Height of Binary Tree in DSA C# - Build from Scratch

Height of Binary Tree

📖 Scenario: You are working on a program that manages a family tree. Each person can have children, forming a tree structure. You want to find out how many generations are in the family tree, which is the height of the tree.

🎯 Goal: Build a program that creates a binary tree representing family members, then calculates and prints the height of this tree.

📋 What You'll Learn

Create a binary tree node class called Node with int data, Node left, and Node right fields.

Create a binary tree with the exact structure given.

Create a method called Height that calculates the height of the binary tree recursively.

Print the height of the binary tree.

💡 Why This Matters

🌍 Real World

Binary trees are used in many applications like family trees, file systems, and decision trees. Calculating the height helps understand the depth or levels in these structures.

💼 Career

Understanding tree height calculation is fundamental for software engineers working with hierarchical data, databases, and algorithms involving trees.

1

Create the Node class and build the binary tree

Create a class called Node with an int data field and two Node fields called left and right. Then create the binary tree with root node data 1, left child 2, right child 3, left child of node 2 as 4, and right child of node 2 as 5.

DSA C#

// Define the Node class and create the binary tree nodes
// Your code here

Hint

Think of each Node as a person in the family tree. Each person can have a left and right child.

2

Create the Height method signature

Create a method called Height that takes a Node parameter called node and returns an int. This method will calculate the height of the binary tree starting from the given node.

DSA C#

public class Node
{
    public int data;
    public Node left;
    public Node right;

    public Node(int data)
    {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}

Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);

// Create the Height method signature below
// Your code here

Hint

The method should return an integer and take one parameter of type Node.

3

Implement the Height method logic

Complete the Height method to calculate the height of the binary tree recursively. If node is null, return 0. Otherwise, calculate the height of the left subtree and right subtree, then return the greater height plus 1.

DSA C#

public class Node
{
    public int data;
    public Node left;
    public Node right;

    public Node(int data)
    {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}

Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);

int Height(Node node)
{
    // Complete the method to calculate height recursively
    // Your code here
}

Hint

Use recursion to find the height of left and right children, then return the bigger one plus one.

4

Print the height of the binary tree

Use Console.WriteLine to print the height of the binary tree by calling Height(root).

DSA C#

public class Node
{
    public int data;
    public Node left;
    public Node right;

    public Node(int data)
    {
        this.data = data;
        this.left = null;
        this.right = null;
    }
}

Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);

int Height(Node node)
{
    if (node == null)
    {
        return 0;
    }
    int leftHeight = Height(node.left);
    int rightHeight = Height(node.right);
    return (leftHeight > rightHeight ? leftHeight : rightHeight) + 1;
}

// Print the height of the binary tree below
// Your code here

Hint

The height of the tree is the number of levels from root to the deepest leaf. Use Console.WriteLine(Height(root)) to print it.

Practice

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

easy

A. The number of edges on the longest path from root to a leaf

B. The total number of nodes in the tree

C. The number of leaf nodes in the tree

D. The number of children of the root node

Solution

1. Step 1: Understand the definition of height in a binary tree

   The height is defined as the longest path from the root node down to the farthest leaf node, counted by edges.

2. Step 2: Compare with other options

   Other options describe different properties: total nodes, leaf count, or root children, which are not height.

3. Final Answer:

   The number of edges on the longest path from root to a leaf -> Option A

4. Quick Check:

   Height = longest root-to-leaf edge count [OK]

Hint: Height counts edges, not nodes or leaves [OK]

Common Mistakes:

• Confusing height with total nodes
• Counting nodes instead of edges
• Thinking height is number of leaves

2. Which of the following C# method signatures correctly defines a recursive function to find the height of a binary tree node named root?

easy

A. public int Height(Node root, int height)

B. public void Height(Node root)

C. public int Height()

D. public int Height(Node root)

Solution

1. Step 1: Identify correct return type and parameters

   The height function must return an integer representing height, so return type is int. It needs the root node as input, so parameter is Node root.

2. Step 2: Check options for matching signature

   public int Height(Node root) matches: returns int and takes Node root. public void Height(Node root) returns void (wrong), C has no parameters (wrong), D has extra parameter not needed for basic height.

3. Final Answer:

   public int Height(Node root) -> Option D

4. Quick Check:

   Return int and take root node parameter [OK]

Hint: Height returns int and takes root node as parameter [OK]

Common Mistakes:

• Using void return type
• Missing root parameter
• Adding unnecessary parameters

3. What is the output of the following C# code snippet that calculates the height of a binary tree?

class Node {
  public int data;
  public Node left, right;
  public Node(int d) { data = d; left = right = null; }
}

int Height(Node root) {
  if (root == null) return -1;
  int leftHeight = Height(root.left);
  int rightHeight = Height(root.right);
  return Math.Max(leftHeight, rightHeight) + 1;
}

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

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

Console.WriteLine(Height(root));

medium

A. 1

B. 3

C. 2

D. 4

Solution

1. Step 1: Understand the height calculation logic

   Height returns -1 for null nodes. For leaf nodes, height = 0. Height is max of left and right subtree heights plus 1.

2. Step 2: Calculate height for given tree

   Node 4: left and right null, height = 0.
   Node 2: left height 0 (node 4), right null (-1), max=0 +1=1.
   Node 3: leaf, height=0.
   Root 1: left height 1, right height 0, max=1 +1=2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Height of root = 2 edges [OK]

Hint: Height counts edges; leaf node height is 0 [OK]

Common Mistakes:

• Counting nodes instead of edges
• Returning 0 for null instead of -1
• Miscomputing max height

4. Identify the error in this C# method to find the height of a binary tree and select the fix:

int Height(Node root) {
  if (root == null) return 0;
  int leftHeight = Height(root.left);
  int rightHeight = Height(root.right);
  return Math.Max(leftHeight, rightHeight);
}

medium

A. Change base case return from 0 to -1

B. Add +1 to the return statement after Math.Max

C. Remove recursive calls to left and right

D. Change Math.Max to Math.Min

Solution

1. Step 1: Analyze base case and return statement

   Base case returns 0 for null, which means height of empty tree is 0. The recursive calls get left and right heights correctly.

2. Step 2: Check final return calculation

   Height should be max of left and right heights plus 1 for current node. The code misses +1, so height is underestimated.

3. Final Answer:

   Add +1 to the return statement after Math.Max -> Option B

4. Quick Check:

   Height = max(left, right) + 1 [OK]

Hint: Add +1 after max to count current node [OK]

Common Mistakes:

• Forgetting +1 in return
• Changing base case incorrectly
• Using min instead of max

5. Given a binary tree where each node stores an integer, write a method to find the height of the tree and then return the sum of all node values at the maximum height level. Which approach correctly solves this problem?

hard

A. First find height, then traverse tree again to sum nodes at that height

B. Sum all nodes during height calculation recursively

C. Return height multiplied by root node value

D. Sum all leaf nodes regardless of height

Solution

1. Step 1: Understand problem requirements

   We need the height of the tree and sum of nodes at that height level (deepest level).

2. Step 2: Choose correct approach

   First find height, then traverse tree again to sum nodes at that height: Find height first, then traverse again to sum nodes at that level. This separates concerns and is clear.
   Sum all nodes during height calculation recursively tries to sum during height calculation, but height is computed bottom-up and summing nodes at max height requires separate traversal.
   Return height multiplied by root node value and D do not meet problem requirements.

3. Final Answer:

   First find height, then traverse tree again to sum nodes at that height -> Option A

4. Quick Check:

   Two-pass approach: height then sum at height [OK]

Hint: Find height first, then sum nodes at that level [OK]

Common Mistakes:

• Trying to sum nodes during height recursion
• Multiplying height by root value
• Summing all leaf nodes ignoring height