Mathematical Expression

#include <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <stack>

bool areBracketsCorrect (std::vector <char> vec1){

    std::stack <char> st;
    bool isEmpty;

    for(size_t i = 0; i < vec1.size(); i++){

        if(vec1[i] == '('){

            st.push(vec1[i]);
        }
    }

    for(size_t j = 0; j < vec1.size(); j++){

        if(vec1[j] == ')'){
            st.pop();
        }
    }

    if(st.empty() == 1){

        isEmpty = 1;
    } else {
        isEmpty = 0;
    }

    return isEmpty;
}

int main (){

    std::string expression;
    std::cin >> expression;

    std::istringstream exprStream(expression);

    std::vector <char> vecOfChar;
    char currentChar;

    while(exprStream >> currentChar){

        vecOfChar.push_back(currentChar);
    }

    if(areBracketsCorrect(vecOfChar) == 1){

        std::cout << "correct" << std::endl;

    } else {

        std::cout << "incorrect" << std::endl;
    }

    return 0;
}