Level Order Tree Traversal in Java (Time Complexity: O(n)) /homework

Input: [3, 9, 20, null, null, 15, 7]
    3
   / \
  9  20
    /  \
   15   7

Output: 
[
  [3],
  [9, 20],
  [15, 7]
]

Understanding the Problem

The core challenge of this problem is to traverse a binary tree level by level and return the values of the nodes at each level in a nested list. This type of traversal is known as level order traversal or breadth-first traversal.

Level order traversal is significant in many applications such as finding the shortest path in an unweighted graph, serialization/deserialization of a binary tree, and more.

Potential pitfalls include handling null nodes and ensuring that nodes are processed level by level.

Approach

To solve this problem, we can use a queue data structure to help us traverse the tree level by level. Here’s a step-by-step approach:

1. Initialize a queue and add the root node to it.
2. While the queue is not empty, do the following:
   • Determine the number of nodes at the current level (size of the queue).
   • For each node at the current level, remove it from the queue, add its value to the current level's list, and add its children to the queue.
   • After processing all nodes at the current level, add the current level's list to the result list.

This approach ensures that nodes are processed level by level.

Algorithm

Here is a step-by-step breakdown of the algorithm:

1. Check if the root is null. If it is, return an empty list.
2. Initialize a queue and add the root node to it.
3. Initialize an empty list to hold the result.
4. While the queue is not empty:
   • Get the number of nodes at the current level.
   • Initialize an empty list to hold the values of nodes at the current level.
   • For each node at the current level:
     • Remove the node from the queue.
     • Add its value to the current level's list.
     • Add its left and right children to the queue (if they exist).
   • Add the current level's list to the result list.
5. Return the result list.

Code Implementation

import java.util.ArrayList;
import java.util.LinkedList;
import java.util.List;
import java.util.Queue;

class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode(int x) { val = x; }
}

public class Solution {
    public List<List<Integer>> levelOrder(TreeNode root) {
        List<List<Integer>> result = new ArrayList<>();
        if (root == null) {
            return result;
        }
        
        Queue<TreeNode> queue = new LinkedList<>();
        queue.add(root);
        
        while (!queue.isEmpty()) {
            int levelSize = queue.size();
            List<Integer> currentLevel = new ArrayList<>();
            
            for (int i = 0; i < levelSize; i++) {
                TreeNode currentNode = queue.poll();
                currentLevel.add(currentNode.val);
                
                if (currentNode.left != null) {
                    queue.add(currentNode.left);
                }
                
                if (currentNode.right != null) {
                    queue.add(currentNode.right);
                }
            }
            
            result.add(currentLevel);
        }
        
        return result;
    }
}

Complexity Analysis

The time complexity of this approach is O(n), where n is the number of nodes in the binary tree. This is because each node is processed exactly once.

The space complexity is also O(n) due to the queue used to store nodes at each level.

Edge Cases

Some potential edge cases include:

• An empty tree (root is null).
• A tree with only one node.
• A tree where all nodes are on one side (e.g., a linked list).

Each of these cases is handled by the algorithm as it checks for null nodes and processes each node level by level.

Testing

To test the solution comprehensively, consider the following test cases:

• An empty tree.
• A tree with a single node.
• A balanced tree.
• An unbalanced tree.

Using a testing framework like JUnit can help automate and validate these test cases.

Thinking and Problem-Solving Tips

When approaching such problems, it’s helpful to:

• Understand the traversal method required (e.g., level order, in-order, pre-order, post-order).
• Use appropriate data structures (e.g., queue for level order traversal).
• Break down the problem into smaller steps and solve each step incrementally.

Practicing similar problems and studying different tree traversal algorithms can improve problem-solving skills.

Conclusion

Level order traversal is a fundamental tree traversal technique with various applications. Understanding and implementing this traversal helps in solving more complex tree-related problems. Practice and exploration of different traversal methods are key to mastering tree algorithms.

Additional Resources

For further reading and practice, consider the following resources:

• LeetCode: Binary Tree Level Order Traversal
• GeeksforGeeks: Level Order Tree Traversal
• Coursera: Data Structures