# Remove Outermost Parentheses

## Jan 10, 2020 11:34 · 411 words · 2 minute read

### Remove Outermost Parentheses

#### Problem Statement

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 = P_1 + P_2 + … + P_k, where P_i 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: "(()())(())"
Output: "()()()"
Explanation:
The input string is "(()())(())", with primitive decomposition "(()())" + "(())".
After removing outer parentheses of each part, this is "()()" + "()" = "()()()".
``````

Example 2

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

Example 3

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

Note

1. S.length <= 10000
2. S[i] is “(” or “)”
3. S is a valid parentheses string

#### Solution

1. We start by ntialising a counter with 0.
2. Next, we scan the string char by char, from left to right.
3. Every time an open parentheses ( is encountered, we increment the counter with 1 and if the count is already greator than 1 indicating (a possible exterior parentheses has already been found), we will add this parentheses to the output string builder.
4. when we encounter a closed parentheses ), we decrement the counter and if the counter is greator than 1 (indicating there is more than 1 open parentheses), we can safely add this character to the output string builder.
5. We return the output string after the loop is finished.
``````package main

import (
"fmt"
"strings"
)

func removeOuterParentheses(S string) string {
var sb strings.Builder
count := 0
for _, c := range S {

if c == '(' {
if count > 0 {
sb.WriteString(string(c))
}
count++
}

if c == ')' {
if count > 1 {
sb.WriteString(string(c))
}
count--
}

}
return sb.String()
}

func main() {
fmt.Println(removeOuterParentheses("(()())(())"))
}
``````