BST Inorder Successor in DSA C# - Time & Space Complexity

Time Complexity: BST Inorder Successor

O(h)

Understanding Time Complexity

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

How does the time grow as the tree gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public TreeNode InorderSuccessor(TreeNode root, TreeNode p) {
    TreeNode successor = null;
    while (root != null) {
        if (p.val < root.val) {
            successor = root;
            root = root.left;
        } else {
            root = root.right;
        }
    }
    return successor;
}
    

This code finds the inorder successor of a given node 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, from root to leaf.

How Execution Grows With Input

As the tree grows taller, the number of steps to find the successor grows roughly with the height.

Input Size (n)	Approx. Operations
10 (small tree)	About 3 to 4 steps
100 (medium tree)	About 6 to 7 steps
1000 (large tree)	About 9 to 10 steps

Pattern observation: The steps grow slowly as the tree height grows, not directly with total nodes.

Final Time Complexity

Time Complexity: O(h)

This means the time depends on the tree height, 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 (n)."

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

Interview Connect

Understanding how tree height affects search time helps you explain and optimize tree operations clearly.

Self-Check

"What if the BST is balanced versus completely unbalanced? 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 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 = smallest greater key [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 C# method signatures correctly represents a function to find the inorder successor of a BST node?

easy

A. public void InorderSuccessor(TreeNode root, TreeNode p)

B. public TreeNode InorderSuccessor(TreeNode root, TreeNode p)

C. public TreeNode FindSuccessor(TreeNode p)

D. public int InorderSuccessor(int root, int p)

Solution

1. Step 1: Check parameter types for BST nodes

   The method should accept the BST root and the target node to find successor, both as TreeNode objects.

2. Step 2: Check return type

   The method returns the successor node, so return type must be TreeNode, not int or void.

3. Final Answer:

   public TreeNode InorderSuccessor(TreeNode root, TreeNode p) -> Option B

4. Quick Check:

   Correct signature uses TreeNode parameters and returns TreeNode [OK]

Hint: Successor method needs root and target node, returns TreeNode [OK]

Common Mistakes:

• Using int instead of TreeNode for parameters
• Returning void instead of TreeNode
• Missing root parameter

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

        20
       /  \
     10    30
       \     \
       15    40

TreeNode successor = InorderSuccessor(root, node15); Console.WriteLine(successor.val);

medium

A. 40

B. 30

C. 20

D. 15

Solution

1. Step 1: Locate node 15 and find its inorder successor

   Node 15 has no right child, so successor is the lowest ancestor whose left child is also ancestor of 15, which is 20.

2. Step 2: Confirm successor value

   20 is the next bigger node after 15 in inorder traversal.

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 30 incorrectly
• Choosing node itself as successor
• Choosing 40 which is too far

4. The following code attempts to find the inorder successor of a node in a BST but returns null incorrectly. What is the bug?

public TreeNode InorderSuccessor(TreeNode root, TreeNode p) {
    if (p.right != null) {
        TreeNode curr = p.right;
        while (curr.left != null) curr = curr.left;
        return curr;
    }
    TreeNode successor = null;
    while (root != null) {
        if (p.val < root.val) {
            successor = root;
            root = root.left;
        } else {
            root = root.right;
        }
    }
    return successor;
}

medium

A. The code does not handle the case when p has no right child

B. The while loop condition should be curr.right instead of curr.left

C. The comparison p.val < root.val should be p.val <= root.val

D. The code is correct and should not return null incorrectly

Solution

1. Step 1: Analyze right subtree handling

   If p has right child, code correctly finds leftmost node in right subtree as successor.

2. Step 2: Analyze ancestor traversal

   If no right child, code moves up tree to find first ancestor greater than p, correctly updating successor.

3. Step 3: Confirm no logical errors

   Comparisons and loops are correct; code returns null only if no successor exists (p is max node).

4. Final Answer:

   The code is correct and should not return null incorrectly -> Option D

5. Quick Check:

   Code handles both cases correctly [OK]

Hint: Check both right subtree and ancestor paths for successor [OK]

Common Mistakes:

• Changing left to right in while loop incorrectly
• Using <= instead of < causing wrong ancestor selection
• Assuming code misses no-right-child case

5. You have a BST and want to find the inorder successor of the node with value 50. The BST is:

          40
         /  \
       20    60
      /  \     \
    10   30    70
                 \
                 80

If the node with value 50 does not exist in the tree, what should your inorder successor function return?

hard

A. null, because the node is not in the BST

B. The smallest node greater than 50, which is 60

C. The largest node smaller than 50, which is 40

D. The root node, which is 40

Solution

1. Step 1: Confirm node presence in BST

   Node with value 50 is not present in the BST, so no direct successor can be found.

2. Step 2: Understand successor function behavior

   Successor function requires the node to find its successor; if node not found, function should return null or indicate absence.

3. Final Answer:

   null, because the node is not in the BST -> Option A

4. Quick Check:

   Node missing means no successor found [OK]

Hint: Successor only valid if node exists in BST [OK]

Common Mistakes:

• Returning closest bigger node even if node missing
• Returning root node incorrectly
• Returning predecessor instead of null