Diameter of Binary Tree in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the diameter of a binary tree?

The diameter of a binary tree is the length of the longest path between any two nodes in the tree. This path may or may not pass through the root.

intermediate

How do you calculate the diameter of a binary tree using recursion?

Calculate the height of left and right subtrees for each node. The diameter at that node is the sum of these heights. The overall diameter is the maximum of all such values.

intermediate

What is the time complexity of the naive approach to find the diameter of a binary tree?

The naive approach has O(n^2) time complexity because it calculates height for each node repeatedly.

advanced

How can you optimize the diameter calculation to O(n)?

Use a single recursive function that returns the height of the subtree and updates the diameter during the recursion, avoiding repeated height calculations.

beginner

In C#, what data structure is commonly used to represent a binary tree node for diameter calculation?

A class with properties for the node's value and references to left and right child nodes, for example: public class TreeNode { public int val; public TreeNode left; public TreeNode right; }

What does the diameter of a binary tree represent?

A The height of the tree

B The longest path between any two nodes

C The number of leaf nodes

D The number of nodes in the tree

The diameter is the longest path between any two nodes in the tree.

Which of these is true about the diameter path in a binary tree?

A It always ends at a leaf node

B It always passes through the root

C It may or may not pass through the root

D It is the same as the height of the tree

The diameter path may or may not pass through the root node.

What is the main drawback of the naive diameter calculation approach?

A Calculates height multiple times causing O(n^2) time

B Does not find the correct diameter

C Uses too much memory

D Only works for balanced trees

The naive approach recalculates heights repeatedly, leading to O(n^2) time complexity.

How can you improve the diameter calculation to run in O(n) time?

A Use iterative traversal only

B Calculate diameter separately for left and right subtrees

C Use breadth-first search

D Calculate height and diameter in the same recursion

Calculating height and updating diameter in the same recursion avoids repeated work.

In C#, which keyword is used to define a binary tree node class?

A class

B struct

C interface

D enum

A binary tree node is typically defined using a class in C#.

Explain how to find the diameter of a binary tree using a single recursive function.

Think about combining height calculation and diameter update in one step.

Describe the difference between the diameter and height of a binary tree.

Focus on what each measurement represents in the tree.

Practice

1. What does the diameter of a binary tree represent?

easy

A. The length of the longest path between any two nodes in the tree

B. The height of the tree from root to the deepest leaf

C. The total number of nodes in the tree

D. The number of leaf nodes in the tree

Solution

1. Step 1: Understand the diameter concept

   The diameter is the longest path between any two nodes, which may or may not pass through the root.

2. Step 2: Differentiate from height and node count

   Height is the longest path from root to leaf, node count is total nodes, and leaf count is number of leaves, none of which define diameter.

3. Final Answer:

   The length of the longest path between any two nodes in the tree -> Option A

4. Quick Check:

   Diameter = longest path between nodes [OK]

Hint: Diameter is longest path, not just height or node count [OK]

Common Mistakes:

• Confusing diameter with tree height
• Thinking diameter counts nodes instead of edges
• Assuming diameter must pass through root

2. Which of the following C# method signatures is correct for a function that calculates the diameter of a binary tree node?

easy

A. Diameter public int(TreeNode root)

B. int Diameter(TreeNode root) void

C. public void Diameter(TreeNode root) int

D. public int Diameter(TreeNode root)

Solution

1. Step 1: Review C# method signature syntax

   In C#, method signature starts with access modifier, return type, method name, and parameters in parentheses.

2. Step 2: Check each option

   public int Diameter(TreeNode root) follows correct syntax: public int Diameter(TreeNode root). Others have incorrect order or missing parts.

3. Final Answer:

   public int Diameter(TreeNode root) -> Option D

4. Quick Check:

   Correct C# method syntax = public int Diameter(TreeNode root) [OK]

Hint: Method signature: access modifier + return type + name + parameters [OK]

Common Mistakes:

• Placing return type after parameters
• Omitting access modifier or return type
• Incorrect order of keywords

3. Given the following binary tree code snippet, what is the diameter of the tree?

class TreeNode {
  public int val;
  public TreeNode left, right;
  public TreeNode(int v) { val = v; }
}

// Tree structure:
//       1
//      / \
//     2   3
//    / 
//   4

TreeNode root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);
root.left.left = new TreeNode(4);

int diameter = CalculateDiameter(root); // Assume CalculateDiameter correctly implemented
Console.WriteLine(diameter);

medium

A. 3

B. 2

C. 4

D. 5

Solution

1. Step 1: Visualize the tree and longest path

   The longest path is from node 4 to node 3: path length = edges 4->2->1->3 = 3 edges.

2. Step 2: Calculate diameter as number of edges

   Diameter counts edges, so longest path length is 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Longest path edges = 3 [OK]

Hint: Count edges on longest path, not nodes [OK]

Common Mistakes:

• Counting nodes instead of edges
• Assuming diameter passes through root only
• Ignoring one side of the tree

4. Identify the bug in this C# code snippet for calculating the diameter of a binary tree:

int maxDiameter = 0;
int Depth(TreeNode node) {
  if (node == null) return 0;
  int left = Depth(node.left);
  int right = Depth(node.right);
  maxDiameter = Math.Max(maxDiameter, left + right + 1);
  return Math.Max(left, right) + 1;
}

int Diameter(TreeNode root) {
  Depth(root);
  return maxDiameter;
}

medium

A. The base case should return 1 instead of 0

B. Diameter should be maxDiameter - 1 because diameter counts edges, not nodes

C. maxDiameter should be reset inside Depth method

D. Depth method should return left + right instead of max

Solution

1. Step 1: Understand diameter counting edges vs nodes

   The code adds left + right + 1 (nodes), but diameter counts edges, so subtract 1.

2. Step 2: Fix return value in Diameter method

   Return maxDiameter - 1 to convert node count to edge count for diameter.

3. Final Answer:

   Diameter should be maxDiameter - 1 because diameter counts edges, not nodes -> Option B

4. Quick Check:

   Diameter edges = nodes - 1 [OK]

Hint: Diameter = nodes on path - 1 (edges) [OK]

Common Mistakes:

• Returning maxDiameter directly without subtracting 1
• Changing base case return value incorrectly
• Resetting maxDiameter inside recursive calls

5. You want to find the diameter of a binary tree but also return the path nodes forming that diameter. Which approach correctly extends the diameter calculation?

hard

A. Calculate diameter first, then do a separate BFS to find the path

B. Store all paths from root to leaves and pick the longest one

C. Modify the recursive function to return both depth and path, updating max path when diameter increases

D. Use a queue to traverse level by level and count nodes

Solution

1. Step 1: Understand diameter and path relationship

   Diameter is longest path between any two nodes, so tracking path during recursion helps capture it.

2. Step 2: Extend recursion to return depth and path

   Modify recursive calls to return depth and path list; update max path when a longer diameter is found.

3. Step 3: Compare other options

   Calculate diameter first, then do a separate BFS to find the path is inefficient; C only finds longest root-to-leaf path, not diameter; D is unrelated to diameter.

4. Final Answer:

   Modify the recursive function to return both depth and path, updating max path when diameter increases -> Option C

5. Quick Check:

   Track depth and path together for diameter path [OK]

Hint: Return depth and path in recursion to track diameter path [OK]

Common Mistakes:

• Trying to find path after diameter without tracking during recursion
• Confusing longest root-to-leaf path with diameter
• Using BFS level order traversal which doesn't find diameter