Checking string has balanced parentheses

Question

I am reading the Algorithm Design Manual Second Edition and this is from an exercise question. Quoting the question

A common problem for comp

Answer 1

using System;
class Solution
{
    public int solution(string S)
    {
        int x1 = 0;
        int x2 = 0;
        for (int i = 0; i < S.Length; i++)
        {
            if (S[i] == ')')
                if (x1 <= 0) return 0;
                else x1--;
            else if (S[i] == '(')
                x1++;
        }
        if (x1 == 0)
            return 1;
        else
            return 0;
    }
}