Find Rightmost Node I

Unit 8 Session 1 (Click for link to problem statements)

Looking for the iterative version of this problem? Go to Find Rightmost Node II

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10 mins
• 🛠️ Topics: Trees, Binary Trees, Recursion

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• Question: What should the function return if the tree is empty?
  • Answer: The function should return None if the tree is empty.

HAPPY CASE
Input: TreeNode(1, None, TreeNode(2, None, TreeNode(3)))
Output: 3
Explanation: The rightmost node in the tree is the node with value 3.

EDGE CASE
Input: TreeNode(1)
Output: 1
Explanation: The tree has only one node, which is also the rightmost node.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

This problem matches a common tree traversal pattern, specifically finding a specific node based on a traversal criterion (rightmost).

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Use recursion to find the rightmost node by always following the right child until it no longer exists.

1) Start with the root node.
2) If the root node or the right child is not present, return the root's value.
3) Recursively call the function with the right child of the current node until you reach the rightmost node.

⚠️ Common Mistakes

• Forgetting to check if the root is None before trying to access its value or children.

4: I-mplement

Implement the code to solve the algorithm.

def right_most(root):
    """
    Return the value of the rightmost node in the binary tree rooted at `root`.
    If the tree is empty, return None.
    """
    if root is None:
        return None
    # If there's no right child, the current node is the rightmost node
    if root.right is None:
        return root.val
    # Recursively continue searching for the rightmost node
    return right_most(root.right)

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Perform a step-by-step verification using test cases, ensuring the function correctly identifies the rightmost node.

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

• Time Complexity: O(n) in the worst case where n is the height of the tree, particularly if it is skewed to one side.
• Space Complexity: O(1) if recursion stack space is not considered, as no extra space beyond input is used.