Searching Ariel's Treasures

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Unit 8 Session 2 Standard (Click for link to problem statements)

Unit 8 Session 2 Advanced (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10-15 mins
• 🛠️ Topics: Trees, Binary Search Trees, Search

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 structure of the tree?
  • The tree is a Binary Search Tree (BST) where each node represents an item from Ariel's collection.
• What operation needs to be performed?
  • The function needs to check if a specific item is present in the BST.
• What should be returned?
  • The function should return True if the item is found, otherwise False.

HAPPY CASE
Input: grotto = TreeNode("Snarfblat", TreeNode("Gadget", TreeNode("Dinglehopper"), TreeNode("Gizmo")), TreeNode("Whatzit", None, TreeNode("Whozit"))), treasure = "Dinglehopper"
Output: True
Explanation: "Dinglehopper" is present in the tree.

EDGE CASE
Input: grotto = TreeNode("Snarfblat", TreeNode("Gadget", TreeNode("Dinglehopper"), TreeNode("Gizmo")), TreeNode("Whatzit", None, TreeNode("Whozit"))), treasure = "Thingamabob"
Output: False
Explanation: "Thingamabob" is not present in the tree.

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 Binary Search Tree (BST) problems, we want to consider the following approaches:

• BST Search: Use the properties of the BST to efficiently locate the target item by navigating left or right based on comparisons.
• Iterative Search: Implement the search iteratively to avoid the overhead of recursion.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Traverse the BST, comparing the target treasure with the current node's value, and move left or right accordingly until the target is found or the tree is fully traversed.

1) Initialize `current_node` to the root of the tree (`grotto`).
2) While `current_node` is not `None`:
    - If `treasure` is equal to `current_node.val`, return `True`.
    - If `treasure` is less than `current_node.val`, move to the left child.
    - If `treasure` is greater than `current_node.val`, move to the right child.
3) If the loop exits, return `False` as the treasure was not found in the tree.

⚠️ Common Mistakes

• Forgetting to return False if the loop exits without finding the treasure.
• Misinterpreting the BST properties and incorrectly traversing the tree.

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 locate_treasure(grotto, treasure):
    current_node = grotto
    
    while current_node:
        if treasure == current_node.val:
            return True
        elif treasure < current_node.val:
            current_node = current_node.left
        else:
            current_node = current_node.right
    
    return False

5: R-eview

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

- Example 1:
    - Input: `grotto = TreeNode("Snarfblat", TreeNode("Gadget", TreeNode("Dinglehopper"), TreeNode("Gizmo")), TreeNode("Whatzit", None, TreeNode("Whozit")))`, `treasure = "Dinglehopper"`
    - Execution: 
        - Start at root "Snarfblat".
        - "Dinglehopper" < "Snarfblat", move to the left child "Gadget".
        - "Dinglehopper" < "Gadget", move to the left child "Dinglehopper".
        - Found "Dinglehopper", return `True`.
    - Output: `True`

- Example 2:
    - Input: `grotto = TreeNode("Snarfblat", TreeNode("Gadget", TreeNode("Dinglehopper"), TreeNode("Gizmo")), TreeNode("Whatzit", None, TreeNode("Whozit")))`, `treasure = "Thingamabob"`
    - Execution: 
        - Start at root "Snarfblat".
        - "Thingamabob" > "Snarfblat", move to the right child "Whatzit".
        - "Thingamabob" < "Whatzit", left child is `None`.
        - "Thingamabob" not found, return `False`.
    - Output: `False`

6: E-valuate

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

Assume N represents the number of nodes in the tree.

• Time Complexity: O(H) where H is the height of the tree. For a balanced BST, H is O(log N), so the search operation is O(log N).
• Space Complexity: O(1) because the search is performed iteratively with constant space usage.