Binary Tree Inorder Traversal

Identifying Problem Isomorphism

“Binary Tree Inorder Traversal” requires traversing a binary tree in the “inorder” sequence (left node, root node, right node).

A similar problem to this is “Validate Binary Search Tree” (LeetCode #98). The isomorphism here is based on the concept that a correct inorder traversal of a Binary Search Tree (BST) will result in a sequence of node values in ascending order.

To solve the “Validate Binary Search Tree” problem, you can perform an inorder traversal of the tree and check if the result is sorted in ascending order. So, even though the problems have different objectives - one is to validate a BST, the other is to return the inorder traversal of a binary tree - the methodology to solve them involves a common concept which is the inorder traversal.

While the problem-solving strategy is similar, the problems are approximately isomorphic due to the difference in their objectives and the specifics of the trees in question (any binary tree vs a BST).

“Binary Tree Inorder Traversal” tests your understanding of binary tree traversal, particularly Inorder Traversal (left, root, right). Here are 10 problems to prepare for it:

104. Maximum Depth of Binary Tree: This problem helps you understand basic tree traversal to find the maximum depth.
101. Symmetric Tree: This problem helps understand the concept of tree symmetry, which indirectly helps with traversal.
102. Binary Tree Level Order Traversal: This problem tests understanding of level order (Breadth-First) traversal.
107. Binary Tree Level Order Traversal II: A variation of the level order traversal problem, but requires reversing the order, which could help with understanding tree traversals.
112. Path Sum: This problem involves traversal to find a path that sums up to a target.
100. Same Tree: This problem will help you understand tree traversal to check if two trees are the same.
572. Subtree of Another Tree: This problem will help you understand how to traverse a tree to find a subtree.
108. Convert Sorted Array to Binary Search Tree: This problem combines understanding of binary trees and arrays. It’s a good problem to practice tree construction.
111. Minimum Depth of Binary Tree: Similar to Maximum Depth of Binary Tree, but this time, you have to find the minimum depth.
144. Binary Tree Preorder Traversal: Understanding different kinds of traversal techniques is important in binary trees, and this problem focuses on the Preorder traversal (root, left, right).

These cover binary trees and how to traverse them, which is essential for the Inorder Traversal problem.

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class Solution:
    def inorderTraversal(self, root: Optional[TreeNode]) -> List[int]:
        st = []
        res = []

        while root or st:
            while root:
                st.append(root)
                root = root.left

            root = st.pop()
            res.append(root.val)

            root = root.right
        
        return res   

Problem Classification

This problem can be classified in the following way:

Binary Tree Traversal: The problem involves traversing a binary tree. The nature of the traversal is specifically in-order, which involves visiting the left subtree, the root, and then the right subtree.
Data Structure Usage (Stack): This problem involves using a stack, a common data structure, to keep track of the nodes being traversed in the tree.
Depth-First Search (DFS): This problem is an example of a Depth-First Search (DFS), where you traverse as deep as possible along each branch before backtracking. In-order traversal is one of the types of DFS in a binary tree.
Recursion: Although this specific solution is iterative, the problem of tree traversal is often associated with recursion and can be solved using recursive techniques as well.

These classifications can guide the selection of appropriate strategies for problem-solving and algorithm design.

Clarification Questions

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

Identifying Problem Isomorphism

Can you help me with finding the isomorphism for this problem?

Which problem does this problem map to the corresponding isomorphic problem on Leetcode ?

Language Agnostic Coding Drills

Here’s how we can break this problem down into smaller learning units:

Binary Trees: Understanding the concept of binary trees is crucial to this problem. This includes the concept of tree nodes, left and right children, and tree traversal methods.
In-Order Traversal: This problem involves in-order traversal of a binary tree. It’s a specific way to visit all nodes in a binary tree, going Left - Root - Right.
Stacks: The problem uses a stack to keep track of the nodes. A stack is a data structure that follows a LIFO (Last In First Out) principle.
Loops (While Loop): This code contains nested while loops, which are used to navigate through the tree.
Conditional Statements: The if-else logic in this problem is simple yet crucial. It checks whether a node exists before accessing its properties.

Targeted Drills in Python

Binary Trees:

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class TreeNode:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None

# Create a binary tree
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)

In-Order Traversal:

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def inorderTraversal(root):
    if root:
        inorderTraversal(root.left)
        print(root.val)
        inorderTraversal(root.right)
        
# Call the function
inorderTraversal(root)

Stacks:

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# Create a stack
stack = []

# Push elements onto the stack
stack.append('a')
stack.append('b')
stack.append('c')

# Pop elements from the stack
print(stack.pop())  # prints 'c'
print(stack.pop())  # prints 'b'

Loops (While Loop):

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# Using a while loop to iterate over the elements in an array
arr = [1, 2, 3]
i = 0
while i < len(arr):
    print(arr[i])
    i += 1

Conditional Statements:

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# If statements
a = 5
if a > 3:
    print("a is greater than 3")

Problem-Solving Approach:

Understand the problem: The task is to traverse a binary tree in an in-order fashion and return the values of the nodes in the order they were visited.
Define the problem requirements: Given a binary tree, return the in-order traversal of its nodes’ values.
Break down the problem: The problem can be broken down into simpler tasks:
- Traverse to the leftmost node of the tree.
- Visit the node, then traverse to its right subtree.
- Repeat this process for each node in the tree.
Develop a solution: The pseudocode for the solution can be written as:
- While there are unvisited nodes in the tree or the stack is not empty, push the current node into the stack and move to its left child.
- When there’s no left child, pop a node from the stack, visit it, and move to its right child.
- Repeat this process until all nodes have been visited.
Test the solution: The solution should be tested with various inputs to ensure it covers all scenarios. Consider edge cases such as an empty tree, a tree with only left children, and a tree with only right children.

Binary Tree Inorder Traversal

Identifying Problem Isomorphism

Problem Classification

Clarification Questions

Identifying Problem Isomorphism

Language Agnostic Coding Drills

Targeted Drills in Python

Similar Problems