Is Binary Tree Vertical Order Traversal easy or hard?

The problem is generally classified as medium difficulty. The challenge lies in correctly tracking column indices while maintaining the required top-to-bottom ordering. Once you recognize that BFS naturally preserves level order, the implementation becomes straightforward.

Binary Tree Vertical Order Traversal Python/Java solution

Implementations typically use BFS with a queue of (node, column) pairs. Python solutions often use collections.deque and defaultdict, while Java implementations rely on Queue and HashMap. Both versions achieve O(n) time and O(n) space complexity.

How to solve Binary Tree Vertical Order Traversal in O(n)?

Use BFS with a queue storing (node, column) pairs. Maintain a hash map from column index to a list of node values. Track the minimum and maximum column indices during traversal so the final result can be constructed without sorting. Each node is visited once, giving O(n) time complexity.

What is the best approach for Binary Tree Vertical Order Traversal?

Breadth-first search with column indexing is the most common approach. Each node is processed with its column number while a hash map groups nodes belonging to the same column. BFS guarantees nodes are visited level by level, which preserves top-to-bottom order. The solution runs in O(n) time and O(n) space.

Is Binary Tree Vertical Order Traversal asked at Google/Amazon/Meta?

Binary tree traversal variations frequently appear in interviews at companies like Google, Amazon, and Meta. Vertical order traversal specifically tests understanding of BFS, coordinate mapping, and hash map grouping. It is a common medium-level problem in technical interview prep sets.

What data structure is used in Binary Tree Vertical Order Traversal?

The core data structures are a queue for BFS traversal and a hash map that maps column indices to lists of node values. The queue ensures nodes are processed level by level, while the hash map groups nodes belonging to the same vertical column.

What is the time complexity of Binary Tree Vertical Order Traversal?

The optimal BFS solution runs in O(n) time because every node in the binary tree is visited exactly once. Space complexity is also O(n) due to the queue and the hash map storing column groups. A DFS-based solution usually requires sorting column indices, increasing time complexity to O(n log n).

Description Hints 4 Solution Video 13:13

314. Binary Tree Vertical Order Traversal

Medium57.8% acceptance9 companiesPremium elsewhere, free here

Given the root of a binary tree, return the vertical order traversal of its nodes' values. (i.e., from top to bottom, column by column).

If two nodes are in the same row and column, the order should be from left to right.

Example 1:

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

Example 2:

Input: root = [3,9,8,4,0,1,7]
Output: [[4],[9],[3,0,1],[8],[7]]

Example 3:

Input: root = [1,2,3,4,10,9,11,null,5,null,null,null,null,null,null,null,6]
Output: [[4],[2,5],[1,10,9,6],[3],[11]]

Constraints:

The number of nodes in the tree is in the range [0, 100].
-100 <= Node.val <= 100

Asked at 9 companies

Meta Snapchat Anduril Bloomberg Apple DoorDash

Google Amazon Microsoft

Topics

Hints open one at a time

Hint 1

Do BFS from the root. Let the root be at column 0. In the BFS, keep in the queue the node and its column.

Hint 2

When you traverse a node, store its value in the column index. For example, the root's value should be stored at index 0.

Hint 3

If the node has a left node, it column should be col - 1. Similarly, if the node has a right node, its column should be col + 1.

Hint 4

At the end, check the minimum and maximum col and output their values.

13:13

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