The Problem:

Given a string containing just the characters ‘(‘ and ‘)’, find the length of the longest valid (well formed) parentheses sub-strings.

#include <iostream>
#include <string>
#include <stack>

using namespace std;

int longest_valid_parentheses(string const& s) {

    int count = 0, max_count = 0;
    stack<char> stk;

    for(auto c : s) {

        if(c == '(')
            stk.push(c);
        else {
            if( stk.empty() ) //|| stk.top() != '(')
                count = 0;
            else {
                count += 2;
                stk.pop();
            }
        }

        max_count = count > max_count ? count : max_count;
    }

    return max_count;
}

You can test the above code using the following test cases @ http://www.cpp.sh/.

int main()
{
  string test1("(()");
  string test2("(()()(");
  string test3(")()()))(((())))");

  cout << "there are " << longest_valid_parentheses(test1) << " valid parentheses in " << test1 << endl;
  cout << "there are " << longest_valid_parentheses(test2) << " valid parentheses in " << test2 << endl;
  cout << "there are " << longest_valid_parentheses(test3) << " valid parentheses in " << test3 << endl;

  return 0;
}

The output would look like as the follows:

there are 2 valid parentheses in (() 
there are 4 valid parentheses in (()()( 
there are 8 valid parentheses in )()()))(((())))