# [Solved] 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.

## Question

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.

Given the `label` of a node in this tree, return the labels in the path from the root of the tree to the node with that `label`.

Example 1:

```Input: label = 14
Output: [1,3,4,14]
```

Example 2:

```Input: label = 26
Output: [1,2,6,10,26]
```

Constraints:

• `1 <= label <= 10^6`

## Python Solution

```class Solution:
def pathInZigZagTree(self, label: int) -> List[int]:
level = 1
l = 1
res = []

while label>=l*2:
l*=2
level+=1

while label!=0:
res.append(label)
level_max = (2**level)-1
level_min = 2**(level-1)
label = (level_max+level_min-label)//2
level-=1
return res[::-1]``` ##### Abhishek Sharma

Started my Data Science journey in my 2nd year of college and since then continuously into it because of the magical powers of ML and continuously doing projects in almost every domain of AI like ML, DL, CV, NLP.

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