# [Solved] A valid parentheses string is either empty “”, “(” + A + “)”, or A + B, where A and B are valid parentheses strings, and + represents string concatenation.

## Question

A valid parentheses string is either empty `""``"(" + A + ")"`, or `A + B`, where `A` and `B` are valid parentheses strings, and `+` represents string concatenation.

• For example, `""``"()"``"(())()"`, and `"(()(()))"` are all valid parentheses strings.

A valid parentheses string `s` is primitive if it is nonempty, and there does not exist a way to split it into `s = A + B`, with `A` and `B` nonempty valid parentheses strings.

Given a valid parentheses string `s`, consider its primitive decomposition: `s = P1 + P2 + ... + Pk`, where `Pi` are primitive valid parentheses strings.

Return `s` after removing the outermost parentheses of every primitive string in the primitive decomposition of `s`.

Example 1:

```Input: s = "(()())(())"
Output: "()()()"
Explanation:
The input string is "(()())(())", with primitive decomposition "(()())" + "(())".
After removing outer parentheses of each part, this is "()()" + "()" = "()()()".
```

Example 2:

```Input: s = "(()())(())(()(()))"
Output: "()()()()(())"
Explanation:
The input string is "(()())(())(()(()))", with primitive decomposition "(()())" + "(())" + "(()(()))".
After removing outer parentheses of each part, this is "()()" + "()" + "()(())" = "()()()()(())".
```

Example 3:

```Input: s = "()()"
Output: ""
Explanation:
The input string is "()()", with primitive decomposition "()" + "()".
After removing outer parentheses of each part, this is "" + "" = "".
```

Constraints:

• `1 <= s.length <= 105`
• `s[i]` is either `'('` or `')'`.
• `s` is a valid parentheses string.

## Python Solution

```class Solution:
def removeOuterParentheses(self, S: str) -> str:
opened=0
res=''

for c in S:
if c=='(' and opened>0:res+=c
if c==')' and opened>1:res+=c
opened += 1 if c == '(' else -1
return res``` ##### Abhishek Sharma

Started my Data Science journey in my 2nd year of college and since then continuously into it because of the magical powers of ML and continuously doing projects in almost every domain of AI like ML, DL, CV, NLP.

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