MissingParentheses | Topcoder Archive

Problem Statement

Given a string of parentheses, you must turn it into a well formed string by inserting as few parentheses as possible, at any position (you cannot delete or change any of the existing parentheses).

A well formed string of parentheses is defined by the following rules:

The empty string is well formed.
If s is a well formed string, (s) is a well formed string.
If s and t are well formed strings, their concatenation st is a well formed string.

As examples, "(()())", "" and "(())()" are well formed strings and "())(", "()(" and ")" are malformed strings.

Given a String par of parentheses, return the minimum number of parentheses that need to be inserted to make it into a well formed string.

Definition

Class:: MissingParentheses
Method:: countCorrections
Parameters:: String
Returns:: int
Method signature:: int countCorrections(String par)
(be sure your method is public)

Constraints

par will contain between 1 and 50 characters, inclusive.
Each character of par will be an opening or closing parenthesis, i.e., '(' or ')'.

Examples

```
"(()(()"
```
```
Returns: 2
```
The string below is a possible well formed string you can get to by inserting the two closing parentheses marked. (())(()) ^ ^
```
"()()(()"
```
```
Returns: 1
```
You can fix the string by inserting a single closing parenthesis at the end.
```
"(())(()())"
```
```
Returns: 0
```
The input string is well formed, so no insertion is needed.

"())(())((()))))()((())))()())())())()()()"

Returns: 7

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