Floor and Ceil in BST in DSA Python - 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 (left < root < right), we can decide to go left or right at each step to find floor or ceil without checking all nodes.

beginner

If the BST contains the value exactly, what are the floor and ceil of that value?

Both floor and ceil are the value itself because it is equal to the given value.

intermediate

What should be returned if there is no floor or no ceil for a given value in BST?

If no floor exists (all values are greater), return None or indicate no floor. Similarly, if no ceil exists (all values are smaller), return None or indicate no ceil.

What is the floor of 15 in a BST containing values [10, 12, 14, 20, 25]?

A 14

B 15

C 20

D 12

14 is the greatest value less than or equal to 15 in the BST.

What is the ceil of 13 in a BST containing values [10, 12, 14, 20, 25]?

A 12

B 13

C 14

D 20

14 is the smallest value greater than or equal to 13 in the BST.

If the BST has values [5, 10, 15] and you search for floor of 4, what should be the result?

A None

B 4

C 5

D 10

No value less than or equal to 4 exists, so floor is None.

Which direction do you move in BST when searching for floor if current node value is greater than target?

A Return current node

B Go right

C Stop search

D Go left

If current node value is greater, floor must be in left subtree.

If the target value is found in BST, what is the floor and ceil?

A Floor is smaller value, ceil is larger value

B Both floor and ceil are the target value

C Floor is None, ceil is target value

D Floor is target value, ceil is None

Exact match means floor and ceil are the target value itself.

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

Think about how BST ordering helps decide direction.

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

Use simple numbers to illustrate.

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 ceil is the smallest value greater than or equal to the given value, so The smallest value in the BST greater than or equal to the given value is incorrect. Options C and D do not relate 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 Python function signature to find the ceil of a value in a BST node?

easy

A. def ceil_find(value, root):

B. def find_ceil(root, value):

C. def findCeil(value):

D. def ceil(root):

Solution

1. Step 1: Check common parameter order for BST functions

   Functions usually take the root node first, then the value to search for.

2. Step 2: Validate each option

   def find_ceil(root, value): matches this order and naming convention. Options B, C, and D either have wrong parameter order or missing parameters.

3. Final Answer:

   def find_ceil(root, value): -> Option B

4. Quick Check:

   Function(root, value) is standard [OK]

Hint: Root node first, then value in function parameters [OK]

Common Mistakes:

• Swapping parameter order
• Missing one parameter
• Using unclear function names

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

       15
      /  \
     10   20
    /  \    \
   8   12    25

medium

A. 14

B. 15

C. 12

D. 10

Solution

1. Step 1: Locate values less than or equal to 14 in BST

   Values ≤ 14 are 10, 8, 12. 15 and above are greater.

2. Step 2: Find the greatest among these

   The greatest value ≤ 14 is 12.

3. Final Answer:

   12 -> Option C

4. Quick Check:

   Floor(14) = 12 [OK]

Hint: Floor ≤ value, pick largest from left subtree [OK]

Common Mistakes:

• Choosing 15 which is greater than 14
• Assuming floor equals the value if not present
• Picking smallest value instead of largest ≤ value

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

def find_ceil(root, value):
    if root is None:
        return None
    if root.val == value:
        return root.val
    if root.val < value:
        return find_ceil(root.right, value)
    else:
        ceil = find_ceil(root.left, value)
        return ceil if ceil is not None else root.val

What is the main error?

medium

A. It should check for None before recursion

B. It should return root.val when root.val == value

C. It should recurse on root.right when root.val > value

D. It should recurse on root.right when root.val < value

Solution

1. Step 1: Analyze recursion direction for ceil

   If root.val < value, ceil must be in right subtree, so recurse on root.right.

2. Step 2: Identify incorrect recursion

   Code incorrectly recurses on root.left when root.val < value, which is wrong.

3. Final Answer:

   It should recurse on root.right when root.val < value -> Option D

4. Quick Check:

   Ceil search goes right if root.val < value [OK]

Hint: Go right if node value < target for ceil [OK]

Common Mistakes:

• Recursing left instead of right
• Confusing floor and ceil logic
• Not handling None cases properly

5. You have a BST with values [5, 10, 15, 20, 25]. You want to find the floor and ceil of 17. Which pair is correct?

hard

A. Floor = 15, Ceil = 20

B. Floor = 20, Ceil = 25

C. Floor = 10, Ceil = 15

D. Floor = 17, Ceil = 17

Solution

1. Step 1: Identify floor of 17 in BST

   Floor is greatest value ≤ 17. Values ≤ 17 are 5, 10, 15. Greatest is 15.

2. Step 2: Identify ceil of 17 in BST

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

3. Final Answer:

   Floor = 15, Ceil = 20 -> Option A

4. Quick Check:

   Floor ≤ 17 = 15, Ceil ≥ 17 = 20 [OK]

Hint: Floor ≤ value, ceil ≥ value in sorted BST [OK]

Common Mistakes:

• Choosing floor or ceil outside BST values
• Assuming floor or ceil equals the value if not present
• Mixing floor and ceil values