Understanding the Problem
We are given a valid parentheses string made up of multiple primitive parts. A primitive parentheses string is a valid sequence that cannot be split into smaller valid parts. For example, "()"
and "(())"
are primitives, but "(()())(())"
contains multiple primitive parts.
Our task is to remove the outermost parentheses from each primitive group. That means for each such primitive, we will drop the very first '('
and the last ')'
.
Step-by-Step Solution with Example
Step 1: Choose an example input
Let’s walk through the string "(()())(())"
.
This contains two primitive parts:
Step 2: Understand how nesting works
We will use a variable open
to track the depth of nesting:
- When we see
'('
, we increase the open
counter.
- When we see
')'
, we decrease the open
counter.
Step 3: Remove outermost parentheses
The outermost '('
is when open
goes from 0 to 1 — we skip adding that character.
The outermost ')'
is when open
becomes 0 again — we also skip adding that character.
All other characters are added to the result.
Step 4: Simulate the process
For input "(()())(())"
:
- First primitive:
"(()())"
→ Remove outermost → "()()"
- Second primitive:
"(())"
→ Remove outermost → "()"
Final output: "()()()"
Edge Cases
- Empty string:
""
→ No primitives, return ""
- Multiple shallow primitives:
"()()"
→ Each is primitive, removing outer gives ""
for each → Final output: ""
- Deeply nested primitive:
"((()))"
→ One primitive → Removing outer gives "(())"
Finally
This approach efficiently processes the string in a single pass using a counter to track the nesting level. By only skipping the first and last parentheses of each primitive, we achieve the desired result. The logic is clean, fast, and works well for all types of valid input strings, including edge cases.
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