Vertical Order Traversal of Binary Tree in DSA C# - Build from Scratch

Vertical Order Traversal of Binary Tree

📖 Scenario: Imagine you have a family tree drawn on paper. You want to read the names vertically from top to bottom, left to right, to see who belongs to which vertical line.

🎯 Goal: Build a program that takes a binary tree and prints the nodes in vertical order traversal. Nodes in the same vertical line are grouped together from top to bottom, and vertical lines are printed from left to right.

📋 What You'll Learn

Create a binary tree using a TreeNode class with int val, TreeNode left, and TreeNode right fields

Use a dictionary to group nodes by their vertical column index

Traverse the tree using a breadth-first search (BFS) approach with a queue

Print the vertical order traversal as lists of node values grouped by their vertical columns

💡 Why This Matters

🌍 Real World

Vertical order traversal helps visualize hierarchical data like family trees, organizational charts, or layered maps where vertical grouping matters.

💼 Career

Understanding tree traversals and grouping data by position is useful in software engineering roles involving data structures, UI rendering, and spatial data processing.

1

Create the Binary Tree Structure

Create a class called TreeNode with an int val field, and two TreeNode fields called left and right. Then create a binary tree with root node value 1, left child value 2, and right child value 3.

DSA C#

// Define TreeNode class and create root with left and right children
// Your code here

Hint

Define the TreeNode class first, then create root and assign its left and right children.

2

Set Up a Dictionary to Group Nodes by Column

Create a dictionary called columnTable that maps int keys to List<int> values. This will store node values grouped by their vertical column index.

DSA C#

public class TreeNode
{
    public int val;
    public TreeNode left;
    public TreeNode right;

    public TreeNode(int val = 0, TreeNode left = null, TreeNode right = null)
    {
        this.val = val;
        this.left = left;
        this.right = right;
    }
}

TreeNode root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);

// Create a dictionary called columnTable to map int to List
// Your code here

Hint

Use Dictionary<int, List<int>> to group node values by their column index.

3

Traverse the Tree and Fill the Dictionary

Use a queue of tuples Queue<(TreeNode node, int column)> to perform a breadth-first search (BFS). Start by enqueueing (root, 0). While the queue is not empty, dequeue an element, add its value to columnTable under the key column. Enqueue the left child with column - 1 and the right child with column + 1 if they exist.

DSA C#

using System.Collections.Generic;

public class TreeNode
{
    public int val;
    public TreeNode left;
    public TreeNode right;

    public TreeNode(int val = 0, TreeNode left = null, TreeNode right = null)
    {
        this.val = val;
        this.left = left;
        this.right = right;
    }
}

TreeNode root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);

Dictionary> columnTable = new Dictionary>();

// Use a Queue for BFS traversal
// Your code here

Hint

Use a queue to visit nodes level by level. Track each node's column index and add its value to the dictionary.

4

Print the Vertical Order Traversal

Sort the keys of columnTable and print the lists of node values for each column in order from smallest to largest key.

DSA C#

using System;
using System.Collections.Generic;

public class TreeNode
{
    public int val;
    public TreeNode left;
    public TreeNode right;

    public TreeNode(int val = 0, TreeNode left = null, TreeNode right = null)
    {
        this.val = val;
        this.left = left;
        this.right = right;
    }
}

TreeNode root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);

Dictionary> columnTable = new Dictionary>();

Queue queue = new Queue();
queue.Enqueue((root, 0));

while (queue.Count > 0)
{
    var (node, column) = queue.Dequeue();
    if (!columnTable.ContainsKey(column))
    {
        columnTable[column] = new List();
    }
    columnTable[column].Add(node.val);

    if (node.left != null)
    {
        queue.Enqueue((node.left, column - 1));
    }
    if (node.right != null)
    {
        queue.Enqueue((node.right, column + 1));
    }
}

// Print the vertical order traversal sorted by column
// Your code here

Hint

Sort the keys of columnTable and print the values in order, separated by commas.

Practice

1. What does the vertical order traversal of a binary tree represent?

easy

A. Nodes grouped by their depth level from top to bottom

B. Nodes grouped by their vertical columns from left to right

C. Nodes visited in preorder (root, left, right)

D. Nodes visited in postorder (left, right, root)

Solution

1. Step 1: Understand vertical order traversal

   Vertical order traversal groups nodes by their vertical columns, where the root is at column 0, left child at column -1, right child at column +1, and so on.

2. Step 2: Compare with other traversals

   Unlike level order or preorder, vertical order focuses on columns, not depth or visit order.

3. Final Answer:

   Nodes grouped by their vertical columns from left to right -> Option B

4. Quick Check:

   Vertical order = nodes by vertical columns [OK]

Hint: Vertical order groups nodes by columns, not levels or visit order [OK]

Common Mistakes:

• Confusing vertical order with level order traversal
• Thinking vertical order is preorder or postorder
• Ignoring the horizontal distance concept

2. Which of the following C# code snippets correctly initializes a dictionary to store vertical order traversal results where keys are integers and values are lists of integers?

easy

A. var dict = new Dictionary();

B. var dict = new Dictionary();

C. var dict = new Dictionary();

D. var dict = new List>();

Solution

1. Step 1: Identify the data structure needed

   We need a dictionary with integer keys (vertical columns) and list of integers as values (nodes in that column).

2. Step 2: Match with C# syntax

   var dict = new Dictionary(); correctly declares Dictionary. Others have wrong types or collections.

3. Final Answer:

   var dict = new Dictionary(); -> Option A

4. Quick Check:

   Dictionary for vertical order [OK]

Hint: Use Dictionary for vertical columns and nodes [OK]

Common Mistakes:

• Swapping key and value types
• Using List instead of Dictionary for mapping
• Incorrect generic type order

3. Given the following binary tree and C# code for vertical order traversal, what is the printed output?

    1
   / \
  2   3
 / \   \
4   5   6

// Code snippet:
var result = new Dictionary();
void Traverse(TreeNode node, int col) {
  if (node == null) return;
  if (!result.ContainsKey(col)) result[col] = new List<int>();
  result[col].Add(node.val);
  Traverse(node.left, col - 1);
  Traverse(node.right, col + 1);
}
Traverse(root, 0);
foreach (var col in result.OrderBy(k => k.Key)) {
  Console.Write(string.Join(",", col.Value) + " ");
}

medium

A. 4 2 1 5 3 6

B. 4,2 1,5,3 6

C. 4 2 1,5 3 6

D. 4,2 1 5,3 6

Solution

1. Step 1: Assign columns to nodes

   Root 1 at col 0; 2 at -1; 3 at +1; 4 at -2; 5 at 0; 6 at +2.

2. Step 2: Group nodes by column and order

   col -2: [4], col -1: [2], col 0: [1,5], col 1: [3], col 2: [6]. Printed as 4 2 1,5 3 6 (commas inside multi-node groups, spaces between columns).

3. Final Answer:

   4 2 1,5 3 6 -> Option C

4. Quick Check:

   Vertical groups with commas inside, spaces between [OK]

Hint: Track column indices and group nodes before printing [OK]

Common Mistakes:

• Mixing node order inside columns
• Printing without commas or spaces correctly
• Ignoring column sorting

4. The following C# code attempts vertical order traversal but throws a runtime error. What is the main issue?

void Traverse(TreeNode node, int col, Dictionary dict) {
  if (node == null) return;
  dict[col].Add(node.val);
  Traverse(node.left, col - 1, dict);
  Traverse(node.right, col + 1, dict);
}

var dict = new Dictionary();
Traverse(root, 0, dict);

medium

A. Dictionary should use List<int> as key

B. Traverse method should return a value

C. Incorrect base case for recursion

D. Dictionary keys are not initialized before adding values

Solution

1. Step 1: Analyze dictionary usage

   Code tries to add to dict[col] without checking if key col exists, causing KeyNotFoundException.

2. Step 2: Fix by initializing keys

   Before adding, check if dict contains col; if not, create new List<int> for that key.

3. Final Answer:

   Dictionary keys are not initialized before adding values -> Option D

4. Quick Check:

   Initialize dictionary keys before adding [OK]

Hint: Always check and initialize dictionary keys before adding [OK]

Common Mistakes:

• Assuming dictionary auto-creates keys
• Ignoring null checks on dictionary values
• Confusing recursion base case with dictionary errors

5. You want to perform vertical order traversal but also sort nodes by their depth (top to bottom) within each vertical column. Which data structure and approach is best in C#?

hard

A. Use a Dictionary> and sort each list by depth after traversal

B. Use a Dictionary and enqueue nodes as visited

C. Use a List<int> and sort by node value after traversal

D. Use a Dictionary and push nodes in preorder

Solution

1. Step 1: Understand sorting by depth requirement

   We must store nodes with their depth info to sort them top to bottom within each vertical column.

2. Step 2: Choose data structure and approach

   Dictionary with key as column and value as list of (depth, value) pairs allows sorting by depth after traversal.

3. Final Answer:

   Use a Dictionary> and sort each list by depth after traversal -> Option A

4. Quick Check:

   Store depth with nodes, then sort by depth [OK]

Hint: Store depth with nodes, then sort lists by depth per column [OK]

Common Mistakes:

• Using queue or stack without depth info
• Sorting by node value instead of depth
• Ignoring depth when grouping nodes