Ivy Cutting II

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

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

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10 mins
• 🛠️ Topics: Binary Tree, Tree Traversal, 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?

• What does the rightmost vine refer to?
  • The rightmost vine is the path from the root to the rightmost leaf node, following the right child at each step.
• How should the function behave differently from the previous problem?
  • In this problem, the function should be implemented recursively.

HAPPY CASE
Input: Binary tree where the rightmost path is ["Root", "Node2", "Leaf3"]
Output: ["Root", "Node2", "Leaf3"]
Explanation: The rightmost path is extracted correctly using recursion.

EDGE CASE
Input: Binary tree with no right child at any node
Output: ["Root"]
Explanation: The rightmost path consists only of the root 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.

For Tree Traversal problems, we want to consider the following approaches:

• Binary Tree Traversal: Traverse the tree to extract the rightmost path using recursion.
• Recursion: Apply a recursive approach to solve the problem by traversing down the rightmost nodes.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Traverse the tree recursively starting from the root and collect the values of nodes in the rightmost path.

1) If the current node is None, return an empty list.
2) If the current node has a right child, return a list with the current node's value followed by the result of recursively calling the function on the right child.
3) If the current node has no right child but has a left child, return a list with the current node's value followed by the result of recursively calling the function on the left child.
4) If the current node is a leaf node, return a list with the current node's value.

⚠️ Common Mistakes

• Incorrectly handling cases where a node has no right child.
• Not properly returning the accumulated path as a list.

4: I-mplement

Implement the code to solve the algorithm.

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

def right_vine(root):
    if root is None:
        return []
    
    # If there is a right child, continue down the right path
    if root.right:
        return [root.val] + right_vine(root.right)
    # Otherwise, if there is a left child, take that path
    elif root.left:
        return [root.val] + right_vine(root.left)
    # If it's a leaf node, just return its value
    else:
        return [root.val]

5: R-eview

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

• Test with the examples given:
  • Input 1: Binary tree where the rightmost path is ["Root", "Node2", "Leaf3"]
  • Expected Output: ["Root", "Node2", "Leaf3"]
  • Input 2: Binary tree with no right children
  • Expected Output: ["Root"]
  • Verify that the outputs are correct.

6: E-valuate

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

Assume H represents the height of the binary tree.

• Time Complexity: O(H) because the algorithm traverses down the height of the tree.
• Space Complexity: O(H) because the recursion stack will use space proportional to the height of the tree.