Umm...what? I mean, if there is a repeatable pattern that you follow in order to solve a problem, which in the case of the OP there is, then you can write a computer program to solve it (that's what programs are...repeatable steps)
From my understanding of the OP (and forgive me, because I may have missed something in the intermediate posts), the way this sort works is basically you grab a DVD, you KNOW what position it should be in, and you insert it there. So for example:
Define this as a single "move":
Look at a DVD...does it belong at the beginning of the list of DVDs? If not, take it out...shift all of the DVDs between its old position and its new position over and insert it at its correct spot.
Now the OP also says they don't care about ascending or descending order...whichever takes fewer of the above moves (but WORST case...in other words, take the WORST POSSIBLE permutation of the DVDs using the above sort, and figure out the fewest number of "moves" it would take to sort them either ascending or descending...that is the REQUIRED number of moves to ENSURE you have sorted them.)
