How can you write a function to achieve vertical order traversal of a binary tree?

How can you write a function to achieve vertical order traversal of a binary tree?

How can you write a function to achieve vertical order traversal of a binary tree?

Approach

To write a function for achieving vertical order traversal of a binary tree, follow this structured framework:

  1. Understand the Problem: Vertical order traversal groups nodes by their horizontal distance from the root.

  2. Choose a Data Structure: Utilize a map (or dictionary) to hold lists of nodes corresponding to each horizontal distance.

  3. Breadth-First Search (BFS) or Depth-First Search (DFS): Implement BFS or DFS to traverse the tree while tracking the horizontal distance of each node.

  4. Sort and Format the Output: After traversing, sort the keys of the map and prepare the output based on the lists of nodes.

Key Points

  • Horizontal Distance Calculation: The root node has a horizontal distance of 0. For each left child, decrease the distance by 1; for each right child, increase it by 1.

  • Data Structure Choice: A defaultdict from the collections module can simplify handling lists for each horizontal distance.

  • Sorting: Ensure that the output is in the correct vertical order by sorting the keys of the map before returning the final result.

Standard Response

Here is a sample function to achieve vertical order traversal of a binary tree in Python:

from collections import defaultdict, deque

class TreeNode:
 def __init__(self, val=0, left=None, right=None):
 self.val = val
 self.left = left
 self.right = right

def vertical_order_traversal(root):
 if not root:
 return []

 node_map = defaultdict(list)
 queue = deque([(root, 0)]) # (node, horizontal distance)
 
 while queue:
 node, hd = queue.popleft()
 node_map[hd].append(node.val)
 
 if node.left:
 queue.append((node.left, hd - 1))
 if node.right:
 queue.append((node.right, hd + 1))
 
 # Sort the keys and prepare the result
 sorted_keys = sorted(node_map.keys())
 result = [node_map[key] for key in sorted_keys]

 return result

# Example usage:
# Constructing a binary tree
# 1
# / \
# 2 3
# / \ \
# 4 5 6
# Example call:
# vertical_order_traversal(root) should return [[4], [2], [1, 5, 6], [3]]

Tips & Variations

Common Mistakes to Avoid

  • Not Handling Edge Cases: Ensure to handle cases where the tree is empty (i.e., the root is None).

  • Incorrect Horizontal Distance Tracking: Make sure to correctly update the horizontal distance as you traverse left and right.

  • Failing to Sort the Output: Always sort the horizontal distances before returning the result to maintain the correct order.

Alternative Ways to Answer

  • Using DFS Instead of BFS: Instead of using a queue for BFS, you can use a recursive DFS approach with an auxiliary function to keep track of the horizontal distance.

Role-Specific Variations

  • Technical Roles: Focus on detailing the algorithm’s time complexity (O(N log N) due to sorting) and space complexity (O(N) for storing nodes).

  • Managerial Roles: Emphasize the importance of clear communication and collaboration among team members when implementing complex algorithms.

  • Creative Roles: Discuss the potential for visualizing the binary tree and how it can aid in understanding data structures.

Follow-Up Questions

  • How would you modify the function to return nodes in a specific order (e.g., left to right)?

  • Can you explain the time and space complexity of your solution?

  • What would you do if the binary tree was very large and memory-consuming?

By following this comprehensive guide, job seekers can effectively prepare for technical interviews, particularly when discussing data structures and algorithms

Question Details

Difficulty
Medium
Medium
Type
Coding
Coding
Companies
Apple
Microsoft
Apple
Microsoft
Tags
Data Structures
Algorithm Design
Problem-Solving
Data Structures
Algorithm Design
Problem-Solving
Roles
Software Engineer
Data Scientist
Computer Scientist
Software Engineer
Data Scientist
Computer Scientist

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