Post order Traversal

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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: What is postorder traversal?
  • Answer: In a postorder traversal of a binary tree, each node is visited in the following order: left child, right child, then the node itself.

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

EDGE CASE
Input: TreeNode(1, None, TreeNode(2))
Output: [2, 1]
Explanation: With no left child, the right child is visited first, then the 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.

This problem is a standard tree traversal problem, specifically a postorder traversal which is fundamental in binary tree operations.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

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

1) Recursively visit the left subtree.
2) Recursively visit the right subtree.
3) Visit the current node (append its value).

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

def postorder_traversal(root):
    values = []
    return postorder_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 postorder sequence is correctly assembled.

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.