Binary Tree Postorder Traversal

Identifying Problem Isomorphism

“Binary Tree Postorder Traversal” can be closely mapped to “Binary Tree Inorder Traversal”.

Both problems are about tree traversal and require the understanding of different depth-first search strategies. The “Binary Tree Postorder Traversal” requires postorder traversal, where you visit the left subtree, right subtree, and then the root node. “Binary Tree Inorder Traversal” requires inorder traversal, where you visit the left subtree, the root node, and then the right subtree.

Though the order of visiting nodes differs, the overall strategy and code structure are quite similar, just with a different order of operations. Both problems require you to understand how to traverse a binary tree, the order of operations, and how to implement it recursively or iteratively.

10 Prerequisite LeetCode Problems

“Binary Tree Postorder Traversal” involves traversing a binary tree in a specific order. Here are 10 problems to prepare for it:

  1. 100. Same Tree: This problem will help you understand the basic traversal in a binary tree.

  2. 101. Symmetric Tree: This problem will help you understand how to traverse and compare two binary trees.

  3. 102. Binary Tree Level Order Traversal: This problem can help you understand level order traversal, which is a type of breadth-first search.

  4. 104. Maximum Depth of Binary Tree: This problem will help you practice depth-first search traversal, which is used in postorder traversal.

  5. 105. Construct Binary Tree from Preorder and Inorder Traversal: By reconstructing a binary tree from its traversals, you can deepen your understanding of binary tree structure and traversal.

  6. 107. Binary Tree Level Order Traversal II: Similar to 102, this will help with breadth-first search, a useful contrast to depth-first search.

  7. 110. Balanced Binary Tree: Checking if a binary tree is balanced involves traversal, similar to postorder traversal.

  8. 111. Minimum Depth of Binary Tree: This problem can help you understand depth-first search traversal.

  9. 112. Path Sum: This problem requires you to find a path in the tree, which can help you understand traversal.

  10. 144. Binary Tree Preorder Traversal: Understanding the different types of traversal will help you better understand postorder traversal.

Clarification Questions

What are the clarification questions we can ask about this problem?

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class Solution:
    def postorderTraversal(self, root: TreeNode) -> List[int]:
        result=[]
        stack=[]

        while root or stack:
            while root:
                stack.append(root) 
                root=root.left if root.left else root.right
            root=stack.pop()
            result.append(root.val) 

            if stack and stack[len(stack)-1].left==root: 
                root=stack[len(stack)-1].right
            else:
                root=None 

        return(result)

Problem Classification

The problem involves traversing through a binary tree in a post-order manner. Here are the classifications:

  1. Data Structures: The problem fundamentally revolves around the use of the binary tree data structure.

  2. Tree Traversal: More specifically, the problem involves performing a post-order traversal on a binary tree.

  3. Iterative Methods: Although tree traversal is often done recursively, this problem requires using an iterative method.

  4. Stacks: The iterative method for post-order traversal makes use of the stack data structure.

Language Agnostic Coding Drills

The problem falls under “Tree Traversal”, specifically the post-order traversal of a binary tree. Here’s how to break it down into the smallest units of learning and the step-by-step problem-solving approach:

  1. Understanding Binary Trees: Before diving into tree traversal, one must first understand the concept of binary trees. A binary tree is a type of data structure in which each node has at most two children, referred to as the left child and the right child.

  2. Tree Traversal: Tree traversal is a process used for visiting each node in a tree data structure, exactly once. Understanding this concept is fundamental to this problem.

  3. Post-Order Traversal: In a post-order traversal, the traversal visits the left subtree, then the right subtree, and finally the root node. The challenge in an iterative post-order traversal is that unlike pre-order and in-order traversals, post-order traversal is not naturally expressible with iteration since it doesn’t visit nodes in the same order as they get discovered.

  4. Using a Stack for Traversal: Iterative traversal solutions usually rely on a stack data structure. Understanding how to use a stack to keep track of visited nodes and the order in which they should be visited is key to solving this problem.

Step-by-step Problem-Solving Approach:

  1. Create an empty stack and initialize root as the top node.

  2. Push the root node into the stack.

  3. Start a while loop that continues until the root is null and the stack is not empty. This will ensure that all nodes are visited.

  4. Inside the while loop, push the nodes first onto the stack, first checking if they have a left child, then if they have a right child. If a node does not have a left child, push the right child onto the stack. If it doesn’t have a right child either, then push the node itself onto the stack.

  5. After a node and its children have been visited and added to the result array, check if the current node is the left child of the next node in the stack. If it is, we need to visit the right child of the next node in the stack, so set root to the right child of the next node in the stack. If not, then we’ve visited both children of the next node in the stack (or it has no children), so we can move on to the next node by setting root to null.

  6. Once the while loop ends (the stack is empty and root is null), we have visited every node in post-order and added each node’s value to the result array. So, we return the result array.

Each of these concepts and steps can be coded separately and, when combined, lead to the final solution.

Targeted Drills in Python

  1. Understanding Binary Trees: Creating a simple binary tree structure.
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class TreeNode:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None

root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
  1. Tree Traversal - Post-Order Traversal: Writing a recursive post-order traversal function.
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def postorderTraversal(root):
    if root:
        postorderTraversal(root.left)
        postorderTraversal(root.right)
        print(root.val)
  1. Using a Stack for Traversal: Using a stack to implement pre-order traversal, which is the simplest to implement with a stack.
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def preorderTraversal(root):
    result = []
    stack = [root]
    while stack:
        node = stack.pop()
        if node:
            result.append(node.val)
            stack.append(node.right)
            stack.append(node.left)
    return result
  1. Problem-Specific Drill - Post-order Traversal with a Stack: Modifying the pre-order traversal algorithm to do post-order traversal by pushing nodes into another stack in the pre-order but reversed (right before left), and then pop elements out.
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def postorderTraversal(root):
    if not root:
        return []
    result = []
    stack1 = [root]
    stack2 = []
    while stack1:
        node = stack1.pop()
        stack2.append(node)
        if node.left:
            stack1.append(node.left)
        if node.right:
            stack1.append(node.right)
    while stack2:
        result.append(stack2.pop().val)
    return result
  1. Final Problem-Specific Drill - Iterative Post-order Traversal without Reversing Pre-order: Implement the problem-specific solution by following the step-by-step approach discussed earlier.
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class Solution:
    def postorderTraversal(self, root: TreeNode) -> List[int]:
        result=[]
        stack=[]
        while root or stack:
            while root:
                stack.append(root) 
                root=root.left if root.left else root.right
            root=stack.pop()
            result.append(root.val) 
            if stack and stack[len(stack)-1].left==root: 
                root=stack[len(stack)-1].right
            else:
                root=None 
        return(result)

Please note that in Python, the List type and the TreeNode class would need to be defined, or imported from a library, for the final code to run.