Stack[TreeNode]()
|
||
stack.push(root)
|
||
while (!stack.isEmpty) {
|
||
val curNode = stack.pop()
|
||
res.append(curNode.value)
|
||
// 这次左节点先入栈,右节点再入栈
|
||
if(curNode.left != null) stack.push(curNode.left)
|
||
if(curNode.right != null) stack.push(curNode.right)
|
||
}
|
||
// 最后需要翻转List
|
||
res.reverse.toList
|
||
}
|
||
}
|
||
```
|
||
|
||
rust:
|
||
|
||
```rust
|
||
use std::cell::RefCell;
|
||
use std::rc::Rc;
|
||
impl Solution {
|
||
//前序
|
||
pub fn preorder_traversal(root: Option<Rc<RefCell<TreeNode>>>) -> Vec<i32> {
|
||
let mut res = vec![];
|
||
let mut stack = vec![root];
|
||
while !stack.is_empty() {
|
||
if let Some(node) = stack.pop().unwrap() {
|
||
res.push(node.borrow().val);
|
||
stack.push(node.borrow().right.clone());
|
||
stack.push(node.borrow().left.clone());
|
||
}
|
||
}
|
||
res
|
||
}
|
||
//中序
|
||
pub fn inorder_traversal(root: Option<Rc<RefCell<TreeNode>>>) -> Vec<i32> {
|
||
let mut res = vec![];
|
||
let mut stack = vec![];
|
||
let mut node = root;
|
||
|
||
while !stack.is_empty() || node.is_some() {
|
||
while let Some(n) = node {
|
||
node = n.borrow().left.clone();
|
||
stack.push(n);
|
||
}
|
||
if let Some(n) = stack.pop() {
|
||
res.push(n.borrow().val);
|
||
node = n.borrow().right.clone();
|
||
}
|
||
}
|
||
res
|
||
}
|
||
//后序
|
||
pub fn postorder_traversal(root: Option<Rc<RefCell<TreeNode>>>) -> Vec<i32> {
|
||
let mut res = vec![];
|
||
let mut stack = vec![root];
|
||
while !stack.is_empty() {
|
||
if let Some(node) = stack.pop().unwrap() {
|
||
res.push(node.borrow().val);
|
||
stack.push(node.borrow().left.clone());
|
||
stack.push(node.borrow().right.clone());
|
||
}
|
||
}
|
||
res.into_iter().rev().collect()
|
||
}
|
||
}
|
||
```
|
||
|
||
<p align="center">
|
||
<a href="https://programmercarl.com/other/kstar.html" target="_blank">
|
||
<img src="../pics/网站星球宣传海报.jpg" width="1000"/>
|
||
</a>
|