Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 109
The obvious way to reduce the problem of covering n 2 fields is to consider the problem of either
performing a next move or finding out that none is possible. Let us define the corresponding algorithm. A
first approach is to employ a linear search in order to find the next move from which the tour can be
completed:
PROCEDURE TryNextMove;
BEGIN
IF board is not full THEN
initialize selection of candidates for the next move and select first one;
WHILE ~(no more candidates) & ~(tour can be completed from this candidate) DO
select next candidate
END;
handle search results
ELSE
handle the case of full board
END
END TryNextMove;
Notice the IF encompassing the procedure body: it ensures that the degenerate case of a full board is
handled correctly. This is a general device that is similar to how arithmetic operations are defined to handle
the zero case: the purpose is convenience and robustness. If such checks are performed outside of the
procedure (as is often done for optimization) then each call must be accompanied by such a check — or
its absense must be properly justified in each case. Introducing such complications is best postponed until a
correct algorithm is constructed and their necessity is seen.
The predicate tour can be completed from this candidate is conveniently expressed as a functionprocedure
that returns a logical value. Since it is necessary to record the sequence of moves being
generated, the function-procedure is a proper place both for recording the next move and for its rejection
because it is in this procedure that the success of completion of the tour is determined.
PROCEDURE CanBeDone ( move ): BOOLEAN;
BEGIN
record move;
TryNextMove;
IF failed to complete the tour THEN
erase move
END;
RETURN tour has been completed
END CanBeDone
The recursion scheme is already evident here.
If we wish to be more precise in describing this algorithm, we are forced to make some decisions on
data representation. We wish to keep track of the history of successive board occupations. Then each
move in the tour sequence can be characterized by an integer i in addition to its two coordinates on the
board x, y.
At this point we can make decisions about the appropriate parameters for the two procedures
TryNextMove and CanBeDone.
The parameters of TryNextMove are to determine the starting conditions for the next move and also to
report on its success. The former task is adequately solved by specifying the coordinates x, y from which
the move is to be made, and by specifying the number i of the move (for recording purposes). The latter
task requires a Boolean result parameter with the meaning the move was successful. The resulting
signature is