DSA interview question

Minimum and Maximum in a BST

Easy · Algorithms · Topics: bst

The problem

A pricing service keeps product prices in a BST and constantly needs the cheapest and most expensive price. In a BST, smaller keys are always to the left, so the minimum is the leftmost node: keep going left until there's no left child. Symmetrically, the maximum is the rightmost node. Each walk follows one path, so it costs O(h), and no comparisons with other nodes are needed.

Example: BST [8, 3, 10, 1, 6, null, 14, null, null, 4, 7, 13] → min 1, max 14.

Function signature

int minValue(TreeNode* root);   // non-empty BST
int maxValue(TreeNode* root);

Test cases

Input (level order)	Output	Explanation
`[8, 3, 10, 1, 6, null, 14, null, null, 4, 7, 13]`	`min 1 max 14`
`[5, 3, 8, 2, 4, 7, 9]`	`min 2 max 9`
`[5, 4, null, 3]`	`min 3 max 5`	The root is the maximum
`[1, null, 2, null, 3]`	`min 1 max 3`	The root is the minimum
`[10]`	`min 10 max 10`

(Confirm: the BST is non-empty and valid.)

How interviewers phrase it

"Find the minimum and maximum element in a binary search tree" (GeeksforGeeks).

Clarifying questions to ask

Is it a BST or a general binary tree? (A BST. A general tree needs a full traversal.)
Can it be empty? (Assume not, or return a sentinel.)
Are duplicates allowed? (Doesn't change the answer.)

Follow-ups to expect

"Why is the leftmost node the minimum?"
"What if the root has no left child?"
"How is this used elsewhere?"
"And for a general binary tree?"
"Complexity?"

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