public static void bubbleSort(Comparable[] theArray, int n) {
// ---------------------------------------------------
// Sorts the items in an array into ascending order.
// Precondition: theArray is an array of n items.
// Postcondition: theArray is sorted into ascending 
// order.
// ---------------------------------------------------
  boolean sorted = false;  // false when swaps occur
  for (int pass = 1; (pass < n) && !sorted; ++pass) {
    // Invariant: theArray[n+1-pass..n-1] is sorted
    //            and > theArray[0..n-pass]
    sorted = true;  // assume sorted
    for (int index = 0; index < n-pass; ++index) {
      // Invariant: theArray[0..index-1] <= theArray[index]
      int nextIndex = index + 1;  
      if (theArray[index].compareTo(theArray[nextIndex]) > 0) {
        // exchange items
        Comparable temp = theArray[index];
        theArray[index] = theArray[nextIndex];
        theArray[nextIndex] = temp;
        sorted = false;  // signal exchange
      }  // end if
    }  // end for

    // Assertion: theArray[0..n-pass-1] < theArray[n-pass]
  }  // end for
}  // end bubbleSort