Data Structures, Algorithms, & Applications in Java
Chapter 9, Exercise 13

We scan the expression from left to right keeping a count of the number of left parentheses that are yet to be matched. Whenever a left parenthesis is encountered, this count is increased by 1 and whenever a right parenthesis is encountered, the count is decreased by 1. If the count ever becomes negative, we have seen more right parentheses than left and so the parentheses are not matched. If the count is positive when we are done scanning the expression, there are more left parentheses than right. So, the parentheses are not matched. 
public class ParenthesisMatching2
{
   /** @return true iff all parentheses in the string expr are matched */
   public static boolean matched(String expr)
   {
      int length = expr.length();
      int count = 0;  // number of unmatched left parentheses so far
   
      // scan expression expr for ( and )
      for (int i = 0; i < length; i++)
         if (expr.charAt(i) == '(')
            count++;  // one more '(' to be matched later
         else
            if (expr.charAt(i) == ')')
               if (count == 0)
                return false;
               else
                  count--;  // taken care of 1 '('
   
      // remaining '(' are unmatched
      return (count > 0) ? false : true;
   }
}
The test program, input, and output are in the files ParenthesisMatching2.*.