Find an equal point in a string of brackets

Difficulty Level : Medium
Last Updated : 05 Apr, 2020

Given a string of brackets, the task is to find an index k which decides the number of opening brackets is equal to the number of closing brackets.
String must be consists of only opening and closing brackets i.e. ‘(‘ and ‘)’.

An equal point is an index such that the number of opening brackets before it is equal to the number of closing brackets from and after.

Examples:

Input : str = "(())))("
Output:   4
After index 4, string splits into (())
and ))(. Number of opening brackets in the 
first part is equal to number of closing 
brackets in the second part.

Input : str = "))"
Output: 2
As after 2nd position i.e. )) and "empty"
string will be split into these two parts:
So, in this number of opening brackets i.e.
0 in the first part is equal to number of 
closing brackets in the second part i.e. 
also 0.

Asked in : Amazon

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Store the number of opening brackets appears in the string up to every index, it must start from starting index.
Similarly, Store the number of closing brackets appears in the string upto each and every index but it should be done from last index.
Check if any index has the same value of opening and closing brackets.

C++

// C++ program to find an index k which
// decides the number of opening brackets
// is equal to the number of closing brackets
#include<bits/stdc++.h>
using namespace std;
  
// Function to find an equal index
int findIndex(string str)
{
    int len = str.length();
    int open[len+1], close[len+1];
    int index = -1;
    memset(open, 0, sizeof (open));
    memset(close, 0, sizeof (close));
  
    open[0] = 0;
    close[len] = 0;
    if (str[0]=='(')
        open[1] = 1;
    if (str[len-1] == ')')
        close[len-1] = 1;
  
    // Store the number of opening brackets
    // at each index
    for (int i = 1; i < len; i++)
    {
        if ( str[i] == '(' )
            open[i+1] = open[i] + 1;
        else
            open[i+1] = open[i];
    }
  
    // Store the number of closing brackets
    // at each index
    for (int i = len-2; i >= 0; i--)
    {
        if ( str[i] == ')' )
            close[i] = close[i+1] + 1;
        else
            close[i] = close[i+1];
    }
  
    // check if there is no opening or closing
    // brackets
    if (open[len] == 0)
        return len;
    if (close[0] == 0)
        return 0;
  
    // check if there is any index at which
    // both brackets are equal
    for (int i=0; i<=len; i++)
        if (open[i] == close[i])
            index = i;
  
    return index;
}
  
// Driver code
int main()
{
    string str = "(()))(()()())))";
    cout << findIndex(str);
    return 0;
}

Java

// Java program to find an index k which
// decides the number of opening brackets
// is equal to the number of closing brackets
  
public class GFG 
{
    // Method to find an equal index
    static int findIndex(String str)
    {
        int len = str.length();
        int open[] = new int[len+1];
        int    close[] = new int[len+1];
        int index = -1;
       
        open[0] = 0;
        close[len] = 0;
        if (str.charAt(0)=='(')
            open[1] = 1;
        if (str.charAt(len-1) == ')')
            close[len-1] = 1;
       
        // Store the number of opening brackets
        // at each index
        for (int i = 1; i < len; i++)
        {
            if ( str.charAt(i) == '(' )
                open[i+1] = open[i] + 1;
            else
                open[i+1] = open[i];
        }
       
        // Store the number of closing brackets
        // at each index
        for (int i = len-2; i >= 0; i--)
        {
            if ( str.charAt(i) == ')' )
                close[i] = close[i+1] + 1;
            else
                close[i] = close[i+1];
        }
       
        // check if there is no opening or closing
        // brackets
        if (open[len] == 0)
            return len;
        if (close[0] == 0)
            return 0;
      
        // check if there is any index at which
        // both brackets are equal
        for (int i=0; i<=len; i++)
            if (open[i] == close[i])
                index = i;
       
        return index;
    }
      
    // Driver Method
    public static void main(String[] args)
    {
        String str = "(()))(()()())))";
        System.out.println(findIndex(str));
    }
}

Python 3

# Method to find an equal index
def findIndex(str):
    l = len(str)
    open = [0] * (l + 1)
    close = [0] * (l + 1)
    index = -1
      
    open[0] = 0
    close[l] = 0
    if (str[0]=='('):
        open[1] = 1
    if (str[l - 1] == ')'):
        close[l - 1] = 1
      
    # Store the number of
    # opening brackets
    # at each index
    for i in range(1, l):
        if (str[i] == '('):
            open[i + 1] = open[i] + 1
        else:
            open[i + 1] = open[i]
      
    # Store the number
    # of closing brackets
    # at each index
    for i in range(l - 2, -1, -1):
        if ( str[i] == ')'):
            close[i] = close[i + 1] + 1
        else:
            close[i] = close[i + 1]
      
    # check if there is no 
    # opening or closing brackets
    if (open[l] == 0):
        return len
    if (close[0] == 0):
        return 0
      
    # check if there is any 
    # index at which both
    # brackets are equal
    for i in range(l + 1):
        if (open[i] == close[i]):
            index = i
      
    return index
      
# Driver Code
str = "(()))(()()())))"
print(findIndex(str))
  
# This code is contributed 
# by ChitraNayal

C#

// C# program to find an index 
// k which decides the number
// of opening brackets is equal 
// to the number of closing brackets
using System;
  
class GFG 
{
// Method to find an equal index
static int findIndex(string str)
{
    int len = str.Length;
    int[] open = new int[len + 1];
    int[] close = new int[len + 1];
    int index = -1;
  
    open[0] = 0;
    close[len] = 0;
    if (str[0] == '(')
        open[1] = 1;
    if (str[len - 1] == ')')
        close[len - 1] = 1;
  
    // Store the number of 
    // opening brackets
    // at each index
    for (int i = 1; i < len; i++)
    {
        if (str[i] == '(')
            open[i + 1] = open[i] + 1;
        else
            open[i + 1] = open[i];
    }
  
    // Store the number 
    // of closing brackets
    // at each index
    for (int i = len - 2; i >= 0; i--)
    {
        if (str[i] == ')')
            close[i] = close[i + 1] + 1;
        else
            close[i] = close[i + 1];
    }
  
    // check if there is no
    // opening or closing
    // brackets
    if (open[len] == 0)
        return len;
    if (close[0] == 0)
        return 0;
  
    // check if there is any
    // index at which both 
    // brackets are equal
    for (int i = 0; i <= len; i++)
        if (open[i] == close[i])
            index = i;
  
    return index;
}
  
// Driver Code
public static void Main()
{
    string str = "(()))(()()())))";
    Console.Write(findIndex(str));
}
}
  
// This code is contributed 
// by ChitraNayal

PHP

<?php
// Method to find an equal index
function findIndex($str)
{
    $len = strlen($str);
    $open = array(0, $len + 1, NULL);
    $close = array(0, $len + 1, NULL);
    $index = -1;
      
    $open[0] = 0;
    $close[$len] = 0;
    if ($str[0] == '(')
    $open[1] = 1;
    if ($str[$len - 1] == ')')
    $close[$len - 1] = 1;
      
    // Store the number 
    // of opening brackets
    // at each index
    for ($i = 1; $i < $len; $i++)
    {
        if ($str[$i] == '(')
            $open[$i + 1] = $open[$i] + 1;
        else
            $open[$i + 1] = $open[$i];
    }
      
    // Store the number 
    // of closing brackets
    // at each index
    for ($i = $len - 2; $i >= 0; $i--)
    {
        if ($str[$i] == ')')
        $close[$i] = $close[$i + 1] + 1;
        else
        $close[$i] = $close[$i + 1];
    }
      
    // check if there is no 
    // opening or closing
    // brackets
    if ($open[$len] == 0)
        return $len;
    if ($close[0] == 0)
        return 0;
      
    // check if there is any 
    // index at which both
    // brackets are equal
    for ($i = 0; $i <= $len; $i++)
        if ($open[$i] == $close[$i])
            $index = $i;
      
    return $index;
}
      
// Driver Code
$str = "(()))(()()())))";
echo (findIndex($str));
  
// This code is contributed
// by ChitraNayal
?>

Output:

Time Complexity : O(n)

This article is contributed by Sahil Chhabra (akku). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Java

Python 3

C#

PHP