Score of Parentheses in C++

Suppose we have a balanced parentheses string S, we have to compute the score of the string based on the following rule −

• The () has score 1
• AB has score A + B, where A and B are two balanced parentheses strings.
• (A) has score 2 * A, where A is a balanced parentheses string.

So if the input is like “(()(()))”, then the output will be 6.

To solve this, we will follow these steps −

• ans := 0, define a stack st
• for i in range 0 to size of string S
  • if S[i] is opening parentheses, then insert -1 into stack
  • otherwise
    • if top of stack is -1, then delete from stack and insert 1 into stack
    • otherwise
      • x := 0
      • while top of stack is not -1
        • increase x by st, delete from st
      • x := x * 2
      • delete from st, and insert x
• while stack is not empty
  • increase ans by top of st, and delete top element
• return ans.

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
   int scoreOfParentheses(string S) {
      int ans = 0;
      stack <int> st;
      for(int i = 0; i < S.size(); i+=1){
         if(S[i] == '('){
            st.push(-1);
         }else{
            if(st.top() == -1){
               st.pop();
               st.push(1);
            }else{
               int x = 0;
               while(st.top() != -1){
                  x += st.top();
                  st.pop();
               }
               x *= 2;
               st.pop();
               st.push(x);
            }
         }
      }
      while(!st.empty()){
         ans += st.top();
         st.pop();
      }
      return ans;
   }
};
main(){
   Solution ob;
   cout << (ob.scoreOfParentheses("(()(()))"));
}

Input

"(()(()))"

Output

6