BST Inorder Successor in DSA Javascript - Build from Scratch

BST Inorder Successor

📖 Scenario: You are working with a Binary Search Tree (BST) that stores numbers. You want to find the next bigger number after a given number in the tree. This is called the inorder successor.Imagine the BST as a family tree of numbers, where each number has smaller numbers on the left and bigger numbers on the right. Finding the inorder successor is like finding the next person in line after someone in a sorted list.

🎯 Goal: Build a program that finds the inorder successor of a given node value in a BST. You will create the BST nodes, set up the tree, write the logic to find the successor, and print the result.

📋 What You'll Learn

Create BST nodes with exact values and structure

Set a target node value to find its inorder successor

Implement the inorder successor logic using BST properties

Print the inorder successor value or 'null' if none exists

💡 Why This Matters

🌍 Real World

Finding the inorder successor is useful in database indexing, scheduling tasks in order, and navigating sorted data efficiently.

💼 Career

Understanding BST operations like inorder successor is important for software engineers working on search algorithms, data retrieval, and optimization problems.

1

Create BST nodes and build the tree

Create a class called Node with a constructor that takes value, left, and right parameters. Then create nodes with these exact values and structure:
root = new Node(20),
root.left = new Node(10),
root.right = new Node(30),
root.left.left = new Node(5),
root.left.right = new Node(15).

DSA Javascript

// Define Node class and create the BST nodes as described
// Your code here

Hint

Remember to create the Node class first, then build the tree by linking nodes with left and right.

2

Set the target node value to find successor

Create a variable called targetValue and set it to 10. This is the value of the node whose inorder successor you want to find.

DSA Javascript

class Node {
  constructor(value, left = null, right = null) {
    this.value = value;
    this.left = left;
    this.right = right;
  }
}

const root = new Node(20);
root.left = new Node(10);
root.right = new Node(30);
root.left.left = new Node(5);
root.left.right = new Node(15);

// Set the target node value
// Your code here

Hint

Just create a constant named targetValue and assign it the number 10.

3

Implement the inorder successor function

Write a function called inorderSuccessor that takes root and targetValue as parameters. Use a loop to find the node with targetValue. Then find its inorder successor using BST rules:
- If the node has a right child, the successor is the leftmost node in the right subtree.
- Otherwise, move up the tree to find the nearest ancestor for which the node is in the left subtree.
Return the successor node or null if none exists.

DSA Javascript

class Node {
  constructor(value, left = null, right = null) {
    this.value = value;
    this.left = left;
    this.right = right;
  }
}

const root = new Node(20);
root.left = new Node(10);
root.right = new Node(30);
root.left.left = new Node(5);
root.left.right = new Node(15);

const targetValue = 10;

// Write the inorderSuccessor function below
// Your code here

Hint

Use a loop to find the target node. Track a successor when moving left. If the node has a right child, find the leftmost node there. Otherwise, return the stored successor.

4

Print the inorder successor value

Call the inorderSuccessor function with root and targetValue. Then print the successor's value if it exists, or print null if there is no successor.

DSA Javascript

class Node {
  constructor(value, left = null, right = null) {
    this.value = value;
    this.left = left;
    this.right = right;
  }
}

const root = new Node(20);
root.left = new Node(10);
root.right = new Node(30);
root.left.left = new Node(5);
root.left.right = new Node(15);

const targetValue = 10;

function inorderSuccessor(root, targetValue) {
  let successor = null;
  let current = root;

  // Find the target node
  while (current !== null) {
    if (targetValue  current.value) {
      current = current.right;
    } else {
      break;
    }
  }

  if (current === null) {
    return null; // target not found
  }

  // If right subtree exists, find leftmost node there
  if (current.right !== null) {
    current = current.right;
    while (current.left !== null) {
      current = current.left;
    }
    return current;
  }

  // Otherwise, successor is the ancestor stored
  return successor;
}

// Print the inorder successor value or null
// Your code here

Hint

Call inorderSuccessor(root, targetValue) and store the result. Then print the value of the result if it exists, otherwise print null.

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