BST Inorder Successor in DSA Typescript - Time & Space Complexity

Time Complexity: BST Inorder Successor

O(h)

Understanding Time Complexity

We want to understand how long it takes to find the next bigger value in a Binary Search Tree (BST).

How does the time needed grow as the tree gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

This code finds the next bigger node after a given node p in a BST by walking down the tree.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves down the tree nodes.
• How many times: At most once per level of the tree, until it reaches a leaf or finds the successor.

How Execution Grows With Input

Each step moves one level down the tree, so the number of steps depends on the tree height.

Input Size (n)	Approx. Operations
10	Up to 4 steps (if tree is balanced)
100	Up to 7 steps
1000	Up to 10 steps

Pattern observation: The steps grow slowly as the tree grows, roughly with the tree height.

Final Time Complexity

Time Complexity: O(h)

This means the time grows with the height of the tree, which is the number of levels from root to leaf.

Common Mistake

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

[OK] Correct: The search only moves down one path, not the whole tree, so it depends on tree height, not total 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 not balanced but skewed like a linked list? How would the time complexity change?"

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 node with a key greater than the current node.

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 node [OK]

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

Common Mistakes:

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

2. Which of the following TypeScript function signatures correctly represents a function to find the inorder successor in a BST node?

easy

A. function inorderSuccessor(root: TreeNode | null, p: TreeNode): TreeNode | null

B. function inorderSuccessor(p: TreeNode): TreeNode

C. function inorderSuccessor(root: TreeNode): void

D. function inorderSuccessor(root: TreeNode, p: TreeNode): number

Solution

1. Step 1: Analyze parameters needed

   To find inorder successor, we need the BST root and the target node p.

2. Step 2: Analyze return type

   The function returns the successor node or null if none exists.

3. Final Answer:

   function inorderSuccessor(root: TreeNode | null, p: TreeNode): TreeNode | null -> Option A

4. Quick Check:

   Correct params and return type [OK]

Hint: Successor function needs root and target node, returns node or null [OK]

Common Mistakes:

• Missing root parameter
• Wrong return type (void or number)
• Not allowing null root

3. Given the BST below and the node with value 5, what is the inorder successor?

      6
     / \
    2   8
   / \   \
  0   4   9
     / \
    3   5

medium

A. Node with value 8

B. Node with value 6

C. Node with value 4

D. Node with value 9

Solution

1. Step 1: Locate node 5 and check right subtree

   Node 5 has no right child, so successor is one of its ancestors.

2. Step 2: Find lowest ancestor whose left child is ancestor of node 5

   Node 6 is the first ancestor where node 5 is in left subtree, so successor is node 6.

3. Final Answer:

   Node with value 6 -> Option B

4. Quick Check:

   Successor of 5 is 6 [OK]

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

Common Mistakes:

• Choosing right child of root instead of ancestor
• Picking node 8 which is too big
• Confusing predecessor with successor

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

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

What is the bug in this code?

medium

A. It may cause infinite loop if root is null

B. It incorrectly updates the successor when p.val > root.val

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

D. It returns the predecessor instead of successor

Solution

1. Step 1: Understand code logic

   The code moves down the tree to find the smallest node greater than p.val, updating successor accordingly.

2. Step 2: Identify missing case

   If p has a right subtree, the successor is the leftmost node in that subtree, but this code ignores that and only searches from root.

3. Final Answer:

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

4. Quick Check:

   Right subtree check missing [OK]

Hint: Check right subtree first for successor [OK]

Common Mistakes:

• Ignoring right subtree of p
• Assuming successor always in ancestors
• Confusing successor with predecessor

5. You have a BST and want to find the inorder successor of a node p. The node p has a right child. Which of the following is the correct approach to find the inorder successor?

hard

A. Return the root of the BST

B. Return the rightmost node in p's left subtree

C. Return the parent of p

D. Return the leftmost node in p's right subtree

Solution

1. Step 1: Check if p has right subtree

   If p has a right child, the inorder successor is the smallest node in that right subtree.

2. Step 2: Find leftmost node in right subtree

   Traverse left children starting from p's right child until no more left child exists.

3. Final Answer:

   Return the leftmost node in p's right subtree -> Option D

4. Quick Check:

   Successor in right subtree's leftmost node [OK]

Hint: Successor with right child = leftmost node in right subtree [OK]

Common Mistakes:

• Returning parent instead of leftmost right subtree node
• Returning rightmost left subtree node
• Returning root regardless of p