Approach

When answering the question, "Write a function that calculates the sum of all nodes in a binary tree that have an even-valued grandparent," it's essential to follow a clear and structured framework. Here's how to break down the thought process:

1. Understand the Problem: Define what is meant by "even-valued grandparent" and clarify how nodes are structured in a binary tree.

2. Choose a Traversal Method: Determine whether to use Depth-First Search (DFS) or Breadth-First Search (BFS) for tree traversal.

3. Implement the Logic: Create a recursive or iterative function that sums the values of the nodes that meet the criteria.

4. Test the Function: Validate the function with various test cases to ensure correctness.

Key Points

• Even-Valued Grandparent: A node's grandparent must be even for that node to be included in the sum.

• Tree Traversal: Either DFS or BFS can be used, but DFS (recursive) is often more straightforward for this kind of problem.

• Node Structure: Be familiar with the binary tree node structure, typically defined with a value and pointers to left and right children.

• Edge Cases: Consider scenarios where the tree is empty or contains a limited number of nodes.

Standard Response

Here is a fully-formed sample answer that follows best practices for implementing the function:

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

def sumEvenGrandparent(root: TreeNode) -> int:
 def dfs(node, parent_val, grandparent_val):
 if not node:
 return 0
 
 # Check if grandparent's value is even
 total = 0
 if grandparent_val % 2 == 0:
 total += node.val
 
 # Recursively call left and right children
 total += dfs(node.left, node.val, parent_val)
 total += dfs(node.right, node.val, parent_val)
 
 return total

 return dfs(root, 1, 1) # Start with dummy values for parent and grandparent

• The TreeNode class defines the structure of each node in the tree.

• The sumEvenGrandparent function initiates the DFS traversal.

• The dfs function checks each node's grandparent and adds its value to the total if the grandparent's value is even.

• Explanation:

Tips & Variations

Common Mistakes to Avoid:

• Ignoring Edge Cases: Ensure you handle cases where the tree is empty or has fewer than three nodes.

• Incorrectly Traversing the Tree: Make sure to pass the correct parent and grandparent values during the recursive calls.

Alternative Ways to Answer:

• Using Iterative Approach: You might prefer an iterative approach using a stack instead of recursion.

Role-Specific Variations:

• For Technical Roles: Focus on performance optimizations and handle larger trees efficiently.

• For Managerial Roles: Emphasize team collaboration in solving complex problems, showcasing leadership skills.

Follow-Up Questions:

• What would you do if the binary tree is very large?

• How would you modify the function to count nodes instead of summing their values?

• Can you explain how you would test this function?

Conclusion

Creating a function to calculate the sum of all nodes in a binary tree with an even-valued grandparent requires clear logic, effective traversal strategies, and thorough testing. By following this structured approach and being aware of common pitfalls, candidates can effectively demonstrate their problem-solving skills in technical interviews