Find an equal point in a string of brackets

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. 
The 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
Explanation: After index 4, string splits into (()) and ))(. The number of opening brackets in the first part is equal to the number of closing brackets in the second part.

Input: str = “))”
Output: 2
Explanation: 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 the number of closing brackets in the second part i.e. also 0.

Asked in: Amazon 

Approach 1:

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

Below is the implementation of the above approach:

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));
    }
}

Python3

# 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
?>

Javascript

<script>

// Javascript program to find an index k which
// decides the number of opening brackets
// is equal to the number of closing brackets

// Method to find an equal index
function findIndex(str)
{
    let len = str.length;
    let open = new Array(len + 1);
    let close = new Array(len + 1);
    for(let i = 0; i < len + 1; i++)
    {
        open[i] = 0;
        close[i] = 0;
    }
    let 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(let 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(let 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(let i = 0; i <= len; i++)
        if (open[i] == close[i])
            index = i;

    return index;
}

// Driver Code
let str = "(()))(()()())))";

document.write(findIndex(str));

// This code is contributed by avanitrachhadiya2155

</script>

Output

9

Time Complexity: O(N), where N is the size of the given string
Auxiliary Space: O(N)

Approach 2: 

• Count the total number of closed brackets in the string and store in a variable, let’s say cnt_close.
• So count of open brackets is length of (string – count) of closed brackets.
• Traverse string again but now keep count of open brackets in string, let’s say cnt_open.
• Now while traversing, let index be i, so count of closed brackets till that index will be (i+1 – cnt_open).
• Hence, we can check for what index, the count of open brackets in first part equals that of count of closed brackets in second part.
• Equation becomes cnt_close – (i+1 – cnt_open) = cnt_open, we have to find i.
• After evaluating above equation we can see cnt_open gets cancelled on both sides so no need.

Implementation:

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)
{
    // STL to count occurrences of ')'
    int cnt_close = count(str.begin(), str.end(), ')');
    for (int i = 0; str[i] != '\0'; i++)
        if (cnt_close == i)
            return i;
    // If no opening brackets
    return str.size();
}

// Driver code
int main()
{
    string str = "(()))(()()())))";
    cout << findIndex(str);
    return 0;
}

// This code is contributed by Dhananjay Dhawale @chessnoobdj

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 cnt_close = 0;
        for (int i = 0; i < len; i++)
            if (str.charAt(i) == ')')
                cnt_close++;
        for (int i = 0; i < len; i++)
            if (cnt_close == i)
                return i;
        // If no opening brackets
        return len;
    }

    // Driver Method
    public static void main(String[] args)
    {
        String str = "(()))(()()())))";
        System.out.println(findIndex(str));
    }
}

// This code is contributed by Aditya Kumar (adityakumar129)

Python3

# Method to find an equal index
def findIndex(str):
    cnt_close = 0
    l = len(str)
    for i in range(0, l):
        if(str[i] == ')'):
            cnt_close = cnt_close + 1

    for i in range(0, l):
        if(cnt_close == i):
            return i
    # If no opening brackets
    return l


# Driver Code
str = "(()))(()()())))"
print(findIndex(str))

# This code is contributed by Aditya Kumar (adityakumar129) and Sankararaman (sankararamank).

C#

using System;

// C# 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
  public static int findIndex(String str)
  {
    var len = str.Length;
    var cnt_close = 0;
    for (int i = 0; i < len; i++) {
      if (str[i] == ')') {
        cnt_close++;
      }
    }
    for (int i = 0; i < len; i++) {
      if (cnt_close == i) {
        return i;
      }
    }

    // If no opening brackets
    return len;
  }

  // Driver Method
  public static void Main(String[] args)
  {
    var str = "(()))(()()())))";
    Console.WriteLine(findIndex(str));
  }
}

// This code is contributed by Aarti_Rathi

Javascript

<script>

// Javascript program to find an index k which
// decides the number of opening brackets
// is equal to the number of closing brackets

// Method to find an equal index
function findIndex(str)
{
    let len = str.length;
    int cnt_close = 0;
    for(let i = 0; i < len; i++)
        if (str[i] == ')')
            cnt_close++;

     for(let i = 0; i < len; i++)
         if (cnt_close == i)
            return i;
        // If no opening brackets
        return len;

// Driver Code
let str = "(()))(()()())))";

document.write(findIndex(str));

// This code is contributed by Aditya Kumar (adityakumar129)

</script>

PHP

<?php
// Method to find an equal index
function findIndex($str)
{
    $len = strlen($str);
    $cnt_close = 0;
      for ($i = 1; $i < $len; $i++)
        if ($str[$i] == ')')
            $cnt_close ++;

      for ($i = 1; $i < $len; $i++)
        if ($cnt_close == $i)
              return $i;
      return $len;
}

// Driver Code
$str = "(()))(()()())))";
echo (findIndex($str));

// This code is contributed by Aditya Kumar (adityakumar129)
?>

Output

9

Time Complexity: O(N), Where N is the size of given string
Auxiliary Space: O(1)

Approach 3: (Solution in 1 iteration) 

• Count the total number of closed brackets in string and store in variable, let’s say cnt_close.
• So count of open brackets is length of (string – count) of closed brackets.
• Traverse string again but now keep count of open brackets in string, let’s say cnt_open.
• Now while traversing, let index be i, so count of closed brackets till that index will be (i+1 – cnt_open).
• Hence, we can check for what index, the count of open brackets in first part equals that of count of closed brackets in second part.
• Equation becomes cnt_close – (i+1 – cnt_open) = cnt_open, we have to find i.
• After evaluating above equation we can see cnt_open gets cancelled on both sides so no need for the extra loop and simply return cnt_close.

C++

// C++ Program to implement above approach
#include<bits/stdc++.h>
using namespace std;

// Method to find an equal index
int findIndex(string str){
    int cnt_close = 0;
    int l = str.length();
    for(int i = 0; i<l; i++){
        if(str[i] == ')')
            cnt_close++;
    }
    return cnt_close;
}

int main(){
    string str = "(()))(()()())))";
    cout<<findIndex(str);
    return 0;
}

// This code is contributed by Yash Agarwal(yashagarwal2852002)

Java

// Java program to implement above approach
import java.util.*;

public class GFG {
    // Method to find an equal index
    static int findIndex(String str)
    {
        int cnt_close = 0;
        int l = str.length();
        for (int i = 0; i < l; i++) {
            if (str.charAt(i) == ')')
                cnt_close++;
        }
        return cnt_close;
    }
    public static void main(String[] args)
    {
        String str = "(()))(()()())))";
        System.out.println("OP: " + findIndex(str));
    }
}

// This code is contributed by Karandeep1234

Python3

# Method to find an equal index
def findIndex(str):
    cnt_close = 0
    l = len(str)
    for i in range(0, l):
        if(str[i] == ')'):
            cnt_close = cnt_close + 1

    return cnt_close

# Driver Code
str = "(()))(()()())))"
print(f"OP: {findIndex(str)}")
# This code is contributed by Sankararaman (sankararamank).

C#

// C# implementation of the above approach

using System;
using System.Collections.Generic;

class GFG {

  // Method to find an equal index
  static int findIndex(string str){
    int cnt_close = 0;
    int l = str.Length;
    for(int i = 0; i < l; i++){
      if(str[i] == ')')
        cnt_close++;
    }
    return cnt_close;
  }

  public static void Main()
  {
    string str = "(()))(()()())))";
    Console.Write("OP: "+findIndex(str));
  }
}

// This code is contributed by poojaagarwal2.

Javascript

// Javascript Program to implement above approach

// Method to find an equal index
function findIndex(str){
    let cnt_close = 0;
    let l = str.length;
    for(let i = 0; i<l; i++){
        if(str[i] == ')')
            cnt_close++;
    }
    return cnt_close;
}

    let str = "(()))(()()())))";
    document.write(findIndex(str));

Output

OP: 9

Time Complexity: O(N), Where N is the size of the given string
Auxiliary Space: O(1)

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