Vertical Order Traversal of Binary Tree in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Vertical Order Traversal of a Binary Tree?

It is a way to print the nodes of a binary tree column by column, from left to right. Nodes in the same vertical line are grouped together.

beginner

How do we assign vertical levels to nodes in Vertical Order Traversal?

The root node is at vertical level 0. Left child nodes decrease the vertical level by 1, and right child nodes increase it by 1.

intermediate

Which data structure is commonly used to keep track of nodes and their vertical levels during traversal?

A queue is used for level order traversal, and a dictionary (or map) stores nodes grouped by their vertical levels.

intermediate

Why do we sort nodes by their horizontal distance and level in Vertical Order Traversal?

Sorting ensures nodes are printed from leftmost vertical line to rightmost, and within the same vertical line, from top to bottom.

advanced

What is the time complexity of Vertical Order Traversal using BFS and a map?

It is O(N log N) because we visit each node once (O(N)) and then sort the keys of the map (O(K log K)) for output, where K is the number of vertical levels.

In Vertical Order Traversal, what vertical level is assigned to the root node?

A Depends on tree height

B 1

C -1

D 0

The root node is always assigned vertical level 0.

Which traversal method is best suited for Vertical Order Traversal?

A Level order (BFS)

B Inorder

C Preorder

D Postorder

Level order traversal helps process nodes level by level, which is useful for vertical grouping.

If a node is at vertical level 2, where is it located relative to the root?

A At the root

B Two steps to the left

C Two steps to the right

D One step to the right

Positive vertical levels mean nodes are to the right of the root.

What data structure is used to group nodes by their vertical levels?

A Dictionary or Map

B Stack

C Queue

D Linked List

A dictionary or map stores nodes grouped by their vertical levels.

What is the main reason for sorting vertical levels before printing?

A To print nodes from top to bottom

B To print nodes from left to right vertical lines

C To print nodes in random order

D To print nodes by their values

Sorting vertical levels ensures printing from leftmost to rightmost vertical lines.

Explain how vertical levels are assigned and used in Vertical Order Traversal of a binary tree.

Think about how you move left or right from the root.

Describe the steps to perform Vertical Order Traversal using a queue and a map.

Consider how you visit nodes and keep track of their positions.

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