Complete Program

Since String objects are immutable, a new object is created each time the append operator (+) is used. Object creation is expensive in terms of computer time; you may want to avoid it. You could use the StringBuffer class in this situation because you can add characters to it without creating new objects. You may wish to do this as an exercise. (But StringBuffer is not part of the AP Computer Science A test.)

Here is the complete program, suitable for running:

class FSTtrimTester
{
  public static void main (String[] args)
  {
    String inString  = null;
    String outString = null;
    FSTtrim fst      = new FSTtrim();
    inString = args[0];                                           
      System.out.println("The trimed string-->" + outString + "<--");
    else
      System.out.println("Missing input string.");
  }
}

class FSTtrim
{
  public String transform(String str)
  {
    final char space = ' '; // any char <= space is white space
    String outString = "";  // the string consisting of no characters
    String buffer = null;   // buffer for suspected middle white space
    int  state = 0;         // the current state
    char current;           // the current character
    int  index = 0 ;        // index of the current character

    if ( str == null ) return null;

    while ( index < str.length()  )
    {
      current = str.charAt( index++ ) ;

      if      ( state==0 && current <= space)
        state = 0;

      else if ( state==0 && current > space )
      {
        state = 1;
        outString += current ;
      }

      else if ( state==1 && current > space )
      {
        state = 1;
        outString += current ;
      }

      else if ( state==1  && current <= space )
      {
        state  = 2;
        buffer = "" + current;
      }

      else if ( state==2  && current <= space )
      {
        state  = 2;
        buffer += current;
      }

      else if ( state==2  && current > space )
      {
        state  = 1;
        outString += buffer + current;
      }
    }

  return outString;
  }

}

You may wish to improve the user interaction of this program by replacing inString = args[0] with something more elaborate.