Floor and Ceil in BST in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the floor of a value in a Binary Search Tree (BST)?

The floor of a value in a BST is the greatest value in the BST that is less than or equal to the given value.

beginner

What is the ceil of a value in a Binary Search Tree (BST)?

The ceil of a value in a BST is the smallest value in the BST that is greater than or equal to the given value.

intermediate

How does the BST property help in finding floor and ceil efficiently?

Because BST nodes are ordered, we can decide to go left or right at each node to find floor or ceil without checking all nodes, making the search faster than scanning the whole tree.

beginner

In a BST, if the current node's value is equal to the target value, what are the floor and ceil?

Both floor and ceil are the current node's value because it exactly matches the target.

intermediate

If the target value is smaller than the current node's value, which subtree should you explore to find the floor?

You should explore the left subtree because all values in the right subtree are greater than the current node's value, which is already bigger than the target.

What does the floor of a value in a BST represent?

A The smallest value greater than or equal to the target

B The exact value only if it exists

C The root value of the BST

D The greatest value less than or equal to the target

Floor is the greatest value in the BST that is less than or equal to the target value.

If the target value is greater than the current node's value, where should you look to find the ceil?

A Right subtree

B Left subtree

C Current node only

D Both subtrees

Since the target is greater, the ceil must be in the right subtree or the current node if it matches.

When the current node's value equals the target, what is the floor and ceil?

A Floor is smaller, ceil is larger

B Both floor and ceil are the current node's value

C Floor is null, ceil is current node's value

D Floor is current node's value, ceil is null

Exact match means floor and ceil are the same as the current node's value.

Which property of BST helps in finding floor and ceil efficiently?

A Nodes are stored in a linked list

B Nodes are stored in a queue

C Left child is always smaller, right child is always larger

D All nodes have two children

BST property that left child < node < right child allows efficient search.

If the target value is smaller than the current node's value, which subtree is explored to find the ceil?

A Left subtree

B Right subtree

C Current node only

D No subtree

Since target is smaller, ceil could be the current node or in the left subtree.

Explain how to find the floor of a given value in a BST step-by-step.

Think about how BST ordering guides your search direction.

Describe the difference between floor and ceil in a BST with examples.

Use simple numbers to illustrate the concept.

Practice

1. What does the floor of a value in a Binary Search Tree (BST) represent?

easy

A. The greatest value in the BST less than or equal to the given value

B. The smallest value in the BST greater than or equal to the given value

C. The root value of the BST

D. The average of all values in the BST

Solution

1. Step 1: Understand the definition of floor in BST

   The floor of a value in BST is the greatest value that is less than or equal to the given value.

2. Step 2: Compare with other options

   The smallest value in the BST greater than or equal to the given value describes ceil, not floor. Options C and D are unrelated to floor concept.

3. Final Answer:

   The greatest value in the BST less than or equal to the given value -> Option A

4. Quick Check:

   Floor = greatest ≤ value [OK]

Hint: Floor is largest value ≤ target in BST [OK]

Common Mistakes:

• Confusing floor with ceil
• Thinking floor is the smallest value
• Assuming floor is always the root

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

easy

A. function findCeil(key: number, root: TreeNode): number

B. function findCeil(root: TreeNode | null, key: number): number | null

C. function findCeil(root: TreeNode, key: string): number

D. function findCeil(root: TreeNode | null): number

Solution

1. Step 1: Check parameter order and types

   Function should accept root node (possibly null) and a key number to find ceil for.

2. Step 2: Validate return type

   Return type should be number or null if no ceil found. function findCeil(root: TreeNode | null, key: number): number | null matches this.

3. Final Answer:

   function findCeil(root: TreeNode | null, key: number): number | null -> Option B

4. Quick Check:

   Correct params and return type [OK]

Hint: Root first, key second, return number or null [OK]

Common Mistakes:

• Swapping parameter order
• Using wrong parameter types
• Missing null in root type

3. Given the BST below and key = 14, what is the ceil value?

       10
      /  \
     5    15
         /  \
        12   20

medium

A. 12

B. 20

C. 15

D. null

Solution

1. Step 1: Locate key 14 in BST or nearest nodes

   14 is not in BST. Check nodes greater than or equal to 14: 15 and 20.

2. Step 2: Find smallest node ≥ 14

   Between 15 and 20, 15 is smaller and ≥ 14, so ceil is 15.

3. Final Answer:

   15 -> Option C

4. Quick Check:

   Ceil = smallest ≥ 14 is 15 [OK]

Hint: Ceil is smallest value ≥ key in BST [OK]

Common Mistakes:

• Choosing 12 which is less than 14
• Choosing 20 which is larger but not smallest ≥ 14
• Returning null when ceil exists

4. Consider this TypeScript function to find floor in BST:

function findFloor(root: TreeNode | null, key: number): number | null {
  if (!root) return null;
  if (root.val === key) return root.val;
  const floorRight = findFloor(root.right, key);
  return floorRight !== null ? floorRight : root.val;
}

What is the bug in this code?

medium

A. It returns root.val even if floorRight is null and root.val > key

B. It does not check for null root

C. It returns key instead of floor value

D. It incorrectly calls findFloor on root.left when root.val < key

Solution

1. Step 1: Identify missing logic for root.val > key

   The code does not recurse into the left subtree when root.val > key. Instead, it always computes floorRight from the right subtree.

2. Step 2: Trace buggy return

   When root.val > key and right subtree yields null for floorRight (common case), it returns root.val which exceeds key, violating floor definition.

3. Final Answer:

   It returns root.val even if floorRight is null and root.val > key -> Option A

4. Quick Check:

   Missing left recursion on root.val > key [OK]

Hint: Check return when right subtree floor is null [OK]

Common Mistakes:

• Ignoring null checks
• Confusing left and right subtree calls
• Assuming root.val always valid floor

5. You have a BST with values [8, 4, 12, 2, 6, 10, 14]. You want to find the floor and ceil of 5. Which pair is correct?

medium

A. Floor = 2, Ceil = 8

B. Floor = 6, Ceil = 4

C. Floor = 5, Ceil = 5

D. Floor = 4, Ceil = 6

Solution

1. Step 1: Identify floor of 5 in BST

   Floor is greatest value ≤ 5. Values ≤ 5 are 2 and 4. Greatest is 4.

2. Step 2: Identify ceil of 5 in BST

   Ceil is smallest value ≥ 5. Values ≥ 5 are 6, 8, 10, 12, 14. Smallest is 6.

3. Final Answer:

   Floor = 4, Ceil = 6 -> Option D

4. Quick Check:

   Floor ≤ 5 = 4, Ceil ≥ 5 = 6 [OK]

Hint: Floor ≤ key, Ceil ≥ key; pick closest values [OK]

Common Mistakes:

• Swapping floor and ceil values
• Assuming floor or ceil equals key if not present
• Choosing values not in BST