BST Delete Operation in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What are the three main cases to consider when deleting a node in a Binary Search Tree (BST)?

1. Node to delete is a leaf (no children).
2. Node to delete has one child.
3. Node to delete has two children.

intermediate

In BST deletion, how do you handle deleting a node with two children?

Replace the node's value with its inorder successor (smallest value in right subtree) or inorder predecessor (largest value in left subtree), then delete that successor/predecessor node.

beginner

What is the inorder successor in a BST?

The node with the smallest value in the right subtree of the current node.

intermediate

Why do we replace a node with its inorder successor or predecessor when deleting a node with two children?

Because it maintains the BST property by ensuring all left subtree nodes are smaller and all right subtree nodes are larger than the replaced node.

beginner

What happens if you delete a leaf node in a BST?

You simply remove the leaf node by setting its parent's pointer to null.

Which of the following is NOT a case to consider when deleting a node in a BST?

A Node has no children

B Node has one child

C Node has three children

D Node has two children

In a BST, a node can have at most two children, so 'three children' is not a valid case.

When deleting a node with two children, which node is commonly used to replace it?

A Inorder successor

B Root node

C Random leaf node

D Parent node

The inorder successor (smallest node in right subtree) is used to replace the deleted node to maintain BST properties.

What is the inorder successor of a node in a BST?

A Smallest node in right subtree

B Parent node

C Largest node in left subtree

D Any leaf node

The inorder successor is the smallest node in the right subtree of the node.

If a node to delete has only one child, what is the deletion process?

A Replace node with inorder successor

B Remove the node and connect its child directly to its parent

C Replace node with inorder predecessor

D Do nothing

The node is removed and its single child is linked directly to the node's parent.

What happens to the BST property after deleting a node and replacing it with its inorder successor?

A BST becomes empty

B BST property is broken

C BST becomes a linked list

D BST property is maintained

Replacing with inorder successor maintains the BST property because the successor fits correctly in the tree order.

Explain the steps to delete a node with two children in a BST.

Think about how to keep the tree ordered after deletion.

Describe how deleting a leaf node differs from deleting a node with one child in a BST.

Consider the connections between nodes.

Practice

1. What happens when you delete a leaf node (a node with no children) from a Binary Search Tree (BST)?

easy

A. The node is simply removed without affecting other nodes.

B. The entire tree is rebuilt from scratch.

C. The node's children replace it in the tree.

D. The root node is always changed.

Solution

1. Step 1: Understand leaf node deletion

   A leaf node has no children, so removing it does not affect other nodes.

2. Step 2: Effect on BST structure

   Since no children exist, simply remove the node and update its parent's pointer to null.

3. Final Answer:

   The node is simply removed without affecting other nodes. -> Option A

4. Quick Check:

   Leaf node deletion = simple removal [OK]

Hint: Leaf nodes delete by direct removal only [OK]

Common Mistakes:

• Thinking children replace the node when none exist
• Assuming root always changes
• Believing tree rebuild is needed

2. Which of the following is the correct syntax to delete a node with value key from a BST in JavaScript?

easy

A. bst.deleteNode(key);

B. bst.delete(key);

C. bst.remove(key);

D. bst.erase(key);

Solution

1. Step 1: Identify common BST delete method

   In many JavaScript BST implementations, the method to delete a node is named delete.

2. Step 2: Check method naming conventions

   Methods like remove, erase, or deleteNode are not standard or common in JavaScript BST examples.

3. Final Answer:

   bst.delete(key); -> Option B

4. Quick Check:

   Standard BST delete method = delete() [OK]

Hint: Use bst.delete(key) to remove nodes [OK]

Common Mistakes:

• Using remove() or erase() which are not standard
• Confusing delete keyword with method name
• Using deleteNode() which is uncommon

3. Consider this BST and the delete operation:

    10
   /  \
  5    15
       / \
      12  20

What will be the in-order traversal output after deleting node with value 15?

medium

A. [5, 10, 12, 15, 20]

B. [5, 10, 20]

C. [5, 10, 12, 20]

D. [5, 10, 15, 20]

Solution

1. Step 1: Identify node to delete and its children

   Node 15 has two children: 12 (left) and 20 (right).

2. Step 2: Replace node 15 with its in-order successor

   The in-order successor is the smallest node in right subtree, which is 20. Replace 15 with 20 and delete original 20 node.

3. Step 3: Perform in-order traversal

   In-order traversal visits nodes in ascending order: 5, 10, 12, 20.

4. Final Answer:

   [5, 10, 12, 20] -> Option C

5. Quick Check:

   In-order after deleting 15 = [5, 10, 12, 20] [OK]

Hint: Replace deleted node with in-order successor [OK]

Common Mistakes:

• Removing 15 without replacement
• Using in-order predecessor instead of successor
• Forgetting to delete the successor node

4. The following code attempts to delete a node from a BST but causes an error. What is the main issue?

function deleteNode(root, key) {
  if (!root) return null;
  if (key < root.val) root.left = deleteNode(root.left, key);
  else if (key > root.val) root.right = deleteNode(root.right, key);
  else {
    if (!root.left) return root.right;
    else if (!root.right) return root.left;
    let minNode = findMin(root.right);
    root.val = minNode.val;
    // Missing deletion of minNode here
  }
  return root;
}

function findMin(node) {
  while (node.left) node = node.left;
  return node;
}

medium

A. The function does not handle leaf nodes correctly.

B. The base case for recursion is missing.

C. The function uses incorrect comparison operators.

D. The code does not delete the in-order successor node after copying its value.

Solution

1. Step 1: Analyze deletion of node with two children

   When deleting a node with two children, we replace its value with the in-order successor's value.

2. Step 2: Check if in-order successor node is deleted

   The code copies the successor's value but does not delete the successor node itself, causing duplicate values and incorrect tree.

3. Final Answer:

   The code does not delete the in-order successor node after copying its value. -> Option D

4. Quick Check:

   Must delete successor node after value copy [OK]

Hint: Always delete successor node after copying value [OK]

Common Mistakes:

• Forgetting to delete the in-order successor node
• Missing base case (though present here)
• Incorrectly handling leaf nodes
• Using wrong comparison operators

5. You have a BST with nodes: 8, 3, 10, 1, 6, 14, 4, 7, 13.
After deleting node 3, what is the correct in-order traversal of the BST?

hard

A. [1, 4, 6, 7, 8, 10, 13, 14]

B. [1, 3, 4, 6, 7, 8, 10, 13, 14]

C. [1, 6, 7, 8, 10, 13, 14]

D. [1, 4, 7, 8, 10, 13, 14]

Solution

1. Step 1: Identify node 3 and its children

   Node 3 has two children: 1 (left) and 6 (right). 6 has children 4 and 7.

2. Step 2: Delete node 3 by replacing with in-order successor

   The in-order successor of 3 is 4 (smallest in right subtree). Replace 3 with 4, then delete original 4 node.

3. Step 3: Perform in-order traversal after deletion

   In-order traversal visits nodes in ascending order: 1, 4, 6, 7, 8, 10, 13, 14.

4. Final Answer:

   [1, 4, 6, 7, 8, 10, 13, 14] -> Option A

5. Quick Check:

   In-order after deleting 3 = [1, 4, 6, 7, 8, 10, 13, 14] [OK]

Hint: Replace deleted node with in-order successor, then traverse [OK]

Common Mistakes:

• Forgetting to delete the in-order successor node
• Using in-order predecessor instead
• Skipping nodes in traversal