Diagonal Traversal Of Binary Tree Leetcode

Understanding how to perform diagonal traversal of a binary tree is a key concept in algorithm design and is often tested in coding interviews or platforms like LeetCode. This traversal technique involves visiting nodes of a binary tree in diagonal lines from the top-right to bottom-left. Unlike traditional traversals like inorder, preorder, or level order, diagonal traversal explores the structure of the tree in a more creative and pattern-based way. This topic will explain the diagonal traversal approach, its implementation in code, and how it can be optimized for performance.

What is Diagonal Traversal in a Binary Tree?

Concept and Intuition

In diagonal traversal, we process all the nodes lying on the same diagonal of the binary tree. Imagine drawing diagonal lines from the root node moving toward the right. Every node that falls along each of these diagonal lines is grouped and processed together.

The key idea is:

• Nodes to the right (right child) stay on the same diagonal level.
• Nodes to the left (left child) move to the next diagonal level.

For example, the root is at diagonal 0. Its right child remains in diagonal 0, but its left child belongs to diagonal 1, and so on.

Example Tree Structure

Consider the following binary tree:

8 / \ 3 10 / \ \ 1 6 14 / \ / 4 7 13

Diagonal traversal of this tree would give:[8, 10, 14], [3, 6, 7, 13], [1, 4]

Why It Matters in Coding Interviews

Leetcode Relevance

Leetcode often includes problems that go beyond basic tree traversals. Diagonal traversal tests your ability to apply BFS (Breadth-First Search) while keeping track of diagonal levels. It shows how well you understand both recursion and iterative solutions, and how you manage data structures like queues and hash maps for efficient computation.

Real-world Applications

Though diagonal traversal is more of a theoretical problem, it is useful in scenarios like image processing, matrix-based transformations, or visualizing data hierarchies diagonally. It teaches critical thinking and pattern recognition in tree manipulation.

Approach to Solve Diagonal Traversal

Using Queue and HashMap

The most efficient method for solving this problem is by using a queue for level-order traversal combined with a map to keep track of nodes grouped by their diagonal levels. This method follows a breadth-first approach.

Steps to Implement

• Use a queue to perform BFS on the tree.
• For each node, maintain a diagonal level (starting at 0 for the root).
• Push the right child with the same diagonal level.
• Push the left child with diagonal level + 1.
• Store nodes in a map or list grouped by diagonal level.

Code Example in Python

Here is a sample implementation of diagonal traversal in Python:

from collections import defaultdict, deque class Node: def init(self, key): self.data = key self.left = None self.right = None def diagonalTraversal(root): if not root: return [] result = defaultdict(list) queue = deque() queue.append((root, 0)) while queue: node, d = queue.popleft() result[d].append(node.data) if node.left: queue.append((node.left, d + 1)) if node.right: queue.append((node.right, d)) # Flatten the result into a list finalresult = [] for diag in sorted(result.keys()): finalresult.extend(result[diag]) return finalresult

Explanation of the Code

• Nodeclass defines each node of the binary tree.
• diagonalTraversalfunction performs BFS while tracking the diagonal index.
• A dictionaryresultis used to store nodes at each diagonal level.
• The final output is created by combining all diagonal groups in order.

Time and Space Complexity

Time Complexity

The time complexity is O(N), where N is the number of nodes in the binary tree. Each node is visited exactly once.

Space Complexity

The space complexity is also O(N) because of the queue used for traversal and the dictionary used for grouping nodes by diagonals.

Alternative Approaches

Recursive Approach

Though a recursive method can be used, it is less efficient due to potential stack overflow for large trees and complex tracking of diagonal levels. A dictionary can still be used to group nodes by diagonal, but the recursive logic needs careful implementation.

Using Vertical and Horizontal Distance

Another complex variation involves tracking horizontal and vertical distances. However, this is generally used for vertical order traversal and not recommended for diagonal traversal due to unnecessary complexity.

Tips for Solving Similar Problems on Leetcode

Understand the Tree Structure

Start by drawing or visualizing the tree. This helps to clearly identify the nodes that belong to the same diagonal.

Practice Other Traversals

Before attempting diagonal traversal, make sure you understand level order, inorder, preorder, and postorder traversals. These basics will help you implement more advanced patterns.

Use Helper Functions

If using recursion, create helper functions that pass additional parameters like diagonal level or current index. This makes the code more modular and easier to debug.

Test with Edge Cases

Try running your function with:

• An empty tree
• A tree with only one node
• A skewed tree (left or right)

These tests help verify the robustness of your solution.

Diagonal traversal of a binary tree is a fascinating problem that challenges your understanding of tree structures and traversal techniques. It is commonly seen in Leetcode-style problems and is excellent for practicing breadth-first traversal with extra logic to group nodes. By using a queue and a map, you can efficiently perform diagonal traversal in linear time and space. Whether you are preparing for interviews or looking to strengthen your skills in tree algorithms, mastering this pattern is a valuable step forward.