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Length of longest balanced parentheses prefix
  • Difficulty Level : Easy
  • Last Updated : 09 Nov, 2020

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

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++



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// CPP Program to find length of longest balanced
// parentheses prefix.
#include <bits/stdc++.h>
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 first bracket is closing bracket
        // then this condition would help
        if (sum < 0)
            break;
  
        // If sum is 0, store the index
        // value.
        if (sum == 0)
            maxi = i + 1;
    }
  
    return maxi;
}
  
// Driven Program
int main()
{
    char str[] = "((()())())((";
    int n = strlen(str);
  
    cout << maxbalancedprefix(str, n) << endl;
    return 0;
}

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Java

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// 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 first bracket is closing bracket
            // then this condition would help
            if (sum < 0)
                break;
  
            // If sum is 0, store the index
            // value.
            if (sum == 0)
                maxi = i + 1;
        }
  
        return maxi;
    }
  
    // 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

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Python3

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# 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 first bracket is closing bracket
       # then this condition would help
        if _sum < 0:
            break
              
        # If sum is 0, store the 
        # index value.
        if _sum == 0:
            maxi = i + 1
    return maxi
      
  
# Driver Code
str = '((()())())(('
n = len(str)
print(maxbalancedprefix (str, n))
  
# This code is contributed by "Abhishek Sharma 44"

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C#

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// 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 first bracket is closing bracket
            // then this condition would help
            if (sum < 0)
                break;
  
            // If sum is 0, store the index
            // value.
            if (sum == 0)
                maxi = i + 1;
        }
  
        return maxi;
    }
  
    // Driven Program
    public static void Main()
    {
        string str = "((()())())((";
        int n = str.Length;
  
        Console.WriteLine(maxbalancedprefix(str, n));
    }
}
  
// This code is contributed by vt_m

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PHP

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<?php
// PHP Program to find length 
// of longest balanced
// parentheses prefix.
  
// Return the length of longest
// balanced parentheses prefix.
function maxbalancedprefix($str, $n)
{
    $sum = 0;
    $maxi = 0;
  
    // Traversing the string.
    for ($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 < 0)
            break;
  
        // If sum is 0, store the index
        // value.
        if ($sum == 0)
            $maxi = $i+1;
    }
  
    return $maxi;
}
  
// Driver Code
$str = array('(', '(', '(', ')', '(', ')', ')', '(', ')', ')', '(', '(');
$n = count($str);
  
echo maxbalancedprefix($str, $n);
  
// This code is contributed by anuj_67..
?>

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Output:

10

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