Remove the Outermost Parentheses using Python

The 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 = 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.

The Test Cases

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 "" + "" = "".

Some things to be aware of

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

The code

def removeOuterParentheses(S):
    ans = ''
    count1 = count2 = i = 0
    start = 1
    while(i < len(S)):
        if(S[i] == '('):
            count1 += 1
        else:
            count2 += 1
        if(count1 == count2):
            end = i
            ans += S[start:end]
            start = i+2
        i += 1
    return ans

Examining the code

We start by declaring a string that we will return at the end, containing our answer. This is called ans.

We create two integer counters, so that we can loop through the string in both directions, these are called count1 and count2 respectively.

Now we set a start value and loop through the string, using it’s length.

At this stage it’s all about checking if the current or inverse string characters match, if they do, then we increment our relevant counts and continue looping. Take note to update the ans here as well, otherwise there will only be a blank string to return at the end of the function’s execution.

Execution

How the code ran:

Your input
"(()())(())"

Output
"()()()"

Expected
"()()()"