Binary Tree Level Order Traversal
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).
Constraints:
- The number of nodes in the tree is in the range [0, 2000]
- -1000 <= Node.val <= 1000
Input Format:
- The root of a binary tree
Output Format:
- An array where each inner array contains the values from a level of the tree
Examples:
Example 1:
Input:
root = [3,9,20,null,null,15,7]
Output:
[[3],[9,20],[15,7]]
Explanation:
Level order traversal returns the values grouped by level, top to bottom, left to right.
Example 2:
Input:
root = [1]
Output:
[[1]]
Explanation:
A tree with just one node has only one level.
Example 3:
Input:
root = []
Output:
[]
Explanation:
An empty tree has no values.
Solutions
BFS with Queue
Use a queue to traverse the tree level by level.
Recursive Approach
Use recursion with a helper function to process each level.
Algorithm Walkthrough
Example input:
Step-by-step execution:
- root = [3,9,20,null,null,15,7]
- queue = [3], result = []
- process level 0: queue = [], currentLevel = [3], result = [[3]]
- add children: queue = [9, 20]
- process level 1: queue = [], currentLevel = [9, 20], result = [[3], [9, 20]]
- add children: queue = [15, 7]
- process level 2: queue = [], currentLevel = [15, 7], result = [[3], [9, 20], [15, 7]]
- queue is empty, return result = [[3], [9, 20], [15, 7]]
Hints
Hint 1
Hint 2
Hint 3
Video Tutorial
Video tutorials can be a great way to understand algorithms visually
Visualization
Visualize the tree and the level-by-level traversal process.
Key visualization elements:
- current node
- current level
- queue state
Implementation Notes
Level order traversal is a breadth-first search (BFS) approach to traversing a tree. It's particularly useful for problems that require processing nodes level by level or finding the shortest path in a tree.