Twinning Trees

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

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10 mins
• 🛠️ Topics: Binary Tree, Tree Comparison, 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 it mean for two trees to be identical?
  • Two trees are identical if they have the same structure and their corresponding nodes have the same values.
• How should the function behave if one or both of the trees are empty?
  • If both trees are empty, return True. If only one tree is empty, return False.

HAPPY CASE
Input: 
root1 = TreeNode(1, TreeNode(2), TreeNode(3))
root2 = TreeNode(1, TreeNode(2), TreeNode(3))
Output: True
Explanation: The trees have identical structures and values.

EDGE CASE
Input: 
root1 = TreeNode(1, TreeNode(2))
root2 = TreeNode(1, None, TreeNode(2))
Output: False
Explanation: The trees have different structures.

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 Comparison problems, we want to consider the following approaches:

• Binary Tree Traversal: Traverse both trees simultaneously to compare corresponding nodes.
• Recursion: Use recursion to compare the structure and values of the trees.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Traverse both trees simultaneously. At each step, check if the nodes at the corresponding positions in both trees have the same value and that their subtrees are also identical.

1) If both nodes (root1 and root2) are None, return True.
2) If one of the nodes is None and the other is not, return False.
3) If the values of root1 and root2 are not equal, return False.
4) Recursively check if the left subtrees are identical.
5) Recursively check if the right subtrees are identical.
6) Return True if both the left and right subtrees are identical.

⚠️ Common Mistakes

• Not correctly handling the case where one tree is empty and the other is not.
• Failing to compare both the structure and values of the trees.

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 is_identical(root1, root2):
    # Base Case
    if root1 is None and root2 is None:
        return True
    if root1 is None or root2 is None:
        return False
    
    # Recursive Case
    if root1.val == root2.val:
        return is_identical(root1.left, root2.left) and is_identical(root1.right, root2.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.

• Test with the examples given:

  • Input 1:

    root1 = TreeNode(1, TreeNode(2), TreeNode(3))
    root2 = TreeNode(1, TreeNode(2), TreeNode(3))
    
    Expected Output: True
    

  • Input 2:

    root1 = TreeNode(1, TreeNode(2))
    root2 = TreeNode(1, None, TreeNode(2))
    
    Expected 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 binary trees.

• Time Complexity: O(N) because the algorithm needs to visit each node in both trees.
• Space Complexity: O(H) where H is the height of the trees, due to the recursive call stack.