Mind, Body, World- Foundations of Cognitive Science, 2013a

first solving a smaller version of the same kind of problem. To move a stack of n discs
to location C, we first move the smaller stack of n – 1 discs to location B. “Moving the
stack” is the same kind of procedure for the n discs and for the n – 1 discs. The whole
approach is recursive in the sense that to move the big stack, the same procedure
must first be used to move the smaller stack on top of the largest disc.
The recursive nature of the solution to the Tower of Hanoi is made obvious if
we write a pseudocode algorithm for moving the disks. Let us call our procedure
MoveStack (). It will take four arguments: the number of discs in the stack to be
moved, the starting location, the “spare” location, and the goal location. So, if we
had a stack of three discs at location A, and wanted to move the stack to location C
using location B as the spare, we would execute MoveStack (3, A, B, C).
The complete definition of the procedure is as follows:
MoveStack (N, Start, Spare, Goal)
If N = 0
Exit
Else
MoveStack (N – 1, Start, Goal, Spare)
MoveStack (1, Start, Spare, Goal)
MoveStack (N – 1, Spare, Start, Goal)
EndIf
Note the explicit recursion in this procedure, because MoveStack () calls itself to
move a smaller stack of disks stacked on top of the disk that it is going to move. Note
too that the recursive nature of this program means that it is flexible enough to work
with any value of N. Figure 3-2 illustrates an intermediate state that occurs when
this procedure is applied to a five-disc version of the problem.
3
2
4
A
C
0
1
B
Figure 3-2. An intermediate state that occurs when MoveStack () is applied to a
five-disc version of the Tower of Hanoi.
Elements of Classical Cognitive Science 63