Binary Tree Level Order Traversal Leetcode Problem 102 [Python]

In the world of programming, solving various coding challenges is a great way to sharpen your problem-solving skills, so Binary Tree Level Order Traversal Leetcode Problem!

In this blog post, we’re going to tackle the Binary Tree Level Order Traversal problem, specifically problem number 102 on LeetCode.

This problem falls under the category of Trees and is of medium difficulty.

We’ll explore this problem step by step, providing a Python solution, discussing time and space complexity, and offering a clear understanding of the constraints and edge cases involved.

By the end of this post, you’ll be well-equipped to tackle this problem on your own.

Let’s get started!

Problem Overview

The problem statement is as follows:
Given the root of a binary tree, your task is to return the level order traversal of its nodes’ values.

The level order traversal means that you should traverse the tree from left to right, level by level.

Here’s an example to illustrate the concept:

Input: root = [3,9,20,null,null,15,7]
Output: [[3],[9,20],[15,7]]

In this example, the tree is structured in such a way that the traversal happens level by level, creating a list of lists as the output.

The first list contains the root node, the second list contains the nodes from the second level, and so on.

To tackle this problem, we’ll use a popular algorithm called Breadth-First Search (BFS).

This algorithm allows us to explore the tree level by level, just as required.

Understanding Constraints

Before diving into the solution, it’s crucial to understand the constraints of the problem.

These constraints define the limits within which our solution should operate.

For the Binary Tree Level Order Traversal problem, the constraints are as follows:

• The number of nodes in the tree is in the range [0, 2000].
• The values of the nodes (Node.val) are in the range of -1000 to 1000. These constraints tell us that we might encounter trees with varying sizes, from empty trees to trees with up to 2000 nodes.

Additionally, the node values can be any integer within the specified range.

Understanding these constraints helps us design a solution that works efficiently for a wide range of inputs.

Binary Tree Level Order Traversal LeetCode Problem Solution

Bruteforce Approach

To solve this problem efficiently, we’ll implement a Python solution using the BFS algorithm.

We’ll start by initializing two important data structures: result (to store the final result) and a queue (to perform the BFS).

Let’s begin by looking at the Python code that implements the BFS algorithm:

def levelOrder(self, root: TreeNode) -> List[List[int]]:
    res = []  # Initialize the result list
    q = collections.deque()  # Initialize a queue
    if root:
        q.append(root)  # Add the root node to the queue

    while q:
        val = []

        for i in range(len(q)):
            node = q.popleft()
            val.append(node.val)

            if node.left:
                q.append(node.left)

            if node.right:
                q.append(node.right)

        res.append(val)  # Add the values of this level to the result

    return res

In this code, we define a function levelOrder that takes the root of the binary tree as input and returns a list of lists containing the level order traversal.

Here’s a step-by-step explanation of the code:

1. We initialize an empty list called res to store the final result.
2. We create a queue using Python’s collections.deque() data structure.

The queue will help us perform BFS efficiently.

3. We check if the input root is not empty.

If the root exists, we add it to the queue to kickstart the BFS process.

4. We enter a while loop that continues until the queue is empty, indicating that we’ve processed all levels of the tree.
5. Inside the loop, we create an empty list called val to store the values of the current level.
6. We use a for loop to iterate through the nodes at the current level.

The length of the queue (len(q)) indicates the number of nodes at the current level.

7. We use q.popleft() to remove and retrieve the leftmost node from the queue.

We append its value to the val list.

8. If the current node has a left child, we add it to the queue for further exploration.
9. If the current node has a right child, we add it to the queue as well.
10. Once we’ve processed all nodes at the current level and added their values to the val list, we append the val list to the res list.
11. We repeat this process for each level of the tree, ensuring that we traverse the tree level by level.
12. Finally, we return the res list, which contains the level order traversal of the binary tree.

Time and Space Complexity

Now, let’s analyze the time and space complexity of our solution:

Time Complexity: The time complexity of this solution is O(n), where n is the number of nodes in the binary tree.

This is because we visit each node exactly once during the BFS traversal.

Space Complexity: The space complexity is also O(n).

In the worst case, our queue could store up to n/2 nodes (for a perfectly balanced binary tree), but this is still O(n).

Reasoning Behind Our Approach

The approach we’ve taken here leverages the Breadth-First Search (BFS) algorithm, which is a natural choice for problems that involve traversing a tree level by level.

The key insight is that BFS allows us to process nodes level by level and create the desired structure for the output.

We use a queue to keep track of nodes at each level, and by iterating through the queue, we collect the values of nodes at each level, creating sublists that represent the levels.

As we move from one level to the next, we continue to explore the tree, ensuring that we maintain the correct order.

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Conclusion

In this blog post, we tackled the LeetCode problem Binary Tree Level Order Traversal (Problem 102).

We provided a Python solution that effectively employs the Breadth-First Search (BFS) algorithm to traverse the binary tree level by level.

We discussed the problem’s constraints, the rationale behind our approach, and the time and space complexity of our solution.

By understanding and implementing this solution, you’ve gained valuable problem-solving skills that can be applied to similar tree traversal problems.

Solving coding challenges like this one is an excellent way to enhance your programming skills and algorithmic thinking.

We encourage you to practice this solution and explore other coding challenges on LeetCode.

If you found this post helpful or have any questions, please feel free to comment, ask questions, make suggestions, and share the content.

Your engagement and feedback are highly valuable.

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Thank you for reading, and happy coding!