DSA interview question

Maximum Nesting Depth of the Parentheses

Medium · Data structures · Topics: string, stack

The problem

A formula editor highlights how deeply nested each expression is, so users can spot overly complicated formulas. Given a valid expression like "(1+(2*3)+((8)/4))+1", it must report the maximum depth of nested parentheses: here 3, reached at (8). Since the expression is valid and there's only one bracket type, a running counter (increment on (, decrement on )) always equals the current depth, so the answer is simply the largest value the counter reaches.

Example: "(1+(2*3)+((8)/4))+1" → 3.

Function signature

int maxDepth(const string& s);  // s is a valid parentheses expression (may include digits and operators)

Test cases

Input `s`	Output	Explanation
`"(1+(2*3)+((8)/4))+1"`	3	The 8 is inside three pairs
`"(1)+((2))+(((3)))"`	3
`"1+(2*3)/(2-1)"`	1
`"1"`	0	No parentheses
`"()(())((()))"`	3

(Confirm: the input is a valid expression; characters other than parentheses are ignored.)

How interviewers phrase it

"Return the maximum nesting depth of a valid parentheses string" (LeetCode 1614).
A warm-up before harder bracket problems: valid parentheses with several bracket types, minimum removals to make valid, longest valid parentheses.

Clarifying questions to ask

Is the string guaranteed to be valid?
Are there other bracket types, like [ and {?
Do other characters appear? (They're ignored.)

Follow-ups to expect

"Why don't you need a stack?"
"What if the string might be invalid?"
"With several bracket types?"
"Complexity?"

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