Solving Binary Tree Level Order Traversal: Navigating Trees by Level

The "Binary Tree Level Order Traversal" problem involves traversing a binary tree level by level, collecting nodes at each level in separate lists.

Problem Statement

Given the root of a binary tree, return the level order traversal of its nodes' values. (i.e., from left to right, level by level).

Example

Consider a binary tree:

Level order traversal of this tree is [[3], [9,20], [15,7]].

Solution Approach - Queue-Based Traversal

class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;

  constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
    this.val = val === undefined ? 0 : val;
    this.left = left === undefined ? null : left;
    this.right = right === undefined ? null : right;
  }
}

function levelOrder(root: TreeNode | null): number[][] {
  if (!root) return [];

  const result: number[][] = [];
  const queue: TreeNode[] = [root];

  while (queue.length) {
    const levelSize = queue.length;
    const currentLevel: number[] = [];

    for (let i = 0; i < levelSize; i++) {
      const node = queue.shift();
      if (node) {
        currentLevel.push(node.val);
        if (node.left) queue.push(node.left);
        if (node.right) queue.push(node.right);
      }
    }

    result.push(currentLevel);
  }

  return result;
}

Breaking Down the Solution

• Queue Mechanism: Use a queue to keep track of nodes at each level.
• Iterative Traversal: Iteratively process nodes in the queue, adding their children to the queue for the next level.
• Collecting Levels: Collect the values of nodes at each level in separate lists.

Conclusion

Binary Tree Level Order Traversal is a fundamental problem in tree algorithms, emphasizing breadth-first traversal and demonstrating the practical use of queues in managing hierarchical data structures.