Minimum number of Parentheses to be added to make it valid

Given a string S of parentheses '(' or ')' where, 0\leq len(S)\leq 1000                   . The task is to find a minimum number of parentheses '(' or ')' (at any positions) we must add to make the resulting parentheses string is valid.

Examples: 

Input: str = "())"
Output: 1
One '(' is required at beginning.

Input: str = "((("
Output: 3
Three ')' is required at end.

Approach 1: Iterative Approach

We keep the track of balance of the string i:e the number of '(' minus the number of ')'. A string is valid if its balance is 0, and also every prefix has non-negative balance.
Now, consider the balance of every prefix of S. If it is ever negative (say, -1), we must add a '(' bracket at the beginning. Also, if the balance of S is positive (say, +P), we must add P times ')' brackets at the end.

Below is the implementation of the above approach:

// C++ Program to find minimum number of '(' or ')'
// must be added to make Parentheses string valid.
#include <bits/stdc++.h>
using namespace std;

// Function to return required minimum number
int minParentheses(string p)
{

    // maintain balance of string
    int bal = 0;
    int ans = 0;

    for (int i = 0; i < p.length(); ++i) {

        bal += p[i] == '(' ? 1 : -1;

        // It is guaranteed bal >= -1
        if (bal == -1) {
            ans += 1;
            bal += 1;
        }
    }

    return bal + ans;
}

// Driver code
int main()
{

    string p = "())";

    // Function to print required answer
    cout << minParentheses(p);

    return 0;
}

// Java Program to find minimum number of '(' or ')' 
// must be added to make Parentheses string valid. 

public class GFG {

    // Function to return required minimum number 
    static int minParentheses(String p) 
    { 
      
        // maintain balance of string 
        int bal = 0; 
        int ans = 0; 
      
        for (int i = 0; i < p.length(); ++i) { 
      
            bal += p.charAt(i) == '(' ? 1 : -1; 
      
            // It is guaranteed bal >= -1 
            if (bal == -1) { 
                ans += 1; 
                bal += 1; 
            } 
        } 
      
        return bal + ans; 
    } 
    
    public static void main(String args[])
    {
        String p = "())"; 
        
        // Function to print required answer 
        System.out.println(minParentheses(p)); 
      
    }
    // This code is contributed by ANKITRAI1
}

# Python3 Program to find 
# minimum number of '(' or ')' 
# must be added to make Parentheses 
# string valid. 

# Function to return required 
# minimum number 
def minParentheses(p):
    
    # maintain balance of string 
    bal=0
    ans=0
    for i in range(0,len(p)):
        if(p[i]=='('):
            bal+=1
        else:
            bal+=-1
            
        # It is guaranteed bal >= -1
        if(bal==-1):
            ans+=1
            bal+=1
    return bal+ans

# Driver code
if __name__=='__main__':
    p = "())"
    
# Function to print required answer 
    print(minParentheses(p))
    
# this code is contributed by 
# sahilshelangia

// C# Program to find minimum number 
// of '(' or ')' must be added to 
// make Parentheses string valid. 
using System;

class GFG
{
// Function to return required 
// minimum number 
static int minParentheses(string p) 
{ 

    // maintain balance of string 
    int bal = 0; 
    int ans = 0; 

    for (int i = 0; i < p.Length; ++i) 
    { 

        bal += p[i] == '(' ? 1 : -1; 

        // It is guaranteed bal >= -1 
        if (bal == -1) 
        { 
            ans += 1; 
            bal += 1; 
        } 
    } 

    return bal + ans; 
} 

// Driver code 
public static void Main() 
{ 
    string p = "())"; 

    // Function to print required answer 
    Console.WriteLine(minParentheses(p)); 
}
} 

// This code is contributed 
// by Kirti_Mangal

<?php 
// PHP Program to find minimum number of 
// '(' or ')' must be added to make 
// Parentheses string valid.

// Function to return required minimum number
function minParentheses($p)
{

    // maintain balance of string
    $bal = 0;
    $ans = 0;

    for ($i = 0; $i < strlen($p); ++$i) 
    {
        if ($p[$i] == '(' )
            $bal += 1 ;
        else
            $bal += -1;

        // It is guaranteed bal >= -1
        if ($bal == -1) 
        {
            $ans += 1;
            $bal += 1;
        }
    }

    return $bal + $ans;
}

// Driver code
$p = "())";

// Function to print required answer
echo minParentheses($p);

// This code is contributed by ita_c
?>

<script>

// Javascript Program to find minimum number of '(' or ')'
// must be added to make Parentheses string valid.

// Function to return required minimum number
function minParentheses( p)
{

    // maintain balance of string
    var bal = 0;
    var ans = 0;

    for (var i = 0; i < p.length; ++i) {

        bal += p[i] == '(' ? 1 : -1;

        // It is guaranteed bal >= -1
        if (bal == -1) {
            ans += 1;
            bal += 1;
        }
    }

    return bal + ans;
}

var p = "())";

// Function to print required answer
document.write( minParentheses(p));

// This code is contributed by SoumikMondal

</script>

1

Complexity Analysis:

• Time Complexity: O(N), where N is the length of S. 
• Space Complexity: O(1).

Approach 2: Using Stack

   We can also solve this problem using a stack data structure.

1. We push the index of every '(' character onto the stack, and whenever we encounter a ')' character, we pop the top index from the stack. 
2. This indicates that the corresponding '(' has been paired with the current ')'.
3. If at any point the stack is empty and we encounter a ')' character, it means we need to add a '(' character to the beginning of the string to make it valid.
4. Similarly, if after processing the entire string there are still indices left in the stack, it means we need to add ')' characters to the end of the string to make it valid.

Below is the implementation of the above approach:

// C++ Program to find minimum number of '(' or ')'
// must be added to make Parentheses string valid.
#include <bits/stdc++.h>
using namespace std;

// Function to return required minimum number
int minParentheses(string p)
{
    stack<int> stk;
    int ans = 0;

    for (int i = 0; i < p.length(); ++i) {

        if (p[i] == '(') {
            stk.push(i);
        }
        else {
            if (!stk.empty()) {
                stk.pop();
            }
            else {
                ans += 1;
            }
        }
    }

    // add remaining '(' characters to end
    ans += stk.size();

    return ans;
}

// Driver code
int main()
{
    string p = "())";

    // Function to print required answer
    cout << minParentheses(p);

    return 0;
}
// This code is contributed by user_dtewbxkn77n

import java.util.Stack;

public class Main {
    // Function to return required minimum number
    public static int minParentheses(String p) {
        Stack<Integer> stk = new Stack<>();
        int ans = 0;

        for (int i = 0; i < p.length(); ++i) {
            if (p.charAt(i) == '(') {
                stk.push(i);
            } else {
                if (!stk.empty()) {
                    stk.pop();
                } else {
                    ans += 1;
                }
            }
        }

        // add remaining '(' characters to end
        ans += stk.size();

        return ans;
    }

    // Driver code
    public static void main(String[] args) {
        String p = "())";

        // Function to print required answer
        System.out.println(minParentheses(p));
    }
}

def minParentheses(p):
    stk = []
    ans = 0

    for i in range(len(p)):
        if p[i] == '(':
            stk.append(i)
        else:
            if len(stk) > 0:
                stk.pop()
            else:
                ans += 1

    # add remaining '(' characters to end
    ans += len(stk)

    return ans

# Driver code
p = "())"
# Function to print required answer
print(minParentheses(p))

using System;
using System.Collections.Generic;

public class Program {
    // Function to return required minimum number
    public static int MinParentheses(string p) {
        Stack<int> stk = new Stack<int>();
        int ans = 0;

        for (int i = 0; i < p.Length; ++i) {
            if (p[i] == '(') {
                stk.Push(i);
            } else {
                if (stk.Count > 0) {
                    stk.Pop();
                } else {
                    ans += 1;
                }
            }
        }

        // add remaining '(' characters to end
        ans += stk.Count;

        return ans;
    }

    // Driver code
    public static void Main() {
        string p = "())";

        // Function to print required answer
        Console.WriteLine(MinParentheses(p));
    }
}

// Function to return required minimum number
function minParentheses(p) {
  let stk = [];
  let ans = 0;

  for (let i = 0; i < p.length; i++) {
    if (p[i] === '(') {
      stk.push(i);
    } else {
      if (stk.length > 0) {
        stk.pop();
      } else {
        ans += 1;
      }
    }
  }

  // add remaining '(' characters to end
  ans += stk.length;

  return ans;
}

// Driver code
let p = "())";

// Function to print required answer
console.log(minParentheses(p));

1

Time Complexity: O(n), where n is the length of the input string. 
Space Complexity:  O(n)

Approach 3: Using string manipulation

• Continuously search for the substring "()" in the input string.
• If the substring "()" is found, replace it with an empty string.
• Repeat steps 1 and 2 until the substring "()" can no longer be found.
• The length of the resulting string is the minimum number of parentheses needed to make the string valid.

Here is the implementation of above approach:

#include <iostream>
#include <string>

using namespace std;

int minParentheses(string s) {
    while (s.find("()") != -1) {
        s.replace(s.find("()"), 2, "");
    }
    return s.length();
}

int main() {
    string s = "(((";
    cout << minParentheses(s) << endl;
    return 0;
}

public class Solution {
    public static int minParentheses(String s) {
        while (s.indexOf("()") != -1) {
            s = s.replace("()", "");
        }
        return s.length();
    }
    
    public static void main(String[] args) {
        String s = "(((";
        System.out.println(minParentheses(s));
    }
}

def minParentheses(s: str) -> int:
    while s.find("()") != -1:
        s = s.replace("()", "")
    return len(s)

# Driver code
s = "((("
print(minParentheses(s))

using System;

public class Program {
    public static void Main() {
        string s = "(((";
        Console.WriteLine(minParentheses(s));
    }

    public static int minParentheses(string s) {
        while (s.IndexOf("()") != -1) {
            s = s.Replace("()", "");
        }
        return s.Length;
    }
}

function minParentheses(s) {
    while(s.indexOf("()") != -1) {
        s = s.replace("()", "");
    }
    return s.length;
}

// Driver code
let s = "(((";
console.log(minParentheses(s));

3

Time Complexity: O(n^2) where n is the length of the input string. This is because the find() and replace() operations are called repeatedly in a loop.

Auxiliary Space: O(n) where n is the length of the input string. This is because the string s is being replaced in place and no additional data structures are being used.