Convert an unbalanced bracket sequence to a balanced sequence

Difficulty Level : Hard
Last Updated : 05 Nov, 2020

Given an unbalanced bracket sequence of ‘(‘ and ‘)’, convert it into a balanced sequence by adding the minimum number of ‘(‘ at the beginning of the string and ‘)’ at the end of the string.

Examples:

Input: str = “)))()”
Output: “((()))()”

Input: str = “())())(())())”
Output: “(((())())(())())”

Approach:

Let us assume that whenever we encounter with opening bracket the depth increases by one and with a closing bracket the depth decreases by one.
Find the maximum negative depth in minDep and add that number of ‘(‘ at the beginning.
Then loop the new sequence to find the number of ‘)’s needed at the end of the string and add them.
Finally, return the string.

Below is the implementation of the approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return balancedBrackets string
string balancedBrackets(string str)
{
    // Initializing dep to 0
    int dep = 0;
 
    // Stores maximum negative depth
    int minDep = 0;
 
    for (int i = 0; i < str.length(); i++)
    {
        if (str[i] == '(')
            dep++;
        else
            dep--;
 
        // if dep is less than minDep
        if (minDep > dep)
            minDep = dep;
    }
 
    // if minDep is less than 0 then there
    // is need to add '(' at the front
    if (minDep < 0) 
    {
        for (int i = 0; i < abs(minDep); i++)
            str = '(' + str;
    }
 
    // Reinitializing to check the updated string
    dep = 0;
 
    for (int i = 0; i < str.length(); i++) 
    {
        if (str[i] == '(')
            dep++;
        else
            dep--;
    }
 
    // if dep is not 0 then there
    // is need to add ')' at the back
    if (dep != 0) 
    {
        for (int i = 0; i < dep; i++)
            str = str + ')';
    }
    return str;
}
 
// Driver code
int main()
{
    string str = ")))()";
    cout << balancedBrackets(str);
}

Java

// Java implementation of the approach
import java.util.*;
 
class GFG {
 
    // Function to return balancedBrackets string
    static String balancedBrackets(String str)
    {
        // Initializing dep to 0
        int dep = 0;
 
        // Stores maximum negative depth
        int minDep = 0;
 
        for (int i = 0; i < str.length(); i++) 
        {
            if (str.charAt(i) == '(')
                dep++;
            else
                dep--;
 
            // if dep is less than minDep
            if (minDep > dep)
                minDep = dep;
        }
 
        // if minDep is less than 0 then there
        // is need to add '(' at the front
        if (minDep < 0) 
        {
            for (int i = 0; i < Math.abs(minDep); i++)
                str = '(' + str;
        }
 
        // Reinitializing to check the updated string
        dep = 0;
 
        for (int i = 0; i < str.length(); i++) 
        {
            if (str.charAt(i) == '(')
                dep++;
            else
                dep--;
        }
 
        // if dep is not 0 then there
        // is need to add ')' at the back
        if (dep != 0) 
        {
            for (int i = 0; i < dep; i++)
                str = str + ')';
        }
        return str;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        String str = ")))()";
        System.out.println(balancedBrackets(str));
    }
}
 
// This code is contributed by ihritik

Python3

# Python3 implementation of the approach
 
# Function to return balancedBrackets String
 
 
def balancedBrackets(Str):
 
    # Initializing dep to 0
    dep = 0
 
    # Stores maximum negative depth
    minDep = 0
 
    for i in Str:
        if (i == '('):
            dep += 1
        else:
            dep -= 1
 
        # if dep is less than minDep
        if (minDep > dep):
            minDep = dep
 
    # if minDep is less than 0 then there
    # is need to add '(' at the front
    if (minDep < 0):
        for i in range(abs(minDep)):
            Str = '(' + Str
 
    # Reinitializing to check the updated String
    dep = 0
 
    for i in Str:
        if (i == '('):
            dep += 1
        else:
            dep -= 1
 
    # if dep is not 0 then there
    # is need to add ')' at the back
    if (dep != 0):
        for i in range(dep):
            Str = Str + ')'
 
    return Str
 
 
# Driver code
Str = ")))()"
print(balancedBrackets(Str))
 
# This code is contributed by Mohit Kumar

C#

// C# implementation of the approach
using System;
 
class GFG {
 
    // Function to return balancedBrackets string
    static string balancedBrackets(string str)
    {
        // Initializing dep to 0
        int dep = 0;
 
        // Stores maximum negative depth
        int minDep = 0;
 
        for (int i = 0; i < str.Length; i++) 
        {
            if (str[i] == '(')
                dep++;
            else
                dep--;
 
            // if dep is less than minDep
            if (minDep > dep)
                minDep = dep;
        }
 
        // if minDep is less than 0 then there
        // is need to add '(' at the front
        if (minDep < 0) 
        {
            for (int i = 0; i < Math.Abs(minDep); i++)
                str = '(' + str;
        }
 
        // Reinitializing to check the updated string
        dep = 0;
 
        for (int i = 0; i < str.Length; i++) 
        {
            if (str[i] == '(')
                dep++;
            else
                dep--;
        }
 
        // if dep is not 0 then there
        // is need to add ')' at the back
        if (dep != 0) 
        {
            for (int i = 0; i < dep; i++)
                str = str + ')';
        }
        return str;
    }
 
    // Driver code
    public static void Main()
    {
        String str = ")))()";
        Console.WriteLine(balancedBrackets(str));
    }
}
 
// This code is contributed by ihritik

Output

((()))()

Time Complexity: O(N)
Auxiliary Space: O(N)

My Personal Notes

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