Calculate score of a string consisting of balanced parentheses

Given a string str consisting of pairs of balanced parentheses, the task is to calculate the score of the given string based on the following rules:

1. “()” has a score of 1.
2. “x y” has a score of x + y where x and y are individual pairs of balanced parentheses.
3. “(x)” has a score twice of x (i.e), 2 * score of x.

Examples:

Input: str = “()()”
Output: 2
Explanation: There are two individual pairs of balanced parentheses “() ()”. Therefore, score = score of “()” + score of “()” = 1 + 1 = 2

Input: str = “(())”
Output: 2
Explanation: Since the input is of the form “(x)”, the total score = 2 * score of “()” = 2 * 1 = 2

Approach: The problem can be solved using Stack. The idea is to iterate over the characters of the string. For every i^th character check if the character is ‘(‘ or not. If found to be true, then insert the character into the stack. Otherwise, calculate the score of the inner parentheses and insert double of the score into the stack. Follow the steps below to solve the problem:

• Initialize a stack to store the current traversed character or the score of inner balanced parentheses.
• Iterate over the characters of the string, str. For every i^th character check the following conditions: 
  • If the current character is ‘(‘ or not. If found to be true, then push the current character into the stack.
  • Otherwise, check if the top element of the stack is ‘(‘ or not. If found to be true, then insert “1” into the stack which represents the score of the inner balanced parentheses.
  • Otherwise, double the top element of the stack and push the obtained value into the stack.
• Finally, print the total score obtained.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach
#include <iostream>
#include <stack>
using namespace std;

// Function to calculate
// score of parentheses
long long scoreOfParentheses(string S)
{

    stack<string> s;

    // Stores index of
    // character of string
    int i = 0;

    // Stores total scores
    // obtained from the string
    long long ans = 0;

    // Iterate over characters
    // of the string
    while (i < S.length()) {

        // If s[i] is '('
        if (S[i] == '(')
            s.push("(");
        else {

            // If top element of
            // stack is '('
            if (s.top() == "(") {
                s.pop();
                s.push("1");
            }
            else {

                // Stores score of
                // inner parentheses
                long long count = 0;

                // Calculate score of
                // inner parentheses
                while (s.top() != "(") {

                    // Update count
                    count += stoi(s.top());
                    s.pop();
                }

                // Pop from stack
                s.pop();

                // Insert score of
                // inner parentheses
                s.push(to_string(2 * count));
            }
        }

        // Update i
        i++;
    }

    // Calculate score
    // of the string
    while (!s.empty()) {

        // Update ans
        ans += stoi(s.top());
        s.pop();
    }
    return ans;
}

// Driver Code
int main()
{
    string S1 = "(()(()))";
    cout << scoreOfParentheses(S1) << endl;

    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;
class GFG
{

  // Function to calculate
  // score of parentheses
  static long scoreOfParentheses(String S)
  {
    Stack<String> s = new Stack<>();

    // Stores index of
    // character of String
    int i = 0;

    // Stores total scores
    // obtained from the String
    long ans = 0;

    // Iterate over characters
    // of the String
    while (i < S.length())
    {

      // If s[i] is '('
      if (S.charAt(i) == '(')
        s.add("(");
      else
      {

        // If top element of
        // stack is '('
        if (s.peek() == "(")
        {
          s.pop();
          s.add("1");
        }
        else
        {

          // Stores score of
          // inner parentheses
          long count = 0;

          // Calculate score of
          // inner parentheses
          while (s.peek() != "(")
          {

            // Update count
            count += Integer.parseInt(s.peek());
            s.pop();
          }

          // Pop from stack
          s.pop();

          // Insert score of
          // inner parentheses
          s.add(String.valueOf(2 * count));
        }
      }

      // Update i
      i++;
    }

    // Calculate score
    // of the String
    while (!s.isEmpty())
    {

      // Update ans
      ans += Integer.parseInt(s.peek());
      s.pop();
    }
    return ans;
  }

  // Driver Code
  public static void main(String[] args)
  {
    String S1 = "(()(()))";
    System.out.print(scoreOfParentheses(S1) +"\n");
  }
}

// This code is contributed by 29AjayKumar.

Python3

# Python3 program to implement
# the above approach

# Function to calculate
# score of parentheses
def scoreOfParentheses(S):
    s = []

    # Stores index of
    # character of string
    i = 0

    # Stores total scores
    # obtained from the string
    ans = 0

    # Iterate over characters
    # of the string
    while (i < len(S)):

        # If s[i] is '('
        if (S[i] == '('):
            s.append("(")
        else:

            # If top element of
            # stack is '('
            if (s[-1] == "("):
                s.pop()
                s.append("1")
            else:

                # Stores score of
                # inner parentheses
                count = 0

                # Calculate score of
                # inner parentheses
                while (s[-1] != "("):

                    # Update count
                    count += int(s[-1])
                    s.pop()

                # Pop from stack
                s.pop()

                # Insert score of
                # inner parentheses
                s.append(str(2 * count))

        # Update i
        i += 1

    # Calculate score
    # of the string
    while len(s) > 0:

        # Update ans
        ans += int(s[-1])
        s.pop()
    return ans

# Driver Code
if __name__ == '__main__':
    S1 = "(()(()))"
    print(scoreOfParentheses(S1))

    # This code is contributed by mohit kumar 29

C#

// C# program to implement
// the above approach
using System;
using System.Collections.Generic;
class GFG
{

  // Function to calculate
  // score of parentheses
  static long scoreOfParentheses(String S)
  {
    Stack<String> s = new Stack<String>();

    // Stores index of
    // character of String
    int i = 0;

    // Stores total scores
    // obtained from the String
    long ans = 0;

    // Iterate over characters
    // of the String
    while (i < S.Length)
    {

      // If s[i] is '('
      if (S[i] == '(')
        s.Push("(");
      else
      {

        // If top element of
        // stack is '('
        if (s.Peek() == "(")
        {
          s.Pop();
          s.Push("1");
        }
        else
        {

          // Stores score of
          // inner parentheses
          long count = 0;

          // Calculate score of
          // inner parentheses
          while (s.Peek() != "(")
          {

            // Update count
            count += Int32.Parse(s.Peek());
            s.Pop();
          }

          // Pop from stack
          s.Pop();

          // Insert score of
          // inner parentheses
          s.Push(String.Join("", 2 * count));
        }
      }

      // Update i
      i++;
    }

    // Calculate score
    // of the String
    while (s.Count != 0)
    {

      // Update ans
      ans += Int32.Parse(s.Peek());
      s.Pop();
    }
    return ans;
  }

  // Driver Code
  public static void Main(String[] args)
  {
    String S1 = "(()(()))";
    Console.Write(scoreOfParentheses(S1) +"\n");
  }
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// JavaScript program to implement
// the above approach

// Function to calculate
// score of parentheses
function scoreOfParentheses(S)
{

    var s = [];

    // Stores index of
    // character of string
    var i = 0;

    // Stores total scores
    // obtained from the string
    var ans = 0;

    // Iterate over characters
    // of the string
    while (i < S.length) {

        // If s[i] is '('
        if (S[i] == '(')
            s.push("(");
        else {

            // If top element of
            // stack is '('
            if (s[s.length-1] == "(") {
                s.pop();
                s.push("1");
            }
            else {

                // Stores score of
                // inner parentheses
                var count = 0;

                // Calculate score of
                // inner parentheses
                while (s[s.length-1] != "(") {

                    // Update count
                    count += parseInt(s[s.length-1]);
                    s.pop();
                }

                // Pop from stack
                s.pop();

                // Insert score of
                // inner parentheses
                s.push((2 * count).toString());
            }
        }

        // Update i
        i++;
    }

    // Calculate score
    // of the string
    while (s.length!=0) {

        // Update ans
        ans += parseInt(s[s.length-1]);
        s.pop();
    }
    return ans;
}

// Driver Code
var S1 = "(()(()))";
document.write( scoreOfParentheses(S1));


</script>

Output:

6

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