Why Floor and Ceil in BST in DSA Javascript?

The Big Idea

What if you could find the closest smaller or bigger number instantly without checking every single one?

The Scenario

Imagine you have a sorted list of numbers on paper, and you want to find the closest number less than or equal to a target (floor), or the closest number greater than or equal to the target (ceil). Doing this by scanning the list every time is slow and tiring.

The Problem

Manually scanning a list for floor or ceil means checking each number one by one. This takes a lot of time if the list is long. It's easy to make mistakes, like missing the closest number or mixing up floor and ceil.

The Solution

A Binary Search Tree (BST) organizes numbers so you can quickly find floor and ceil by moving left or right based on comparisons. This saves time and reduces errors by following a clear path instead of guessing.

Before vs After

✗ Before

function findFloor(arr, target) {
  let floor = null;
  for (let num of arr) {
    if (num <= target && (floor === null || num > floor)) {
      floor = num;
    }
  }
  return floor;
}

✓ After

function findFloorInBST(root, target) {
  let floor = null;
  let current = root;
  while (current !== null) {
    if (current.value === target) return current.value;
    if (current.value < target) {
      floor = current.value;
      current = current.right;
    } else {
      current = current.left;
    }
  }
  return floor;
}

What It Enables

It enables lightning-fast searches for closest smaller or larger values in sorted data, making programs smarter and faster.

Real Life Example

When booking flights, finding the closest cheaper or slightly more expensive ticket quickly helps you decide the best option without checking every price manually.

Key Takeaways

Manual search for floor and ceil is slow and error-prone.

BST structure allows quick navigation to find floor and ceil efficiently.

Using BST for floor and ceil saves time and reduces mistakes in large data.

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 floor concept in BST

   The floor of a value is the largest value in the BST 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 the ceil, not the floor. Options C and D are unrelated to floor.

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 is the correct JavaScript function signature to find the ceil of a value in a BST?

easy

A. function ceilFind(value, root) {}

B. function findFloor(value) {}

C. function findCeil(root, value) {}

D. function ceil(root) {}

Solution

1. Step 1: Identify correct parameter order and naming

   The function to find ceil should take the BST root and the target value as parameters, typically as (root, value).

2. Step 2: Check options for correct signature

   function findCeil(root, value) {} matches this pattern. function ceilFind(value, root) {} reverses parameters, C is for floor and missing root, D misses value parameter.

3. Final Answer:

   function findCeil(root, value) {} -> Option C

4. Quick Check:

   Correct params: root, value [OK]

Hint: Function needs root and value parameters [OK]

Common Mistakes:

• Swapping parameter order
• Missing root or value parameter
• Using wrong function name

3. Given the BST below and value = 14, what is the floor of 14?

       15
      /  \
     10  20
    /  \   \
   8   12  25

medium

A. 15

B. 10

C. 14

D. 12

Solution

1. Step 1: Locate floor value in BST for 14

   Floor is greatest value ≤ 14. Values ≤ 14 are 8, 10, 12. 12 is the greatest among these.

2. Step 2: Confirm no value closer to 14 exists

   15 is greater than 14, so not floor. 14 is not in BST.

3. Final Answer:

   12 -> Option D

4. Quick Check:

   Floor(14) = 12 [OK]

Hint: Floor ≤ value, pick largest such node [OK]

Common Mistakes:

• Choosing 15 which is > 14
• Assuming floor must be exact value
• Picking smaller values like 10 instead of 12

4. Consider this buggy JavaScript code to find ceil in BST:

function findCeil(root, value) {
  if (!root) return -1;
  if (root.val === value) return root.val;
  if (root.val < value) return findCeil(root.right, value);
  let ceil = findCeil(root.left, value);
  return (ceil >= value) ? ceil : root.val;
}

What is the main error?

medium

A. It searches left subtree when root.val < value instead of right

B. It returns -1 when root is null instead of null

C. It compares ceil with value incorrectly

D. It does not handle root.val === value case

Solution

1. Step 1: Analyze subtree traversal logic

   If root.val < value, ceil must be in right subtree, but code wrongly searches left subtree.

2. Step 2: Check other parts

   Return -1 is acceptable as sentinel. Comparison and equality check are correct.

3. Final Answer:

   It searches left subtree when root.val < value instead of right -> Option A

4. Quick Check:

   Wrong subtree chosen for root.val < value [OK]

Hint: Go right if root.val < value for ceil [OK]

Common Mistakes:

• Searching wrong subtree
• Ignoring base case
• Incorrect comparison logic

5. You want to find both floor and ceil of value 17 in this BST:

       16
      /  \
     10  20
    /  \   \
   8   12  25

Which pair is correct?

hard

A. [16, 17]

B. [16, 20]

C. [17, 20]

D. [15, 20]

Solution

1. Step 1: Find floor of 17

   Floor is greatest value ≤ 17. Values ≤ 17 are 8, 10, 12, 16. Largest is 16.

2. Step 2: Find ceil of 17

   Ceil is smallest value ≥ 17. Values ≥ 17 are 20, 25. Smallest is 20.

3. Final Answer:

   [16, 20] -> Option B

4. Quick Check:

   Floor=16, Ceil=20 [OK]

Hint: Floor ≤ value, ceil ≥ value, pick closest [OK]

Common Mistakes:

• Assuming floor or ceil equals value if not present
• Choosing wrong subtree values
• Mixing floor and ceil values