BST Inorder Successor in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the inorder successor of a node in a Binary Search Tree (BST)?

The inorder successor of a node in a BST is the node with the smallest key greater than the given node's key. It is the next node visited in an inorder traversal.

beginner

How do you find the inorder successor if the node has a right child?

If the node has a right child, the inorder successor is the leftmost node in the right subtree.

intermediate

How do you find the inorder successor if the node has no right child?

If the node has no right child, the inorder successor is one of its ancestors. It is the lowest ancestor whose left child is also an ancestor of the node.

beginner

What is the inorder traversal order of a BST?

Inorder traversal visits nodes in ascending order: left subtree, current node, then right subtree.

intermediate

Why is the inorder successor important in BST operations?

The inorder successor helps in operations like deletion of a node, finding next higher value, and range queries by providing the next node in sorted order.

What is the inorder successor of a node with a right subtree?

A The leftmost node in the right subtree

B The rightmost node in the left subtree

C The parent node

D The root node

If a node has a right child, its inorder successor is the leftmost node in that right subtree.

If a node has no right child, how do you find its inorder successor?

A There is no inorder successor

B Find the rightmost node in the left subtree

C Find the root of the BST

D Find the lowest ancestor whose left child is also an ancestor of the node

When no right child exists, the inorder successor is the lowest ancestor where the node lies in its left subtree.

What traversal order does inorder traversal follow in a BST?

A Node, right subtree, left subtree

B Node, left subtree, right subtree

C Left subtree, node, right subtree

D Right subtree, node, left subtree

Inorder traversal visits nodes in ascending order: left subtree, current node, then right subtree.

Which of these is NOT a use of inorder successor in BST?

A Finding the next higher value

B Balancing the BST

C Deleting a node

D Range queries

Inorder successor is not used for balancing the BST; balancing uses rotations or other methods.

If a node is the maximum node in a BST, what is its inorder successor?

A Null (no successor)

B Its parent

C Its left child

D The root node

The maximum node has no inorder successor because no node has a greater key.

Explain how to find the inorder successor of a node in a BST when it has a right child and when it does not.

Think about the next bigger value in sorted order.

Describe why inorder traversal of a BST visits nodes in ascending order and how this relates to finding the inorder successor.

Consider how BST properties and traversal order connect.

Practice

1. What is the inorder successor of a node in a Binary Search Tree (BST)?

easy

A. The node with the smallest key greater than the given node's key

B. The node with the largest key smaller than the given node's key

C. The root node of the BST

D. The left child of the given node

Solution

1. Step 1: Understand inorder traversal order

   Inorder traversal visits nodes in ascending order of their keys in a BST.

2. Step 2: Define inorder successor

   The inorder successor of a node is the next node visited after it in inorder traversal, which is the smallest key greater than the node's key.

3. Final Answer:

   The node with the smallest key greater than the given node's key -> Option A

4. Quick Check:

   Inorder successor = next bigger key [OK]

Hint: Inorder successor is next bigger node in sorted order [OK]

Common Mistakes:

• Confusing successor with predecessor
• Thinking successor is always the right child
• Assuming successor is the root node

2. Which of the following is the correct JavaScript function signature to find the inorder successor of a node in a BST?

easy

A. function inorderSuccessor(node) {}

B. function inorderSuccessor(root, node) {}

C. function findSuccessor(root) {}

D. function successor(node, root) {}

Solution

1. Step 1: Identify required inputs

   To find the inorder successor, we need the BST root to traverse and the target node to find its successor.

2. Step 2: Match function signature

   function inorderSuccessor(root, node) {} correctly takes both root and node as parameters, enabling traversal and comparison.

3. Final Answer:

   function inorderSuccessor(root, node) {} -> Option B

4. Quick Check:

   Function needs root and node [OK]

Hint: Successor function needs both root and target node [OK]

Common Mistakes:

• Using only node without root
• Wrong parameter order
• Incorrect function naming

3. Given the BST below and the node with value 15, what is the inorder successor?

      20
     /  \
   10    30
     
     15

medium

A. 10

B. 30

C. 20

D. 15

Solution

1. Step 1: Locate node 15 and its right subtree

   Node 15 has no right child, so successor is an ancestor.

2. Step 2: Find the lowest ancestor whose left child is also ancestor of 15

   Node 20 is the first ancestor where 15 is in left subtree, so successor is 20.

3. Final Answer:

   20 -> Option C

4. Quick Check:

   Successor of 15 is 20 [OK]

Hint: If no right child, go up to first bigger ancestor [OK]

Common Mistakes:

• Choosing right child when none exists
• Picking the node itself as successor
• Confusing successor with predecessor

4. Consider this buggy JavaScript code to find the inorder successor of a node in a BST:

function inorderSuccessor(root, node) {
  if (!root) return null;
  if (node.val >= root.val) {
    return inorderSuccessor(root.right, node);
  } else {
    let left = inorderSuccessor(root.left, node);
    return left ? left : root;
  }
}

What is the main issue with this code?

medium

A. It does not handle the case when node has a right subtree

B. It incorrectly compares node.val with root.val

C. It returns the node itself instead of successor

D. It causes infinite recursion

Solution

1. Step 1: Analyze code logic

   The code only traverses the tree comparing values but never checks if node has a right subtree.

2. Step 2: Identify missing right subtree check

   If node has a right child, successor is the leftmost node in right subtree, which this code ignores.

3. Final Answer:

   It does not handle the case when node has a right subtree -> Option A

4. Quick Check:

   Missing right subtree check causes wrong successor [OK]

Hint: Check right subtree first for successor [OK]

Common Mistakes:

• Ignoring right subtree
• Wrong base case
• Returning node instead of successor

5. You have a BST and want to find the inorder successor of node 25. The BST structure is:

        20
       /  \
     10    30
           /  \
         25    40

What is the inorder successor of node 25 and why?

hard

A. 40, because 40 is the right child of 30

B. 20, because it is the root

C. None, because 25 is the largest node in its subtree

D. 30, because 25 has no right child and 30 is the next bigger ancestor

Solution

1. Step 1: Check if node 25 has right subtree

   Node 25 has no right child, so successor is an ancestor.

2. Step 2: Find the lowest ancestor whose left subtree contains node 25

   Node 30 is the parent of 25 and is the next bigger node, so successor is 30.

3. Final Answer:

   30, because 25 has no right child and 30 is the next bigger ancestor -> Option D

4. Quick Check:

   Successor of 25 is 30 [OK]

Hint: If no right child, successor is nearest bigger ancestor [OK]

Common Mistakes:

• Choosing right child of parent instead of parent
• Assuming no successor if no right child
• Confusing root as successor