Initialize an empty result string to store the processed output
Initialize a counter (level) to track the depth of parentheses
Traverse through the string character by character:
If the current character is '(', increment the level counter. If the level is greater than 1 (indicating we're inside a valid primitive), add '(' to the result string
If the current character is ')', decrement the level counter. If the level is greater than 0 (indicating we're still inside a valid primitive), add ')' to the result string
After the entire string has been traversed, return the result string

Code

#include <bits/stdc++.h>
using namespace std;

class Solution {
public:
    // Function to remove outer parentheses
    string removeOuterParentheses(string s) {
        // Initialize result string
        string result = "";  
        // Initialize nesting level counter
        int level = 0;       

        // Traverse the string
        for (char ch : s) {
            // If we encounter '(', increase the level
            if (ch == '(') {
                // If we're inside a primitive, add '(' to result
                if (level > 0) result += ch;
                // Increase the nesting level for '('
                level++;  
            } 
            // If we encounter ')', decrease the level
            else if (ch == ')') {
                // Decrease the nesting level for ')'
                level--;  
                // If we're inside a primitive, add ')' to result
                if (level > 0) result += ch;
            }
        }

        // Return the final result after removing the outer parentheses
        return result;
    }
};

int main() {
    string s = "(()())(())";  
    // Create object of Solution class
    Solution sol;             

    // Get result
    string ans = sol.removeOuterParentheses(s);

    // Print result