path-in-zigzag-labelled-binary-tree

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Algorithms

In an infinite binary tree where every node has two children, the nodes are labelled in row order.

In the odd numbered rows (ie., the first, third, fifth,...), the labelling is left to right, while in the even numbered rows (second, fourth, sixth,...), the labelling is right to left.

<img alt="" src="https://assets.leetcode.com/uploads/2019/06/24/tree.png" style="width: 300px; height: 138px;" />

Given the <code>label</code> of a node in this tree, return the labels in the path from the root of the tree to the&nbsp;node with that <code>label</code>.

&nbsp;
Example 1:

<pre>
Input: label = 14
Output: [1,3,4,14]
</pre>

Example 2:

<pre>
Input: label = 26
Output: [1,2,6,10,26]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= label &lt;= 10^6</code></li>
</ul>

pathInZigZagTree

Path In Zigzag Labelled Binary Tree

Cycle Length Queries in a Tree

cycle-length-queries-in-a-tree

查询树中环的长度

Tree

Math

Binary Tree

在一棵无限的二叉树上，每个节点都有两个子节点，树中的节点 逐行 依次按&nbsp;&ldquo;之&rdquo; 字形进行标记。

如下图所示，在奇数行（即，第一行、第三行、第五行&hellip;&hellip;）中，按从左到右的顺序进行标记；

而偶数行（即，第二行、第四行、第六行&hellip;&hellip;）中，按从右到左的顺序进行标记。

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2019/06/28/tree.png" style="height: 138px; width: 300px;">

给你树上某一个节点的标号 <code>label</code>，请你返回从根节点到该标号为 <code>label</code> 节点的路径，该路径是由途经的节点标号所组成的。

&nbsp;

示例 1：

<pre>输入：label = 14
输出：[1,3,4,14]
</pre>

示例 2：

<pre>输入：label = 26
输出：[1,2,6,10,26]
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= label &lt;= 10^6</code></li>
</ul>