Bird
Raised Fist0
DSA Javascriptprogramming~5 mins

BST Inorder Successor in DSA Javascript - Time & Space Complexity

Choose your learning style10 modes available
LearnWhyDeepVisualTryChallengeProjectRecallTime
Time Complexity: BST Inorder Successor
O(h)
Understanding Time Complexity

We want to understand how the time needed to find the inorder successor in a Binary Search Tree changes as the tree grows.

How does the number of steps grow when the tree has more nodes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.


function inorderSuccessor(root, p) {
  if (p.right) {
    let curr = p.right;
    while (curr.left) curr = curr.left;
    return curr;
  }
  let successor = null;
  let curr = root;
  while (curr) {
    if (p.val < curr.val) {
      successor = curr;
      curr = curr.left;
    } else {
      curr = curr.right;
    }
  }
  return successor;
}

This code finds the next bigger node (inorder successor) of a given node in a BST.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

  • Primary operation: Traversing down the tree nodes using while loops.
  • How many times: At most, the number of steps equals the height of the tree.
How Execution Grows With Input

As the tree grows, the height usually grows too, so the steps increase roughly with the height.

Input Size (n)Approx. Operations (height)
10About 3 to 4 steps
100About 6 to 7 steps
1000About 9 to 10 steps

Pattern observation: The number of steps grows slowly, roughly proportional to the tree height, which is often much smaller than total nodes.

Final Time Complexity

Time Complexity: O(h)

This means the time depends on the height of the tree, not the total number of nodes.

Common Mistake

[X] Wrong: "Finding the inorder successor always takes time proportional to the total number of nodes."

[OK] Correct: The search only follows a path down the tree, so it depends on the height, not all nodes.

Interview Connect

Understanding this helps you explain how tree shape affects search speed, a key skill for working with trees in real problems.

Self-Check

"What if the BST is balanced versus completely unbalanced? How would the time complexity change?"

Practice

(1/5)
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
Recommended

Ready to prove it?

Pass the test and this pattern moves unknown strong while earning +1 Grip toward your certificate.

10 questions~5 mineasy hard