Remove Outermost Parentheses

Remove Outermost Parentheses

What is this problem about?

The Remove Outermost Parentheses interview question gives you a string of parentheses that is a concatenation of valid primitive parenthesized strings. You must remove the outermost parentheses of each primitive component and return the result. A primitive string is one that cannot be split into two non-empty valid parenthesized strings.

Why is this asked in interviews?

This problem is asked at Uber, Microsoft, Flipkart, Meta, Amazon, and Bloomberg as a warm-up stack and string interview question. It tests whether a candidate understands how to detect the boundary between primitive components using a depth counter, and can manipulate strings or use a stack to collect inner characters while skipping the outermost layer. It also introduces the concept of decomposing strings into semantic units.

Algorithmic pattern used

The pattern is a depth counter (or stack-size tracking). Iterate through the string. Use a counter depth starting at 0. For (: if depth > 0, include it in the result. Then increment depth. For ): decrement depth first. If depth > 0, include it in the result. This naturally skips the outermost ( (encountered at depth=0) and the outermost ) (which decrements depth to 0).

Example explanation

Input: "(()())(())"

• (: depth=0 → skip (outermost). depth becomes 1.
• (: depth=1 > 0 → include. depth becomes 2.
• ): depth becomes 1 > 0 → include.
• (: depth=1 → include. depth becomes 2.
• ): depth becomes 1 → include.
• ): depth becomes 0 → skip (outermost close).
• (: depth=0 → skip. depth becomes 1.
• (: depth=1 → include. depth becomes 2.
• ): depth becomes 1 → include.
• ): depth becomes 0 → skip.

Result: "()()"+ "()" = "()()()".

Common mistakes candidates make

• Including the outermost ( by checking depth after incrementing instead of before.
• Forgetting that each primitive group independently starts at depth 0.
• Using a full stack when a simple integer counter is sufficient.
• Confusing this with a balanced parentheses validation problem.

Interview preparation tip

For the Remove Outermost Parentheses coding problem, the string and stack interview pattern simplifies to a clean depth counter. Practice the order of operations: for (, check then increment; for ), decrement then check. This ordering is the difference between correct and incorrect solutions. Interviewers at Bloomberg often ask a follow-up: "What if the input had multiple types of brackets?" — extending the depth counter to a stack handles that elegantly.