public static int binarySearch(int[] anArray, int first, int last, int value) {

// Searches the array items anArray[first] through
// anArray[last] for value by using a binary search.
// Precondition: 0 <= first, last <= SIZE-1, where
// SIZE is the maximum size of the array, and
// anArray[first] <= anArray[first+1] <= ... <= anArray[last].
// Postcondition: If value is in the array, the method
// returns the index of the array item that equals value;
// otherwise the method returns -1.

  int index;

  if (first > last) {

    index = -1;      // value not in original array

  } 
  else {

    // Invariant: If value is in anArray, 
    // anArray[first] <= value <= anArray[last]

    int mid = (first + last)/2;

    if (value == anArray[mid]) {

      index = mid;  // value found at anArray[mid]

    } 
    else if (value < anArray[mid]) {

      index = binarySearch(anArray, first, mid-1, value);   // point X

    } 
    else {

      index = binarySearch(anArray, mid+1, last, value);    // point Y

    }  // end if
  }  // end if

  return index;
}  // end binarySearch