Height of Binary Tree in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return 0 when the node is null.

DSA C#

if (node == null) return [1];

Drag options to blanks, or click blank then click option'

A1

B0

C-1

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 1 instead of 0 for null node.

Returning null which causes errors.

When the node is null, the height is 0 because there are no nodes below.

2fill in blank

medium

Complete the code to calculate the height of the left subtree.

DSA C#

int leftHeight = [1](node.left);

Drag options to blanks, or click blank then click option'

Aheight

BHeight

CGetHeight

DCalculateHeight

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect method names causing compile errors.

Using uppercase 'Height' if method is lowercase.

The method name is 'height' and it is called recursively on the left child.

3fill in blank

hard

Fix the error in returning the height by adding 1 to the maximum of left and right heights.

DSA C#

return 1 + Math.[1](leftHeight, rightHeight);

Drag options to blanks, or click blank then click option'

AMaxValue

BMin

CMax

DMaximum

Attempts:

3 left

💡 Hint

Common Mistakes

Using Math.Min which returns the smaller value.

Using incorrect method names like Maximum.

We use Math.Max to get the larger height between left and right subtrees.

4fill in blank

hard

Fill both blanks to calculate the height of left and right subtrees recursively.

DSA C#

int leftHeight = [1](node.left);
int rightHeight = [2](node.right);

Drag options to blanks, or click blank then click option'

Aheight

BGetHeight

CCalculateHeight

DHeight

Attempts:

3 left

💡 Hint

Common Mistakes

Using different method names causing errors.

Using uppercase when method is lowercase.

The method 'height' is called recursively on both left and right children.

5fill in blank

hard

Fill all three blanks to complete the height function of a binary tree.

DSA C#

public int height(Node node) {
    if (node == null) return [1];
    int leftHeight = [2](node.left);
    int rightHeight = [3](node.right);
    return 1 + Math.Max(leftHeight, rightHeight);
}

Drag options to blanks, or click blank then click option'

A0

Bheight

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 1 for null node.

Using different method names in recursive calls.

Return 0 for null node, then recursively call 'height' on left and right children.

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