# Length of longest balanced parentheses prefix

Given a string of open bracket ‘(‘ and closed bracket ‘)’. The task is to find the length of longest balanced prefix.

Examples:

```Input : S = "((()())())(("
Output : 10
From index 0 to index 9, they are forming
a balanced parentheses prefix.

Input : S = "()(())((()"
Output : 6
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is take value of open bracket ‘(‘ as 1 and value of close bracket ‘)’ as -1. Now start finding the prefix sum of the given string. The farthest index, say maxi, where the value of sum is 0 is the index upto which longest balanced prefix exists. So the answer would be maxi + 1.

Below is the implementation of this approach:

## C++

 `// CPP Program to find length of longest balanced ` `// parentheses prefix. ` `#include ` `using` `namespace` `std; ` ` `  `// Return the length of longest balanced parentheses  ` `// prefix. ` `int` `maxbalancedprefix(``char` `str[], ``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``int` `maxi = 0; ` ` `  `    ``// Traversing the string. ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// If open bracket add 1 to sum. ` `        ``if` `(str[i] == ``'('``) ` `            ``sum += 1; ` ` `  `        ``// If closed bracket subtract 1 ` `        ``// from sum ` `        ``else` `            ``sum -= 1; ` ` `  `        ``// If sum is 0, store the index ` `        ``// value. ` `        ``if` `(sum == 0) ` `            ``maxi = i; ` `    ``} ` ` `  `    ``return` `maxi + 1; ` `} ` ` `  `// Driven Program ` `int` `main() ` `{ ` `    ``char` `str[] = ``"((()())())(("``; ` `    ``int` `n = ``strlen``(str); ` ` `  `    ``cout << maxbalancedprefix(str, n) << endl; ` `    ``return` `0; ` `} `

## Java

 `// Java Program to find length of longest  ` `// balanced parentheses prefix. ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// Return the length of longest  ` `    ``// balanced parentheses prefix. ` `    ``static` `int` `maxbalancedprefix(String str, ``int` `n) ` `    ``{ ` `        ``int` `sum = ``0``; ` `        ``int` `maxi = ``0``; ` `     `  `        ``// Traversing the string. ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` `     `  `            ``// If open bracket add 1 to sum. ` `            ``if` `(str.charAt(i) == ``'('``) ` `                ``sum += ``1``; ` `     `  `            ``// If closed bracket subtract 1 ` `            ``// from sum ` `            ``else` `                ``sum -= ``1``; ` `     `  `            ``// If sum is 0, store the index ` `            ``// value. ` `            ``if` `(sum == ``0``) ` `                ``maxi = i; ` `        ``} ` `     `  `        ``return` `maxi + ``1``; ` `    ``} ` `     `  `    ``// Driven Program ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{ ` `        ``String str = ``"((()())())(("``; ` `        ``int` `n = str.length(); ` `     `  `        ``System.out.println( maxbalancedprefix(str, n)); ` `             `  `    ``} ` `} ` ` `  `// This code is contributed by vt_m `

## Python3

 `# Python3 code to find length of  ` `# longest balanced parentheses prefix. ` ` `  `# Function to return the length of  ` `# longest balanced parentheses prefix. ` `def` `maxbalancedprefix (``str``, n): ` `    ``_sum ``=` `0` `    ``maxi ``=` `0` `     `  `    ``# Traversing the string. ` `    ``for` `i ``in` `range``(n): ` `     `  `        ``# If open bracket add 1 to sum. ` `        ``if` `str``[i] ``=``=` `'('``: ` `            ``_sum ``+``=` `1` `         `  `        ``# If closed bracket subtract 1 ` `        ``# from sum ` `        ``else``: ` `            ``_sum ``-``=` `1` `             `  `        ``# If sum is 0, store the  ` `        ``# index value. ` `        ``if` `_sum ``=``=` `0``: ` `            ``maxi ``=` `i ` `    ``return` `maxi ``+` `1` `     `  ` `  `# Driver Code ` `str` `=` `'((()())())(('` `n ``=` `len``(``str``) ` `print``(maxbalancedprefix (``str``, n)) ` ` `  `#This code is contributed by "Abhishek Sharma 44" `

## C#

 `// C# Program to find length of longest  ` `// balanced parentheses prefix. ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// Return the length of longest  ` `    ``// balanced parentheses prefix. ` `    ``static` `int` `maxbalancedprefix(``string` `str, ``int` `n) ` `    ``{ ` `        ``int` `sum = 0; ` `        ``int` `maxi = 0; ` `     `  `        ``// Traversing the string. ` `        ``for` `(``int` `i = 0; i < n; i++) { ` `     `  `            ``// If open bracket add 1 to sum. ` `            ``if` `(str[i] == ``'('``) ` `                ``sum += 1; ` `     `  `            ``// If closed bracket subtract 1 ` `            ``// from sum ` `            ``else` `                ``sum -= 1; ` `     `  `            ``// If sum is 0, store the index ` `            ``// value. ` `            ``if` `(sum == 0) ` `                ``maxi = i; ` `        ``} ` `     `  `        ``return` `maxi + 1; ` `    ``} ` `     `  `    ``// Driven Program ` `    ``public` `static` `void` `Main ()  ` `    ``{ ` `        ``string` `str = ``"((()())())(("``; ` `        ``int` `n = str.Length; ` `     `  `        ``Console.WriteLine( maxbalancedprefix(str, n)); ` `             `  `    ``} ` `} ` ` `  `// This code is contributed by vt_m `

## PHP

 ` `

Output:

```10
```

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