BST Inorder Predecessor in DSA Typescript - Time & Space Complexity

Time Complexity: BST Inorder Predecessor

O(h)

Understanding Time Complexity

We want to understand how long it takes to find the inorder predecessor in a Binary Search Tree (BST).

The question is: how does the time grow as the tree gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function inorderPredecessor(root: TreeNode | null, key: number): TreeNode | null {
  let predecessor: TreeNode | null = null;
  let current = root;
  while (current) {
    if (key <= current.val) {
      current = current.left;
    } else {
      predecessor = current;
      current = current.right;
    }
  }
  return predecessor;
}
    

This code finds the inorder predecessor of a given key 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 predecessor.

How Execution Grows With Input

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

Input Size (n)	Approx. Operations
10	About 3 to 4 steps (tree height)
100	About 6 to 7 steps
1000	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 height of the tree, which is the number of levels from root to leaf.

Common Mistake

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

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

Interview Connect

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

Self-Check

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

Practice

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

easy

A. The right child of the given node

B. The node with the largest value smaller than the given node

C. The left child of the given node

D. The node with the smallest value larger than the given node

Solution

1. Step 1: Understand inorder traversal in BST

   Inorder traversal visits nodes in ascending order of their values.

2. Step 2: Define inorder predecessor

   The inorder predecessor of a node is the node visited just before it in inorder traversal, which means it has the largest value smaller than the given node.

3. Final Answer:

   The node with the largest value smaller than the given node -> Option B

4. Quick Check:

   Inorder predecessor = largest smaller value [OK]

Hint: Predecessor is just before in sorted order [OK]

Common Mistakes:

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

2. Which TypeScript function signature correctly represents a method to find the inorder predecessor of a BST node?

easy

A. function findInorderPredecessor(root: TreeNode): void

B. function findInorderPredecessor(node: TreeNode): number

C. function findInorderPredecessor(root: TreeNode, node: TreeNode): TreeNode | null

D. function findInorderPredecessor(): boolean

Solution

1. Step 1: Identify required inputs and outputs

   To find the inorder predecessor, we need the BST root and the target node, and we return the predecessor node or null if none.

2. Step 2: Match function signature

   function findInorderPredecessor(root: TreeNode, node: TreeNode): TreeNode | null matches this: it takes root and node, returns TreeNode or null.

3. Final Answer:

   function findInorderPredecessor(root: TreeNode, node: TreeNode): TreeNode | null -> Option C

4. Quick Check:

   Correct inputs and output type [OK]

Hint: Function needs root, node, returns node or null [OK]

Common Mistakes:

• Missing root parameter
• Returning wrong type like number or boolean
• No parameters or void return type

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

       20
      /  \
    10    30
      \
      15

medium

A. 10

B. 15

C. 20

D. 30

Solution

1. Step 1: Perform inorder traversal around node 15

   Inorder traversal visits nodes in order: 10, 15, 20, 30.

2. Step 2: Find node before 15 in traversal

   The node before 15 is 10, so 10 is the inorder predecessor.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Predecessor of 15 = 10 [OK]

Hint: Predecessor is previous in sorted order [OK]

Common Mistakes:

• Choosing the node itself as predecessor
• Choosing parent node incorrectly
• Confusing predecessor with successor

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

function inorderPredecessor(root: TreeNode | null, node: TreeNode): TreeNode | null {
  let predecessor: TreeNode | null = null;
  while (root) {
    if (node.val <= root.val) {
      root = root.left;
    } else {
      predecessor = root;
      root = root.right;
    }
  }
  return predecessor;
}

What is the bug in this code?

medium

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

B. It incorrectly updates predecessor when node.val > root.val

C. It returns the successor instead of predecessor

D. It causes infinite loop when root is null

Solution

1. Step 1: Understand inorder predecessor logic

   If node has a left subtree, predecessor is the rightmost node in that subtree, which this code does not check.

2. Step 2: Analyze code behavior

   The code only moves down from root to find predecessor by comparing values, missing the left subtree check for node.

3. Final Answer:

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

4. Quick Check:

   Left subtree check missing for predecessor [OK]

Hint: Check left subtree for predecessor first [OK]

Common Mistakes:

• Ignoring left subtree of node
• Assuming predecessor is always ancestor
• Confusing predecessor with successor logic

5. You want to find the inorder predecessor of a node with value 25 in this BST:

        40
       /  \
     20    60
    /  \  /  \
  10  30 50  70
       /
     25

Which steps correctly find the inorder predecessor of 25?

hard

A. Check left subtree of 25 (none), then move up to ancestors; predecessor is 50

B. Check left subtree of 25 (none), then move up to ancestors; predecessor is 30

C. Check left subtree of 25 (none), then move up to ancestors; predecessor is 10

D. Check left subtree of 25 (none), then move up to ancestors; predecessor is 20

Solution

1. Step 1: Check left subtree of node 25

   Node 25 has no left child, so no predecessor in left subtree.

2. Step 2: Move up to ancestors to find predecessor

   Ancestor nodes smaller than 25 are candidates; 20 is the closest smaller ancestor.

3. Final Answer:

   Check left subtree of 25 (none), then move up to ancestors; predecessor is 20 -> Option D

4. Quick Check:

   Predecessor found by ancestor smaller than node [OK]

Hint: If no left child, predecessor is nearest smaller ancestor [OK]

Common Mistakes:

• Choosing successor instead of predecessor
• Ignoring ancestors when left subtree is empty
• Picking wrong ancestor value