Use a linked list of file sizes, initially holding the given data in
non-decreasing order. Also, initialize a pointer to the head of the
list. Iterate while more than one element on the list: insert the sum
of the two smallest elements into the proper place on the list by
advancing the pointer; delete the two smallest elements. The body of
this loop maintains the invariant asserting that the list is
non-empty, sorted in non-decreasing order and that the element given
by the pointer is not greater than the sum of the two smallest
elements on the list. The complexity of a single execution of the body
can only be bound by <i>n</i>, but in total the number of times the
pointer advances (to which the complexity of the algorithm is
proportional) is bounded by the total number of deleted elements,
which is <i>2n-2</i>.<hr> (courtesy of a midterm submission)