BST Find Maximum Element in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Find the maximum element in a BST

What is the output of the following C# code that finds the maximum element in a Binary Search Tree (BST)?

DSA C#

using System;

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

class BST {
    public Node root;

    public int FindMax(Node node) {
        if (node == null) return int.MinValue;
        while (node.right != null) {
            node = node.right;
        }
        return node.data;
    }
}

class Program {
    static void Main() {
        BST tree = new BST();
        tree.root = new Node(10);
        tree.root.left = new Node(5);
        tree.root.right = new Node(20);
        tree.root.right.left = new Node(15);
        tree.root.right.right = new Node(25);

        Console.WriteLine(tree.FindMax(tree.root));
    }
}

A 25

B 10

C 15

D 20

💡 Hint

In a BST, the maximum element is the rightmost node.

The code traverses the right children until it reaches the rightmost node, which holds the maximum value. Here, 25 is the rightmost node.

❓ Predict Output

intermediate

Output when BST is empty

What will be the output of the following code when the BST is empty (root is null)?

DSA C#

using System;

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

class BST {
    public Node root;

    public int FindMax(Node node) {
        if (node == null) return int.MinValue;
        while (node.right != null) {
            node = node.right;
        }
        return node.data;
    }
}

class Program {
    static void Main() {
        BST tree = new BST();
        Console.WriteLine(tree.FindMax(tree.root));
    }
}

A Throws NullReferenceException

B 0

C No output (program crashes silently)

D -2147483648

💡 Hint

Check the return value when the input node is null.

The method returns int.MinValue when the root is null, which is -2147483648 in C#.

🔧 Debug

advanced

Identify the error in FindMax method

What error will the following code produce when trying to find the maximum element in a BST?

DSA C#

public int FindMax(Node node) {
    while (node.right != null) {
        node = node.left;
    }
    return node.data;
}

A Returns minimum element instead of maximum

B Throws NullReferenceException

C Infinite loop

D Returns maximum element correctly

💡 Hint

Check which child node is used inside the loop.

The code incorrectly moves to the left child inside the loop instead of the right child, so it returns the minimum element, not the maximum.

❓ Predict Output

advanced

Maximum element after inserting nodes

After inserting the following nodes into an empty BST in this order: 30, 10, 40, 35, 50, what is the maximum element found by FindMax?

DSA C#

using System;

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

class BST {
    public Node root;

    public void Insert(int key) {
        root = InsertRec(root, key);
    }

    private Node InsertRec(Node root, int key) {
        if (root == null) {
            root = new Node(key);
            return root;
        }
        if (key < root.data) root.left = InsertRec(root.left, key);
        else if (key > root.data) root.right = InsertRec(root.right, key);
        return root;
    }

    public int FindMax(Node node) {
        if (node == null) return int.MinValue;
        while (node.right != null) {
            node = node.right;
        }
        return node.data;
    }
}

class Program {
    static void Main() {
        BST tree = new BST();
        tree.Insert(30);
        tree.Insert(10);
        tree.Insert(40);
        tree.Insert(35);
        tree.Insert(50);
        Console.WriteLine(tree.FindMax(tree.root));
    }
}

A 35

B 40

C 50

D 30

💡 Hint

The maximum element is the rightmost node after all insertions.

After inserting all nodes, 50 is the rightmost node and thus the maximum element.

🧠 Conceptual

expert

Why is FindMax efficient in a BST?

Why does the FindMax method in a BST run efficiently compared to searching the entire tree?

A Because it uses recursion to check all nodes in the tree.

B Because it only traverses the right children, which leads directly to the maximum element.

C Because it balances the tree before searching.

D Because it traverses both left and right children equally.

💡 Hint

Think about the BST property and where the maximum element is located.

In a BST, all right children are greater than their parents, so the maximum element is the rightmost node. Traversing only right children is efficient.

Practice

1. In a Binary Search Tree (BST), where is the maximum element always located?

easy

A. At the root node

B. At the rightmost node

C. At the leftmost node

D. At any leaf node

Solution

1. Step 1: Understand BST property

   In a BST, left child nodes have smaller values and right child nodes have larger values compared to their parent.

2. Step 2: Locate maximum element

   The maximum element is the largest value, so it must be the rightmost node because values increase to the right.

3. Final Answer:

   At the rightmost node -> Option B

4. Quick Check:

   Maximum element = rightmost node [OK]

Hint: Maximum is always the rightmost node in BST [OK]

Common Mistakes:

• Thinking maximum is at the root
• Confusing leftmost with maximum
• Assuming maximum can be any leaf

2. Which of the following C# code snippets correctly finds the maximum element in a BST node called root?

easy

A. while (root.Left != null) { root = root.Left; } return root.Value;

B. if (root.Left == null) return root.Value; else return root.Left.Value;

C. while (root.Right != null) { root = root.Right; } return root.Value;

D. return root.Value; // root is always max

Solution

1. Step 1: Check traversal direction

   To find max, traverse right child nodes until no more right child exists.

2. Step 2: Verify code correctness

   while (root.Right != null) { root = root.Right; } return root.Value; uses a while loop to move right until root.Right is null, then returns root.Value, which is correct.

3. Final Answer:

   while (root.Right != null) { root = root.Right; } return root.Value; -> Option C

4. Quick Check:

   Traverse right until null, then return value [OK]

Hint: Traverse right child until null to find max [OK]

Common Mistakes:

• Traversing left child instead of right
• Returning root value without traversal
• Using incorrect condition in loop

3. What will be the output of the following C# code snippet that finds the maximum element in a BST?

class Node {
  public int Value;
  public Node Left, Right;
  public Node(int val) { Value = val; Left = Right = null; }
}

Node root = new Node(10);
root.Left = new Node(5);
root.Right = new Node(15);
root.Right.Right = new Node(20);

Node current = root;
while (current.Right != null) {
  current = current.Right;
}
Console.WriteLine(current.Value);

medium

A. 5

B. 15

C. 10

D. 20

Solution

1. Step 1: Trace the BST structure

   Root is 10, right child 15, right child of 15 is 20. So rightmost node is 20.

2. Step 2: Follow the loop

   The loop moves current from 10 to 15, then to 20, then stops because 20.Right is null.

3. Final Answer:

   20 -> Option D

4. Quick Check:

   Rightmost node value = 20 [OK]

Hint: Rightmost node value is maximum [OK]

Common Mistakes:

• Stopping at 15 instead of 20
• Printing root value instead of max
• Confusing left and right children

4. The following C# method is intended to find the maximum element in a BST. What is the error?

int FindMax(Node root) {
  if (root == null) return int.MinValue;
  if (root.Right == null) return root.Value;
  return FindMax(root.Left);
}

medium

A. It should recurse on root.Right, not root.Left

B. It should return int.MaxValue when root is null

C. It should check root.Left instead of root.Right

D. No error, code is correct

Solution

1. Step 1: Analyze recursion direction

   To find max, recursion must go right, but code recurses left incorrectly.

2. Step 2: Identify correct recursion

   Change FindMax(root.Left) to FindMax(root.Right) to find max correctly.

3. Final Answer:

   It should recurse on root.Right, not root.Left -> Option A

4. Quick Check:

   Max found by right recursion [OK]

Hint: Max search recurses right child, not left [OK]

Common Mistakes:

• Recursing left child instead of right
• Returning wrong base case value
• Ignoring null root check

5. Given a BST where some nodes have duplicate values, which approach correctly finds the maximum value considering duplicates?

int FindMaxWithDuplicates(Node root) {
  if (root == null) return int.MinValue;
  int rightMax = FindMaxWithDuplicates(root.Right);
  return Math.Max(root.Value, rightMax);
}

What is the output of FindMaxWithDuplicates on this BST? Root: 10 Left: 5 Right: 10 Right.Right: 15 Right.Right.Right: 15

hard

A. 15

B. 10

C. 5

D. Error due to duplicates

Solution

1. Step 1: Understand duplicate handling

   The method compares current node value with max from right subtree, so duplicates do not affect max finding.

2. Step 2: Trace values

   Right subtree max is 15 (rightmost node). Root value 10 is less than 15, so max is 15.

3. Final Answer:

   15 -> Option A

4. Quick Check:

   Max value with duplicates = 15 [OK]

Hint: Compare node value with right subtree max for duplicates [OK]

Common Mistakes:

• Assuming duplicates cause errors
• Returning first max found without comparison
• Ignoring right subtree values