How do you solve Path In Zigzag Labelled Binary Tree on LeetCode?

Path In Zigzag Labelled Binary Tree (LeetCode #1104) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(log n) space complexity. Key insight: The zigzag pattern alternates the direction of node labeling, which can be leveraged to find parent nodes efficiently.

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

The optimal solution for Path In Zigzag Labelled Binary Tree runs in O(log n) time and uses O(log n) space. The time complexity is O(log n) because we only traverse the height of the tree, which is logarithmic in relation to the label value.

What is the brute force solution for Path In Zigzag Labelled Binary Tree?

The brute force approach for Path In Zigzag Labelled Binary Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we will simulate the traversal from the root to the target node, calculating each parent node until we reach the root. This is straightforward but inefficient for larger labels. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Path In Zigzag Labelled Binary Tree?

Path In Zigzag Labelled Binary Tree uses the following concepts: Math, Tree, Binary Tree. The recommended patterns to study are: Bit Manipulation, Tree Traversal.

What are the interview tips for Path In Zigzag Labelled Binary Tree?

Always clarify the problem and ask about edge cases before jumping into coding. Think about the properties of binary trees and how they can simplify your calculations. Practice explaining your thought process as you code; it helps in interviews.

What are common mistakes when solving Path In Zigzag Labelled Binary Tree?

Failing to account for the zigzag pattern when calculating parent nodes. Not reversing the path after constructing it from leaf to root.

#1104

Path In Zigzag Labelled Binary Tree

Medium

MathTreeBinary TreeBit ManipulationTree Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(log n)
Space	O(1)	O(log n)

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Intuition

Time O(log n)Space O(log n)

This approach leverages the properties of binary trees and the zigzag pattern to calculate the path directly without simulating each step, making it efficient.

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Algorithm

5 steps

1Step 1: Initialize an empty list for the path and a variable to keep track of the current label.
2Step 2: Determine the depth of the given label by counting how many times we can divide it by 2 until we reach 1.
3Step 3: For each level from the depth to 0, calculate the label of the parent node based on the zigzag pattern.
4Step 4: Append the root and the calculated labels to the path list.
5Step 5: Reverse the path list before returning it.

solution.py11 lines

1def pathInZigZagTree(label):
2    path = []
3    depth = label.bit_length() - 1
4    while label > 0:
5        path.append(label)
6        depth -= 1
7        label //= 2
8        if depth % 2 == 1:
9            label = (1 << depth) - 1 - label
10    path.reverse()
11    return path

ℹ

Complexity note: The time complexity is O(log n) because we only traverse the height of the tree, which is logarithmic in relation to the label value.

1The zigzag pattern alternates the direction of node labeling, which can be leveraged to find parent nodes efficiently.
2Understanding the binary representation of numbers helps in determining the depth and relationships in the tree.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.