Problem Description
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.
Key Insights
- The binary tree is infinite and follows a specific labeling pattern.
- Odd rows are labeled from left to right, while even rows are labeled from right to left.
- The path to any node can be derived by calculating its row and position within that row.
Space and Time Complexity
Time Complexity: O(log n) - because the height of the tree grows logarithmically with respect to the label. Space Complexity: O(log n) - required for the output path storage.
Solution
To find the path from the root to the node with a given label, we can use the properties of binary trees and the specific labeling pattern. The approach involves determining the level of the node, calculating the position of the node within that level, and then backtracking to the root while taking into account the zigzag pattern. We will utilize a list to store the path as we backtrack through the tree.