Insertion in BST in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding BST Insertion Position

In a Binary Search Tree (BST), where is a new node inserted if its value is less than the current node's value?

A Always as the root node

B It replaces the current node

C As the right child or in the right subtree of the current node

D As the left child or in the left subtree of the current node

💡 Hint

Think about how BST keeps smaller values on one side.

In a BST, values smaller than a node go to the left subtree to maintain order.

📋 Factual

intermediate

Number of Children of a Newly Inserted Node in BST

When a new node is inserted into a BST, how many children does it have immediately after insertion?

A Two children

B One child

C No children (leaf node)

D Depends on the tree height

💡 Hint

New nodes start as leaves before any further insertions.

New nodes are inserted as leaf nodes, so they have no children initially.

🔍 Analysis

advanced

Resulting BST Structure After Insertions

Given an empty BST, nodes are inserted in this order: 10, 5, 15, 3, 7. What is the left child of the node with value 5?

A 7

B 3

C 10

D 15

💡 Hint

Visualize the tree after each insertion.

After inserting 5, 3 is inserted to the left of 5 because 3 < 5.

❓ Reasoning

advanced

Insertion Path in BST

When inserting a new value into a BST, which of the following best describes the path taken to find the insertion point?

A Traverse right if new value is greater, left if smaller

B Always traverse right regardless of value

C Always traverse left regardless of value

D Traverse left if new value is greater, right if smaller

💡 Hint

Remember the BST property about left and right children.

In BST, if the new value is greater than current node, go right; if smaller, go left.

🚀 Application

expert

Number of Nodes in BST After Insertions

Starting with an empty BST, you insert the values 8, 3, 10, 1, 6, 14, 4, 7, 13. How many nodes does the BST contain after all insertions?

A 9

B 8

C 10

D 7

💡 Hint

Count each unique insertion carefully.

Each value is unique and inserted once, so total nodes equal the number of inserted values: 9.

Practice

1. What happens when you insert a new value smaller than the current node in a Binary Search Tree (BST)?

easy

A. The new value replaces the current node.

B. The new value is inserted in the right subtree of the current node.

C. The new value is inserted in the left subtree of the current node.

D. The new value is ignored.

Solution

1. Step 1: Understand BST insertion rule for smaller values

   In a BST, if the new value is smaller than the current node, it must go to the left subtree.

2. Step 2: Apply the rule to the insertion process

   The new value is inserted into the left subtree, maintaining BST order.

3. Final Answer:

   The new value is inserted in the left subtree of the current node. -> Option C

4. Quick Check:

   Smaller value goes left [OK]

Hint: Smaller values always go to the left subtree [OK]

Common Mistakes:

• Inserting smaller values to the right subtree
• Replacing the current node instead of inserting
• Ignoring the new value

2. Which of the following is the correct way to insert a value into an empty Binary Search Tree (BST)?

easy

A. Set the new value as the root node of the BST.

B. Insert the new value as the left child of a random node.

C. Ignore the new value since the tree is empty.

D. Insert the new value as the right child of a random node.

Solution

1. Step 1: Identify insertion behavior for an empty BST

   When the BST is empty, the first inserted value becomes the root node.

2. Step 2: Confirm the correct insertion method

   Setting the new value as the root node initializes the BST correctly.

3. Final Answer:

   Set the new value as the root node of the BST. -> Option A

4. Quick Check:

   Empty tree insertion sets root [OK]

Hint: First insertion always becomes the root node [OK]

Common Mistakes:

• Trying to insert as child without a root
• Ignoring insertion in empty tree
• Inserting randomly without root

3. Consider the BST below:

    10
   /  
  5   15

What will the BST look like after inserting the value 12?

medium

A. 10
/
5 15
/
12

B. 10
/
5 12

15

C. 10
/
5 15

12

D. 10
/
5 12
/
15

Solution

1. Step 1: Compare 12 with root and right child

   12 is greater than 10, so move to right subtree. 12 is less than 15, so it goes to the left of 15.

2. Step 2: Insert 12 as left child of 15

   Place 12 as the left child of node 15 to maintain BST order.

3. Final Answer:

   12 is inserted as left child of 15. -> Option A

4. Quick Check:

   12 > 10 and 12 < 15, so left of 15 [OK]

Hint: Compare stepwise: left if smaller, right if larger [OK]

Common Mistakes:

• Inserting 12 as right child of 15
• Inserting 12 as right child of 10
• Ignoring BST order rules

4. Identify the error in the following BST insertion pseudocode:

function insert(node, value):
  if node is null:
    return new Node(value)
  if value > node.value:
    node.left = insert(node.left, value)
  else:
    node.right = insert(node.right, value)
  return node

medium

A. The code inserts smaller values to the left subtree instead of right.

B. The code does not handle the base case for empty tree.

C. The code incorrectly returns null instead of the node.

D. The code inserts larger values to the left subtree instead of right.

Solution

1. Step 1: Analyze insertion direction for larger values

   The code inserts values greater than current node into the left subtree, which is incorrect.

2. Step 2: Correct insertion direction for BST

   Larger values should be inserted into the right subtree to maintain BST order.

3. Final Answer:

   The code inserts larger values to the left subtree instead of right. -> Option D

4. Quick Check:

   Larger values go right, not left [OK]

Hint: Larger values always go right subtree [OK]

Common Mistakes:

• Swapping left and right insertion conditions
• Missing base case for null node
• Returning wrong node after insertion

5. You have a BST with values 20, 10, 30, 25, and 40 inserted in that order. Now you want to insert 30 again. Where should the new 30 be inserted according to standard BST insertion rules?

hard

A. As the left child of the existing 30 node.

B. As the right child of the existing 30 node.

C. Replace the existing 30 node with the new 30.

D. Do not insert duplicates in BST.

Solution

1. Step 1: Understand BST insertion for equal values

   Standard BST insertion places values equal to the current node in the right subtree.

2. Step 2: Insert new 30 as right child of existing 30

   The new 30 should be inserted as the right child of the existing 30 node.

3. Final Answer:

   As the right child of the existing 30 node. -> Option B

4. Quick Check:

   Equal values go right subtree [OK]

Hint: Equal values go to right subtree in BST [OK]

Common Mistakes:

• Inserting duplicates to the left subtree
• Replacing existing nodes instead of inserting
• Ignoring duplicates insertion rules