DSA interview question

Floor and Ceil in a BST (One Walk)

Easy · Algorithms · Topics: bst, recursion

The problem

A price-matching engine stores available price points in a BST. For a customer's target price, it needs the floor (the largest price ≤ target) and the ceil (the smallest price ≥ target), or −1 where none exists. Both candidates lie on the search path for the target. Walking down as if searching, every node with value ≤ target is a better floor than any seen before, and every node with value ≥ target is a better ceil. So a single walk produces both answers.

Example: BST [8, 4, 12, 2, 6, 10, 14], target 5 → floor 4, ceil 6.

Function signature

pair<int, int> floorAndCeil(TreeNode* root, int key);  // {floor, ceil}; -1 when absent

Test cases

Input `(tree, key)`	Output	Explanation
`([8,4,12,2,6,10,14], 5)`	`floor 4 ceil 6`
`([8,4,12,2,6,10,14], 8)`	`floor 8 ceil 8`	An exact match is both
`([8,4,12,2,6,10,14], 1)`	`floor -1 ceil 2`	Below everything
`([8,4,12,2,6,10,14], 15)`	`floor 14 ceil -1`	Above everything
`([8,4,12,2,6,10,14], 11)`	`floor 10 ceil 12`

(Confirm: keys are distinct and positive, so −1 can mean "none".)

How interviewers phrase it

"Find the floor and ceil of a given key in a BST" (GeeksforGeeks "Floor in BST" and "Ceil in BST").

Clarifying questions to ask

Floor is the largest ≤ key, and ceil the smallest ≥ key? (Yes.)
What should be returned if none exists? (−1.)
Are keys distinct? (Yes.)

Follow-ups to expect

"Why are both answers on the search path?"
"Why is the last candidate the best?"
"What happens on an exact match?"
"How do these generalise?"
"Complexity?"

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