I'd like to solve a special sorting task with Perl and wonder if this is a standard computer science problem.

Say I have three slots 1..3 and an empty slot 0

slot 1 => c
slot 2 => a
slot 3 => b
slot 0 => 0

The slots hold a labeled object (it's a tape library with magazine slots)

The goal is

slot 1 => a
slot 2 => b
slot 3 => c

and a list of move actions where ideally the number of moves is minimal.

A pragmatic solution is for instance

move( 1, 0 ); # ( 0, a, b, c )
move( 2, 1 ); # ( a, 0, b, c )
move( 3, 2 ); # ( a, b, 0, c )
move( 0, 3 ); # goal order achieved

where the function move( <from-slot>, <to-slot> ) moves an object from one slot to a different slot.

The question is not so much how to implement this in Perl but whether there exists an known algorithm. Of course I'm happy to post a Perl solution here.

Many thanks, Axel.