Vertical Order Traversal of Binary Tree
A hard Binary Trees problem included in Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Binary Trees
- Sheets
- 1
- Core for
- 4 roles
- Platform
- LeetCode
The problem
Given the root of a binary tree, return the vertical order traversal of its nodes' values. For each vertical column from left to right, list the node values top to bottom, and within the same row and column, sort by value.
Example 1
- Input
- [3,9,20,null,null,15,7]
- Output
- [[9],[3,15],[20],[7]]
- Why
- Column -1 has 9, column 0 has 3 and 15, column 1 has 20, column 2 has 7.
Example 2
- Input
- [1,2,3,4,5,6,7]
- Output
- [[4],[2],[1,5,6],[3],[7]]
- Why
- Nodes are grouped by their horizontal distance from the root.
Example 3
- Input
- [1]
- Output
- [[1]]
- Why
- A single node forms one column.
Constraints
- The number of nodes is in the range [1, 1000].
- -1000 <= Node.val <= 1000
How to think about it
Updated 2026-09-09Every node occupies an exact 2D coordinate: root is at (row 0, col 0), moving left yields (row + 1, col - 1), and moving right yields (row + 1, col + 1). Grouping nodes by column and ordering each column primarily by row and secondarily by value turns a spatial layout into sorted bucket aggregation.
Approaches, worst first
DFS coordinate collection and global sort
time O(n log n) · space O(n)
Traverse tree tracking `(col, row, val)`. Store all triplets in a list. Sort by `col` ascending, then `row` ascending, then `val` ascending. Group matching columns into output arrays.
BFS column map with row-group sortingWrite this one
time O(n log n) · space O(n)
Use BFS queue storing `(node, col, row)`. Use a map of `col -> row -> list` to preserve natural top-to-bottom row ordering. Sort only nodes that collide on both the same row and column, then assemble columns from minimum to maximum.
Where people lose marks · 3
- Failing to sort nodes that share the exact same row and column by value; natural traversal order does not satisfy the tie-breaking rule.
- Using DFS without tracking rows causes deeper nodes to appear before shallower nodes in the same column.
- Assuming column indices are non-negative; left subtrees produce negative column coordinates.
The theory behind it
Binary Trees — the ground this problem stands on. All Binary Trees problems
What Binary Trees is
A binary tree is a branching data structure that starts at a single top node called the root, like an upside-down family tree. Every node holds a piece of data and can branch out to at most two children below it, known as the left child and the right child. Because there is no ordering rule about which values go left or right, finding a specific item can require checking every single node in the entire tree.
When to reach for it
Reach for binary trees when problems present hierarchical data with left and right child pointers. Questions asking for tree height, maximum depth, path sums from root to leaf, diameter, lowest common ancestor, or checking whether two trees are mirror reflections of each other all signal binary tree traversals. Any problem asking to inspect or reconstruct a tree layer by layer or path by path belongs here.
How the pattern works
Think recursively by focusing on what a single node must do. If the current node is null, return the base answer immediately. Otherwise, ask the left child for its result, ask the right child for its result, and combine both answers with the current node value before returning up to the parent. For horizontal scans, use a queue to read nodes layer by layer, measuring the queue length at the start of each layer to group nodes by depth.
What each operation costs
| Operation | Time |
|---|---|
| traverse all nodes using recursion or queue | O(n) |
| search for an arbitrary value in an unordered tree | O(n) |
| call stack memory on balanced tree | O(log n) |
| call stack memory on skewed tree | O(n) |
What usually goes wrong with Binary Trees
- Dereferencing left or right child pointers without checking if the current node is null, throwing null pointer errors on empty trees or leaf nodes.
- Defining a leaf node incorrectly by stopping when either child is null instead of checking that both left and right children are simultaneously null.
- Computing tree diameter by taking left height plus right height inside a recursive helper without updating a global maximum across every visited node.
Which roles need this problem
Binary Trees is a core topic for these 4 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 5 more roles, including Full-Stack Developer, Android Developer, iOS Developer.
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