Floor and Ceil in BST in DSA Javascript - Execution Trace

Concept Flow - Floor and Ceil in BST

Start at root node

↓

Compare target with current node value

↓

Go left

↓

Update floor

↓

Repeat until leaf node

↓

Return floor and ceil values

Start from the root, compare target with node value, move left or right updating floor or ceil until no more nodes to visit.

Execution Sample

DSA Javascript

function floorCeilBST(root, target) {
  let floor = null, ceil = null;
  let current = root;
  while (current) {
    if (current.val === target) return { floor: target, ceil: target };
    else if (current.val < target) {
      floor = current.val;
      current = current.right;
    } else {
      ceil = current.val;
      current = current.left;
    }
  }
  return { floor, ceil };
}

Find floor and ceil of target in BST by traversing and updating floor or ceil accordingly.

Execution Table

Step	Operation	Current Node Value	Target	Floor	Ceil	Pointer Move	Visual State
1	Start at root	8	6	null	null	Compare 6 with 8	8 / \ 3 10 / \ 1 6 14
2	target=6 < current=8, update ceil=8	8	6	null	8	Move left	8 / \ 3 10 / \ 1 6 14
3	At node 3, 3 < 6	3	6	3	8	Move right	8 / \ 3 10 / \ 1 6 14
4	At node 6, 6 == 6	6	6	6	6	Found exact match	8 / \ 3 10 / \ 1 6 14
5	Return floor and ceil	-	6	6	6	Stop	8 / \ 3 10 / \ 1 6 14

💡 Exact match found at node with value 6, floor and ceil both are 6.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
floor	null	null	null	3	6	6
ceil	null	null	8	8	6	6
current	root(8)	8	3	6	6	null

Key Moments - 3 Insights

Why do we update floor when current node value is less than target?

Because floor is the greatest value less than or equal to target. When current.val < target, current.val can be a candidate floor. See execution_table step 3 where floor updates to 3.

Why do we update ceil when current node value is greater than target?

Because ceil is the smallest value greater than or equal to target. When current.val > target, current.val can be a candidate ceil. See execution_table step 2 where ceil updates to 8.

What happens if target matches a node value exactly?

We return that value as both floor and ceil immediately. See execution_table step 4 where current.val == target, so floor and ceil both become 6.

Visual Quiz - 3 Questions

Look at the execution_table, what is the floor value after step 3?

A null

B 6

C 3

D 8

💡 Hint

Check the 'Floor' column in execution_table row for step 3.

At which step does the algorithm find an exact match for the target?

A Step 4

B Step 3

C Step 2

D Step 5

💡 Hint

Look for the step where current node value equals target in execution_table.

If the target was 5 instead of 6, what would be the ceil after step 3?

A 3

B 8

C 6

D null

💡 Hint

Check the 'Ceil' column in execution_table and variable_tracker after step 3.

Concept Snapshot

Floor and Ceil in BST:
- Floor: greatest value ≤ target
- Ceil: smallest value ≥ target
- Start at root, compare target with node
- Move left if node ≥ target (update ceil)
- Move right if node < target (update floor)
- Stop when node is null or exact match found

Full Transcript

To find floor and ceil in a BST, start at the root node. Compare the target with the current node's value. If the current node's value equals the target, return it as both floor and ceil. If the current node's value is less than the target, update floor to current node's value and move right. If greater, update ceil and move left. Repeat until no more nodes to visit. The final floor and ceil are returned. This method efficiently uses BST properties to find closest values.