8 queens problem Essays - Chess Problems, Eight Queens Puzzle

(* Aqueen.sml start out solely solutions to the eight-spot Queens chore utilise to a greater extent general eons and depth-first search.*) twist AQueens =struct grammatical construction Seq = ImpSeq maneuver upto (m,n) = if mn and because else m upto (m+1,n) figure memgaiety x mem ys = string.exists (fn y = y=x) ys amusement secr f y x = f(x,y) swordplay depthFirst following(a) x = permit mutation dfs = Seq.nill dfs (yys) = Seq.cons(y, fn()= dfs (next y ys)) in dfs x oddity drama safeQueen oldqs newq = allow playing period nodiag (i, )= professedly nodiag (i, qqs) = Int.abs (newq-q)i andalso nodiag(i+1, qs) in non (newq mem oldqs) andalso nodiag (1,oldqs) demise cheer nextQueen n qs = be out (secr op qs) (string.filter (safeQueen qs) (upto(1,n))) bid isFull n qs = (length qs = n) merriment depthQueen n = Seq.filter (isFull n) (depthFirst (nextQueen n) )(* at once the foolish bits to work out an enkindle convert *) delight flagel lum (x,y) (x,y) = (x = x) orelse (y = y) orelse (x+y = x+y) orelse (x-y = x-y) playing period nextstates (,,soln) = nextstates (posnrest, right, soln) = permit manoeuvre panicsplits = threatsplits (p ps) = allow val ts = typify (fn (a,aas) = (a, paas)) (threatsplits ps) in if threat posn p indeed (p,ps)ts else ts curio in map (fn (p,ps)= (rest, ps, (posn, p)soln)) (threatsplits right) give up playing period initialstate queens1 queens2 = permit val adepttoeight = upto(1,8) in (stringPair.zip (onetoeight,queens1), stringPair.zip (onetoeight,queens2), ((int*int)*(int*int)) string) exterminate sportsman isTerminal ( odd,right,soln) = naught left gambol depthMorph queens1 queens2 = Seq.map (fn (a,b,c)=c) (Seq.filter isTerminal (depthFirst nextstates (initialstate queens1 queens2)))(* depthMorph takes a couplet of int be presumptions representing the cardinal solutions and returns an (int*int)*(int*in t) arguing season which enumerates the practical slipway of sacking from one to the next*) diversion isdiag ((xint,yint),(x,y)) = if (x x) andalso (y y) then 1 else 0(* recite of apoplexy moves in a run of pairs of pairs representing a handing over *)val diagcount = foldl (fn (move,n)=n+(isdiag move)) 0(* given a list of accomplishable morphs, rise up the one with the superior anatomy of diagonals *)val bestmorph = foldl (fn (morph, (bestsofar, bestcount)) = let val v = diagcount morph in if v bestcount then (morph, v) else (bestsofar,bestcount) ratiocination) (,1) entertainment bestmorph (a (b cs)) = (b,1)(* makeloopy takes a sequence and turns it into a cyclic one. Of course, if the headmaster is infinite, the destroy upshot is very(a) from what you started with. *) enjoyment makeloopy secondary(a) = if Seq.null small then Seq.empty else Seq.cycle (fn f = Seq.cons(Seq.hd small,fn ()=emailprotected(S eq.tl small, f())))val infinitequeens = makeloopy (depthQueen 8) bid infinitemorphs st = let val h1 = Seq.hd st val t1 = Seq.tl st val h2 = Seq.hd t1 in Seq.cons(1 (bestmorph (Seq.toList (depthMorph h1 h2))), fn ()=infinitemorphs t1) annulval theend = infinitemorphs infinitequeensend