Escaping the Sea Caves

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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 is the leftmost path in a binary tree?
  • The leftmost path is the path that starts from the root and continues to follow the left child at each step until a leaf node is reached.
• What should the function return if there are no left children?
  • The function should return a list with only the root node's value.

HAPPY CASE
Input: Binary tree with nodes ["CaveA", "CaveB", "CaveD", "CaveE", "CaveC", "CaveF"]
Output: ["CaveA", "CaveB", "CaveD"]
Explanation: The leftmost path is ["CaveA", "CaveB", "CaveD"].

EDGE CASE
Input: Binary tree with nodes ["CaveA", "CaveB", "CaveC"] where only the root has children.
Output: ["CaveA"]
Explanation: The root has no left children, so the path only includes the root.

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 Path problems, we want to consider the following approaches:

• Binary Tree Traversal: Traverse the tree following the left child at each step to collect the values.
• Iteration or Recursion: Either iterate through the tree or use recursion to collect the values along the leftmost path.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Traverse the tree starting from the root, following the left child at each step, and collect the values in a list.

1) Initialize an empty list to store the path.
2) While the current node is not None:
    a) Add the current node's value to the path.
    b) Move to the left child of the current node.
3) Return the path list after traversing.

⚠️ Common Mistakes

• Not correctly handling cases where the tree has no left children, which could lead to incomplete paths.
• Assuming that every node has a left child, leading to errors when traversing.

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 leftmost_path(root):
    path = []
    
    # Traverse the tree while there's a node
    while root:
        path.append(root.val)  # Add the current node's value to the path
        root = root.left       # Move to the left child (if it exists)
    
    return path

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 with nodes ["CaveA", "CaveB", "CaveD", "CaveE", "CaveC", "CaveF"]
  • Expected Output: ["CaveA", "CaveB", "CaveD"]
  • Input 2: Binary tree with nodes ["CaveA", "CaveB", "CaveC"] where only the root has children.
  • Expected Output: ["CaveA"]
  • Verify that the outputs match the expected results.

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 only traverses the height of the tree.
• Space Complexity: O(H) because the path list stores up to H elements, one for each level of the tree.