For the array implementation of a queue the constructor sets last - CAPACITY -1: because The invariant of the class states that "For an empty queue, last is some valid index and first always equal to next_Index(last)." this prevents the queue from running out of room. the queue counts backwards. last is kept always at this spot to mark the end of the array. A makefile saves time because the use of the -c option moans that the files don't ever have to o linked. only those files that have been changed are recompiled. the dependencies structure things so that they are compiled in a more efficient order. a programmer can type "make" faster than they can type "g++" cc" The difference between a virtual function and a purely virtual function is that a purely virtual function returns 0. a purely virtual function has no implementation in the parent class. a purely virtual function has no implementation in the child classes. a purely virtual function will allow the parent to call the function in the child