How would you implement an algorithm to determine if a binary tree contains a path with a specified sum?

How would you implement an algorithm to determine if a binary tree contains a path with a specified sum?

How would you implement an algorithm to determine if a binary tree contains a path with a specified sum?

Approach

When responding to the interview question, "How would you implement an algorithm to determine if a binary tree contains a path with a specified sum?", it's crucial to follow a structured framework. Here’s how to break down your thought process:

  1. Understand the Problem: Clarify what is meant by a path in a binary tree and what it means for that path to sum to a certain value.

  2. Define the Data Structure: Recognize that you will be working with a binary tree, which consists of nodes that contain values and pointers to left and right child nodes.

  3. Plan the Algorithm: Decide on a method to traverse the tree, such as Depth-First Search (DFS) or Breadth-First Search (BFS).

  4. Implement the Solution: Write the code that embodies your algorithm.

  5. Test the Implementation: Consider edge cases and test your solution with various binary tree structures and target sums.

Key Points

  • Clarity: Make sure to explain your understanding of what constitutes a path and how sums are calculated.

  • Efficiency: Discuss the time and space complexity of your solution.

  • Edge Cases: Acknowledge potential edge cases, such as empty trees or trees with negative values.

Standard Response

Here’s a sample answer that follows best practices:

To determine if a binary tree contains a path whose sum equals a specified value, I would implement a recursive Depth-First Search (DFS) algorithm. The basic idea is to traverse the tree and maintain a running total of the path’s sum from the root to the current node. Here's how I would approach it:

  • Base Case: If the current node is null, return false because there is no path.

  • Leaf Node Check: If the current node is a leaf (both left and right children are null), check if the running total equals the target sum. If it does, return true.

  • Recursive Case: Subtract the current node's value from the target sum and recursively check the left and right subtrees.

Here’s a sample Python implementation:

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

def hasPathSum(root, targetSum):
 if not root:
 return False
 if not root.left and not root.right: # Leaf node
 return root.value == targetSum
 targetSum -= root.value
 return hasPathSum(root.left, targetSum) or hasPathSum(root.right, targetSum)

Explanation

  • Function Definition: The hasPathSum function takes the root of the binary tree and the target sum as arguments.

  • Base Case: If the root is null, we return false.

  • Leaf Node Check: If we reach a leaf node, we check if the path sum equals the target.

  • Recursive Calls: The function calls itself for both the left and right child nodes, decreasing the target sum by the current node's value.

Tips & Variations

Common Mistakes to Avoid

  • Not Handling Edge Cases: Failing to consider empty trees or trees where all values are negative.

  • Overcomplicating the Solution: Trying to implement a solution without recursion can lead to unnecessary complexity.

Alternative Ways to Answer

  • Iterative Approach: Instead of recursion, you can implement an iterative approach using a stack to track nodes and their path sums.

  • BFS Implementation: Use a queue to explore nodes level by level, which can also be effective.

Role-Specific Variations

  • Technical Positions: Emphasize time and space complexity, discussing the O(N) time complexity due to the need to visit all nodes.

  • Creative Roles: While the technical implementation is crucial, focus on how understanding algorithms can enhance problem-solving skills in creative contexts.

  • Managerial Positions: Discuss the importance of algorithm efficiency and how it impacts system performance and scalability.

Follow-Up Questions

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

  • Time complexity is O(N) because we potentially visit every node once. Space complexity is O(H), where H is the height of the tree, due to the recursion stack.

  • How would you modify your algorithm if the tree was very large?

  • For large trees, I might consider using an iterative approach to avoid recursion limits or employing a breadth-first search to manage memory more effectively.

  • What if the path can start from any node in the tree?

  • I would need to modify the algorithm to initiate the path sum check from every node in the

Question Details

Difficulty
Medium
Medium
Type
Technical
Technical
Companies
Google
Google
Tags
Algorithm Design
Problem-Solving
Data Structures
Algorithm Design
Problem-Solving
Data Structures
Roles
Software Engineer
Data Scientist
Algorithm Engineer
Software Engineer
Data Scientist
Algorithm Engineer

Ace Your Next Interview with Real-Time AI Support

Get real-time support and personalized guidance to ace live interviews with confidence.

Interview Copilot: Your AI-Powered Personalized Cheatsheet

Interview Copilot: Your AI-Powered Personalized Cheatsheet

Interview Copilot: Your AI-Powered Personalized Cheatsheet