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From: rsk@pucc-j (Wombat)
Newsgroups: net.lang.prolog
Subject: Re: PROLOG Digest   V4 #22
Message-ID: <1389@pucc-j>
Date: Fri, 20-Jun-86 21:16:20 EDT
Article-I.D.: pucc-j.1389
Posted: Fri Jun 20 21:16:20 1986
Date-Received: Sun, 22-Jun-86 04:26:08 EDT
References: <8606180752.AA07915@ucbvax.Berkeley.EDU>
Reply-To: rsk@pucc-j.UUCP (Wombat)
Organization: Purdue University
Lines: 50
Keywords: eight queens

Here is another solution to the eight queens problem; I found this one
easier to understand, though others may differ on that point.  It was
written by Malcolm Slaney while he was at Purdue University; he is
reachable at pur-ee!malcolm.

% All of the work is done by not_threaten, queens and validlist.

findqueens :- repeat,				% Find all possible solutions
	      queens([[0,Y0],[1,Y1],[2,Y2],[3,Y3],[4,Y4],[5,Y5],
		[6,Y6],[7,Y7]|[]]),
	      write([0,Y0]), write(' '),
	      write([1,Y1]), write(' '),
	      write([2,Y2]), write(' '),
	      write([3,Y3]), write(' '),
	      write([4,Y4]), write(' '),
	      write([5,Y5]), write(' '),
	      write([6,Y6]), write(' '),
	      write([7,Y7]), write(' '),
	      nl,
	      fail.

not_threaten([X1,Y1],[X2,Y2]) :-	% Check to see if two queens are ok
	not(X1 = X2),
	not(Y1 = Y2),
	D1 is X1-X2,
	D2 is Y1-Y2,
	D3 is -D2,
	not(D1 = D2),
	not(D1 = D3).

queens([]).				% Generate Valid list of Queens
queens([[X,Y]|List]) :- queens(List),
			isvalid(Y),
			validlist(X,Y,List).
				  
validlist(X,Y,[]).			% Check to see if List is OK.
validlist(X1,Y1,[[X2,Y2]|List]) :- not_threaten([X1,Y1],[X2,Y2]),
				   validlist(X1,Y1,List).

isvalid(0).				% Generate Valid Board Positions
isvalid(1).				% (There must to be a better way!!!)
isvalid(2).
isvalid(3).
isvalid(4).
isvalid(5).
isvalid(6).
isvalid(7).

-- 
Rich Kulawiec, pucc-j!rsk, rsk@j.cc.purdue.edu