Is Path In Zigzag Labelled Binary Tree easy or hard?

The problem is rated Medium because the tree structure is simple but the zigzag labeling creates a non-obvious parent relationship. Once you recognize the mirror transformation between reversed and normal levels, the solution becomes a straightforward logarithmic backtracking process.

Path In Zigzag Labelled Binary Tree Python or Java solution?

In Python or Java, compute the node level using logarithms, then repeatedly transform the label using the mirror formula and divide by two to move to the parent. Append each label to a list and reverse it at the end. The implementation stays concise and runs in O(log n) time.

How to solve Path In Zigzag Labelled Binary Tree in O(log n)?

Determine the level of the label using logarithms. For each step toward the root, compute the mirrored value within that level using level_min + level_max - label. Convert to the parent by dividing by two, then continue until reaching the root. Reverse the collected nodes to produce the root-to-label path.

What is the best approach for Path In Zigzag Labelled Binary Tree?

The best approach is backtracking from the given label using level math and mirroring. Each level has a numeric range, and zigzag ordering can be converted to normal ordering using the formula level_min + level_max - label. After converting, the parent is simply label / 2. This method runs in O(log n) time and O(log n) space.

What data structure is used in Path In Zigzag Labelled Binary Tree?

The problem conceptually uses a binary tree, but the optimal solution avoids constructing the tree. Instead, it relies on mathematical properties of binary tree levels and stores the path in a list or array while backtracking from the label to the root.

What is the time complexity of Path In Zigzag Labelled Binary Tree?

The optimal solution runs in O(log n) time because you move from the given label up to the root, visiting one node per level. Since the height of a binary tree with label n is about log2(n), only logarithmic steps are required. Space complexity is also O(log n) for storing the path.

Is Path In Zigzag Labelled Binary Tree asked at Google, Amazon, or Meta?

This problem is a common medium-level tree and math question similar to those asked in interviews at companies like Amazon, Google, and Meta. It tests understanding of binary tree structure, level ranges, and mathematical transformations rather than pure traversal.

Description Hints 1 Solution Video 27:54

1104. Path In Zigzag Labelled Binary Tree

Medium75.9% acceptance2 companies

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

Asked at 2 companies

Spinny Bloomberg

Topics

Hints open one at a time

Hint 1

Based on the label of the current node, find what the label must be for the parent of that node.

27:54

Still stuck?Read 3 approaches, or watch a walkthrough.

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