BST Insert Operation in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Binary Search Tree (BST)?

A Binary Search Tree is a tree data structure where each node has at most two children. For every node, all values in the left subtree are smaller, and all values in the right subtree are larger.

beginner

What is the main rule to follow when inserting a new value into a BST?

Compare the new value with the current node's value. If smaller, go to the left child; if larger, go to the right child. Repeat until you find an empty spot to insert the new node.

intermediate

What happens if you try to insert a value that already exists in the BST?

Typically, BSTs do not allow duplicate values. The insert operation will ignore the duplicate or handle it based on specific rules, such as inserting duplicates to the right subtree.

beginner

Show the step-by-step insertion of 5 into this BST: 10 -> 4 -> 15

Start at root 10: 5 < 10, go left to 4. 5 > 4, go right which is empty. Insert 5 as right child of 4.

intermediate

What is the time complexity of inserting a node in a BST?

The average time complexity is O(log n) when the tree is balanced. In the worst case (skewed tree), it can be O(n).

When inserting a value into a BST, where do you go if the value is less than the current node?

A Replace the current node

B Go to the right child

C Stop insertion

D Go to the left child

In a BST, smaller values go to the left subtree.

What is the first step when inserting a new value into a BST?

A Insert at the leaf

B Compare with the root node

C Delete a node

D Balance the tree

Insertion starts by comparing the new value with the root node.

If the BST is empty, where do you insert the new node?

A As the root node

B As the left child

C As the right child

D Cannot insert

If the tree is empty, the new node becomes the root.

What is the worst-case time complexity of inserting into a BST?

A O(n log n)

B O(log n)

C O(n)

D O(1)

In the worst case, the BST is skewed and insertion takes O(n) time.

Which of these is NOT true about BST insertion?

A Duplicates are always inserted to the left

B Insertion compares values to decide direction

C Insertion finds an empty spot to add the node

D Insertion maintains BST property

Duplicates are usually not inserted or handled specifically; they are not always inserted to the left.

Explain how to insert a new value into a Binary Search Tree step-by-step.

Think about walking down the tree comparing values.

Describe the time complexity of inserting a node in a BST and what affects it.

Consider how tree shape affects search path length.

Practice

1. What is the main purpose of the Insert operation in a Binary Search Tree (BST)?

easy

A. To delete a node from the BST

B. To add a new node while keeping the BST property intact

C. To find the maximum value in the BST

D. To balance the BST automatically

Solution

1. Step 1: Understand the Insert operation

   The Insert operation adds a new value to the BST while maintaining the order property: left child < parent < right child.

2. Step 2: Identify the purpose of Insert

   Insert does not delete nodes, find max, or balance the tree automatically. Its main job is to add nodes correctly.

3. Final Answer:

   To add a new node while keeping the BST property intact -> Option B

4. Quick Check:

   Insert = Add node correctly [OK]

Hint: Insert adds nodes preserving BST order [OK]

Common Mistakes:

• Confusing insert with delete operation
• Thinking insert balances the tree automatically
• Assuming insert finds max or min values

2. Which of the following is the correct C# method signature for inserting a value into a BST node class?

easy

A. public void Insert(int value)

B. void InsertNode(int value, Node root)

C. private Node Insert(int value, Node root)

D. public int Insert(int value)

Solution

1. Step 1: Understand typical Insert method signature

   Insert usually returns the updated root node after insertion, so return type is Node, and it takes the root and value as parameters.

2. Step 2: Check method access and parameters

   Private method with signature Node Insert(int value, Node root) fits common recursive insert pattern.

3. Final Answer:

   private Node Insert(int value, Node root) -> Option C

4. Quick Check:

   Insert returns updated node [OK]

Hint: Insert returns updated root node [OK]

Common Mistakes:

• Using void return type for recursive insert
• Incorrect parameter order or missing root node
• Making Insert public when it should be private helper

3. What will be the in-order traversal output after inserting 15 into this BST?

      10
     /  \
    5    20
         /
        17

Insert operation: Insert(15)

medium

A. 5 -> 10 -> 15 -> 17 -> 20 -> null

B. 5 -> 10 -> 17 -> 15 -> 20 -> null

C. 5 -> 10 -> 15 -> 20 -> 17 -> null

D. 5 -> 10 -> 20 -> 17 -> 15 -> null

Solution

1. Step 1: Insert 15 into BST

   Starting at root 10, 15 > 10, go right to 20. 15 < 20, go left to 17. 15 < 17, insert as left child of 17.

2. Step 2: Perform in-order traversal

   In-order visits left, root, right: 5, 10, 15, 17, 20.

3. Final Answer:

   5 -> 10 -> 15 -> 17 -> 20 -> null -> Option A

4. Quick Check:

   In-order sorted = 5,10,15,17,20 [OK]

Hint: Insert left if smaller, right if larger, then in-order sorts [OK]

Common Mistakes:

• Inserting 15 as right child of 17
• Misordering nodes in traversal
• Ignoring BST property during insertion

4. Given this Insert method snippet, what is the error?

private Node Insert(int value, Node root) {
  if (root == null) {
    root = new Node(value);
  } else if (value < root.Value) {
    Insert(value, root.Left);
  } else {
    Insert(value, root.Right);
  }
  return root;
}

medium

A. Missing assignment when inserting into left or right subtree

B. Incorrect base case for null root

C. Method should return void instead of Node

D. Using else instead of else if for right subtree insertion

Solution

1. Step 1: Analyze recursive calls

   Recursive calls to Insert on left or right subtree do not assign the returned node back to root.Left or root.Right.

2. Step 2: Identify fix

   Must assign: root.Left = Insert(value, root.Left); and similarly for right to update tree links.

3. Final Answer:

   Missing assignment when inserting into left or right subtree -> Option A

4. Quick Check:

   Assign recursive result to subtree [OK]

Hint: Always assign recursive insert result to child node [OK]

Common Mistakes:

• Not assigning recursive insert result
• Changing base case incorrectly
• Confusing return type with void

5. You have a BST with nodes 10, 5, 15. You want to insert 12 and 18. After insertion, which of the following represents the correct pre-order traversal?

hard

A. 10 -> 15 -> 18 -> 12 -> 5 -> null

B. 10 -> 5 -> 12 -> 15 -> 18 -> null

C. 10 -> 15 -> 5 -> 12 -> 18 -> null

D. 10 -> 5 -> 15 -> 12 -> 18 -> null

Solution

1. Step 1: Insert 12 and 18 into BST

   Start with root 10, left child 5, right child 15. Insert 12: 12 < 15, goes left of 15. Insert 18: 18 > 15, goes right of 15.

2. Step 2: Perform pre-order traversal

   Pre-order visits root, left, right: 10, 5, 15, 12, 18.

3. Final Answer:

   10 -> 5 -> 15 -> 12 -> 18 -> null -> Option D

4. Quick Check:

   Pre-order = root-left-right [OK]

Hint: Pre-order: root first, then left, then right [OK]

Common Mistakes:

• Mixing pre-order with in-order or post-order
• Inserting nodes in wrong subtree
• Misplacing 12 and 18 in traversal