Pre order Traversal

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

Problem Highlights

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

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: How should the function behave if the tree is empty?
  • Answer: Return an empty list as there are no nodes to traverse in an empty tree.

HAPPY CASE
Input: TreeNode(1, TreeNode(2), TreeNode(3))
Output: [1, 2, 3]
Explanation: Preorder traversal visits the node first, then left child, and right child, resulting in the sequence 1, 2, 3.

EDGE CASE
Input: None
Output: []
Explanation: An empty tree results in an empty traversal list.

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 is a standard tree traversal problem, specifically a preorder traversal which is fundamental in binary tree operations for processing a node before its children.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Recursively traverse the tree to access each node in the preorder sequence.

1) Visit the current node and add its value to the list.
2) Recursively visit the left subtree.
3) Recursively visit the right subtree.

⚠️ Common Mistakes

• Not maintaining the order of traversal which could lead to incorrect results.

4: I-mplement

Implement the code to solve the algorithm.

def preorder_helper(current_node, values):
    if not current_node:
        return values
    values.append(current_node.val)  # Visit the node
    preorder_helper(current_node.left, values)  # Traverse the left subtree
    preorder_helper(current_node.right, values)  # Traverse the right subtree
    return values

def preorder_traversal(root):
    values = []
    return preorder_helper(root, values)

5: R-eview

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

• Step through the code with a test tree to ensure that the preorder sequence is correctly assembled from the root through the subtrees.

6: E-valuate

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

• Time Complexity: O(n) where n is the number of nodes in the tree. Each node is visited exactly once during the traversal.
• Space Complexity: O(n) for the recursion stack in the worst case when the tree is skewed, otherwise O(log n) in a balanced tree.