Magic square : Help with my homework

This is a multi-part message in MIME format. ------=mesnews_0_1116091355 Content-Type: text/plain; charset="iso-8859-15" Content-Transfer-Encoding: quoted-printable Hello! Yes it is a homework. We've been asked to make a generic magic squares generator (N x N). I've done a 3 x 3 generator, but whenever it must deal with an arbitrary number of things I am stuck!! I am not asking for a full solution but some hints on data structure and how to loop through data... Thank you ------=mesnews_0_1116091355 Content-Type: text/html Content-Transfer-Encoding: quoted-printable <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content=3D"text/html; charset=3Dwindows-1252" http-equiv=3DContent-Type> <META name=3DGENERATOR content=3D"MSHTML 8.00.6001.18852"></HEAD> <BODY> <DIV>Hello!</DIV> <DIV> </DIV> <DIV>Yes it is a homework. We've been asked to make a generic magic squares generator (N x N).</DIV> <DIV> </DIV> <DIV>I've done a 3 x 3 generator, but whenever it must deal with an arbitrary number of things I am stuck!!</DIV> <DIV> </DIV> <DIV>I am not asking for a full solution but some hints on data structure and how to loop through data...</DIV> <DIV> </DIV> <DIV>Thank you</DIV></BODY></HTML> ------=mesnews_0_1116091355--

On 2009-11-16, Thriller <rthriller@gmail.com> wrote: > This is a multi-part message in MIME format. > > Content-Type: text/html > Content-Transfer-Encoding: quoted-printable > ><!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> > [...] Please change your settings not to post HTML content. -- Jon Solberg (remove "nospam." from email address).

On Nov 16, 8:55=A0pm, Thriller <rthril...@gmail.com> wrote: > Yes it is a homework. We've been asked to make a generic magic squares ge= nerator (N x N). > I've done a 3 x 3 generator, but whenever it must deal with an arbitrary = number of things I am stuck!! > I am not asking for a full solution but some hints on data structure and = how to loop through data... > Thank you There're many methods to make a magic square. Some methods are too easy and tricky that, for example, you put 1 in the lower middle cell and put 2, 3, ..., 9 one by one right-downwardly, excepting that when the target cell is occupied you treat the upper cell as new target cell, and the magic square is done. Do not waste time to write this kind of program. It also can be done by generating many alternative magic square. A very brute method is to compute permutations of 9 numbers, ?- permu([1,2,3,4,5,6,7,8,9], Sq). Sq =3D [[1,2,3],[4,5,6],[7,8,9]]; Sq =3D [[1,2,3],[4,5,6],[7,9,8]]; etc., and check whether they are magic squares. However, it wastes time on checking useless data. The method I prefer is that it construct the structure of magic square step by step according some rules.

On Mon, 16 Nov 2009 13:55:47 +0100, Thriller <rthriller@gmail.com> wrote: >Hello! > >Yes it is a homework. We've been asked to make a generic magic squares generator (N x N). > >I've done a 3 x 3 generator, Show the code A.L.

On Nov 16, 7:55=A0am, Thriller <rthril...@gmail.com> wrote: > Hello! > > Yes it is a homework. We've been asked to make a generic magic squares ge= nerator (N x N). > > I've done a 3 x 3 generator, but whenever it must deal with an arbitrary = number of things I am stuck!! > > I am not asking for a full solution but some hints on data structure and = how to loop through data... > > Thank you Here is a program in B-Prolog. This is not meant to be a solution, but you may get some hints from it. This program contains too much ad hoc syntax. I strongly feel that Prolog (and CLP(FD) needs standard syntax for arrays and loop & list comprehension constructs. magicSquare(N) :- new_array(Matrix,[N,N]), NN is N*N, term_variables(Matrix,Vars), Vars :: 1..NN, Sum is NN*(NN+1)//(2*N), Matrix^rows @=3DRows, foreach(Row in Rows, sum(Row)#=3DSum), Matrix^columns @=3DCols, foreach(Col in Cols, sum(Col)#=3DSum), Matrix^diagonal1 @=3D Diag1, sum(Diag1) #=3D Sum, Matrix^diagonal2 @=3D Diag2, sum(Diag2) #=3D Sum, all_different(Vars), labeling([ffc],Vars), foreach(Row in Rows, writeln(Row)). Cheers, Neng-Fa This program contains too much nonstandard

afa <neng.zhou@gmail.com> writes: >Here is a program in B-Prolog. This is not meant to be a solution, but >you may get some hints from it. This program contains too much ad hoc >syntax. I strongly feel that Prolog (and CLP(FD) needs standard syntax >for arrays and loop & list comprehension constructs. > >magicSquare(N) :- > new_array(Matrix,[N,N]), > NN is N*N, > term_variables(Matrix,Vars), > Vars :: 1..NN, > Sum is NN*(NN+1)//(2*N), > Matrix^rows @=Rows, > foreach(Row in Rows, sum(Row)#=Sum), > Matrix^columns @=Cols, > foreach(Col in Cols, sum(Col)#=Sum), > Matrix^diagonal1 @= Diag1, > sum(Diag1) #= Sum, > Matrix^diagonal2 @= Diag2, > sum(Diag2) #= Sum, > all_different(Vars), > labeling([ffc],Vars), > foreach(Row in Rows, writeln(Row)). Let's start with the good news first! You are using strict ISO syntax! Fine! That is, you do not need to plead the very hairy 5.5.1 Syntax for a syntax extension. Every standard conforming processor should be able to read your program - syntactically - by using appropriate operator declarations *only*. I wish things would be that easy in other areas. There are many ad hoc syntax extensions that render programs entirely unreadable by other systems. What you effectively extended was in some sense 5.5.2 Predefined operators. Let's start with the basic syntax for domains. Markus Triska had this ingenious idea to improve the syntax for domains as follows (see SWI or YAP's library(clpfd). For the query ?- X in 0..9, X #\= 3, #\= 5. The domain of X develops traditionally as follows (SICStus 3 syntax): | ?- X in 0..9, ( true ; X #\= 3, ( true ; X #\= 5 ) ). X in 0..9 ? ; X in(0..2)\/(4..9) ? ; X in(0..2)\/{4}\/(6..9) ? ; no Now, in SWI thanks to :- op( 450, xfx, ..). we have: ?- X in 0..9, ( true ; X #\= 3, ( true ; X #\= 5 ) ). X in 0..9 ? X in 0..2\/4..9 ? X in 0..2\/4\/6..9. So this was a minimal syntax tree change: singletons are now represented as the integers themselves. That removed the { }. And then the slight change of the operator declaration for .. results in the removal of all the other parentheses. In fact, in my running SICStus 3 programs I changed the predefined operator declaration op(550, xfx, ..) to the one above. This makes things not only much smoother to look at. It is als much less of a chore when writing things down. To keep this posting short only one more comment: Using library(apply)'s maplist/2 - common practice since at least 1984 (originally 1981 under the name have_property/2 with the less fortunate argument order) and using library(lambda) in - of course - ISO syntax: > foreach(Row in Rows, sum(Row)#=Sum), maplist(Sum+\Row^sum(Row,#=,Sum), Rows) http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl

This solution seems using Prolog to write a procedural program. On Nov 17, 12:13=A0am, afa <neng.z...@gmail.com> wrote: > Here is a program in B-Prolog. This is not meant to be a solution, but .... > magicSquare(N) :- > =A0 =A0 new_array(Matrix,[N,N]), > =A0 =A0 NN is N*N, > =A0 =A0 term_variables(Matrix,Vars), > =A0 =A0 Vars :: 1..NN, > =A0 =A0 Sum is NN*(NN+1)//(2*N), > =A0 =A0 Matrix^rows @=3DRows, > =A0 =A0 foreach(Row in Rows, sum(Row)#=3DSum), > =A0 =A0 Matrix^columns @=3DCols, > =A0 =A0 foreach(Col in Cols, sum(Col)#=3DSum), > =A0 =A0 Matrix^diagonal1 @=3D Diag1, > =A0 =A0 sum(Diag1) #=3D Sum, > =A0 =A0 Matrix^diagonal2 @=3D Diag2, > =A0 =A0 sum(Diag2) #=3D Sum, > =A0 =A0 all_different(Vars), > =A0 =A0 labeling([ffc],Vars), > =A0 =A0 foreach(Row in Rows, writeln(Row)). > > Cheers, > Neng-Fa > > This program contains too much nonstandard

On Nov 16, 8:55=A0pm, Thriller <rthril...@gmail.com> wrote: > Hello! > Yes it is a homework. We've been asked to make a generic magic squares ge= nerator (N x N). > I've done a 3 x 3 generator, but whenever it must deal with an arbitrary = number of things I am stuck!! > I am not asking for a full solution but some hints on data structure and = how to loop through data... > Thank you Back to the problem. When thinking of what properties cause a magic square, we say that if a number X is picked out from the list [1,2,3,4,5,6,7,8,9], other numbers can be paired two by two and the sum of each pair is (45/3 - X), e.g., [(1, 9), (2, 8), (3, 7), (4, 6)]. Surrounding numbers are made of four of these pairs. The property implies one of vertical lines, one of horizontal lines, and two diagonal lines have the same sum. Then, the other property for checking sums of other lines must be added. You may need some domain definition which Ulrich described. My domain definition and operation was achieved by defining two goals: range/3 and element_at/3, range(M, N, []) :- M > N, !. range(N, N, [N]) :- !. range(M, N, [M|Z]) :- M1 is M+1, range(M1, N, Z). element_at([X|_], 1, X). element_at([_|Y], N, Z) :- element_at(Y, N1, Z), N is N1+1.

YauHsienHuang <g9414002.pccu.edu.tw@gmail.com> writes: >On Nov 16, 8:55=A0pm, Thriller <rthril...@gmail.com> wrote: >> Hello! >> Yes it is a homework. We've been asked to make a generic magic squares ge= >nerator (N x N). >> I've done a 3 x 3 generator, but whenever it must deal with an arbitrary = >number of things I am stuck!! >> I am not asking for a full solution but some hints on data structure and = >how to loop through data... >> Thank you > >Back to the problem. When thinking of what properties cause a magic >square, we say that if a number X is picked out from the list >[1,2,3,4,5,6,7,8,9], other numbers can be paired two by two and the >sum of each pair is (45/3 - X), e.g., [(1, 9), (2, 8), (3, 7), (4, >6)]. Surrounding numbers are made of four of these pairs. The property >implies one of vertical lines, one of horizontal lines, and two >diagonal lines have the same sum. Then, the other property for >checking sums of other lines must be added. > >You may need some domain definition which Ulrich described. My domain >definition and operation was achieved by defining two goals: range/3 >and element_at/3, > >range(M, N, []) :- M > N, !. >range(N, N, [N]) :- !. >range(M, N, [M|Z]) :- M1 is M+1, range(M1, N, Z). ?- range(1,0,Xs), Xs=[1]. false. ?- Xs = [1], range(1,0,Xs). Xs = [1]. It is for such reasons, that constraints are often preferable even in "simple" programs. In fact, I consider constraint programs most often easer to write and debug than their traditional counterparts (for similar purposes indeed).

We use ECLiPSe CLP Here is my code for 3 * 3 square: /* carre(C1,C2,C3,C4,C5,C6,C7,C8,C9). */ :- lib(ic). carre(C1,C2,C3,C4,C5,C6,C7,C8,C9):- Dcarre=[C1,C2,C3,C4,C5,C6,C7,C8,C9], Dcarre #::1..9, alldifferent(Dcarre), C1+C2+C3 #= C4+C5+C6, C1+C2+C3 #= C7+C8+C9, C1+C2+C3 #= C1+C5+C9, C1+C2+C3 #= C3+C5+C7, labeling(Dcarre). Apr�s m�re r�flexion, Thriller a �crit : > Hello! > > Yes it is a homework. We've been asked to make a generic magic squares > generator (N x N). > > I've done a 3 x 3 generator, but whenever it must deal with an arbitrary > number of things I am stuck!! > > I am not asking for a full solution but some hints on data structure and how > to loop through data... > > Thank you

On Nov 16, 11:36=A0am, ulr...@mips.complang.tuwien.ac.at (Ulrich Neumerkel) wrote: > > Let's start with the good news first! > You are using strict ISO syntax! Fine! That is, you do not need to Good and bad. The Prolog syntax is very old. After 35 years, maybe it's time to reconsider it. For example, for the constraint Matrix^rows @=3DRows, foreach(Row in Rows, sum(Row)#=3DSum), I would like to write it using list comprehension as follows: foreach(I in 1..N,sum([Matrix[I][J] || J in 1..N])#=3D3), and for the constraint Matrix^diagonal1 @=3D Diag1, sum(Diag1) #=3D Sum, I'd like to write it as follows: sum([Matrix[I][I] || I in 1..N]) #=3D 3, Earlang and most functional languages have list comprehensions and loop constructs. We should learn from them now. > > =A0 =A0foreach(Row in Rows, sum(Row)#=3DSum), > > =A0 maplist(Sum+\Row^sum(Row,#=3D,Sum), Rows) > > http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl I think foreach is more readable than maplist for this case. I just realized that the last line of my program should be like the following: foreach(Row in Rows, (foreach(I in Row, format("~4d ",[I])),nl)). which prints the matrix more neatly. Cheers, Neng-Fa

afa <neng.zhou@gmail.com> writes: >On Nov 16, 11:36=A0am, ulr...@mips.complang.tuwien.ac.at (Ulrich >Neumerkel) wrote: > >> >> Let's start with the good news first! >> You are using strict ISO syntax! Fine! That is, you do not need to > >Good and bad. The Prolog syntax is very old. After 35 years, maybe >it's time to reconsider it. For example, for the constraint How often have I heard similar complaints. So far it always turned out that coming back to Prolog is the better option. Maybe it's just that Prolog is much more stable than all experimental languages due to its dual use both for pure and impure things alike. For long, people said that lambda expressions need special syntax support. Now we know: no need for that. Then (some time ago) higher order programming was claimed to be not (elegantly) possible in Prolog - while ignoring call/N, indeed. Then, that some particular versatile higher order styles (apply/3) were not possible with call/N. False again. You know the age of s-expressions - just to put 35 years into perspective? Maybe, after 35 years, it's time to fully exploit it. >I would like to write it using list comprehension as follows: > > foreach(I in 1..N,sum([Matrix[I][J] || J in 1..N])#=3), Only looking at Matrix[I][J] - something like m(M, I, J) would not do? Probably not, some nesting seems to be useful - but I do not see any reason why the current syntax could not support this adequately. Why not Matrix^I^J or similar... After all, the most complex question involved is that of variable scoping. >Erlang and most functional languages have list comprehensions and >loop constructs. We should learn from them now. On the other hand, comprehensions are often used to simulate Prolog's capabilities in FP. Haven't we recently attended a talk on some constraint monad? Certainly I agree with you that we need more in that direction. >> maplist(Sum+\Row^sum(Row,#=,Sum), Rows) >> >> http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl > >I think foreach is more readable than maplist for this case. I just >realized that the last line of my program should be like the >following: > > foreach(Row in Rows, (foreach(I in Row, format("~4d ",[I])),nl)). > >which prints the matrix more neatly. What is very unituitive in maplist/2 is this unnatural separation of Rows and Row above. I do not like that in Lisp as well. The things that belong together should be next to each other visually. In your foreach construct they are very close. There are examples were the distance is even larger - if more than one goal is involved - or some nested goal. But are you sure of the scoping involved? call/N - although presented the first time publicly in 1987 - has still not received the attention it deserves. By consequence, there has not been much work on methodologies based on call/N. We have maplist/N. Fine, but there is more to it. Much more - if you look into FP. There, comprehensions were not created ex nihilo, but they developed out of various existing higher order methodologies. It seems that we would have to take a somewhat similar path to reach the same goals. Certainly if we would reach the goals, it would be much more general - as usual in Prolog. For pure, monotonic relations - such constructs should preserve monotonicity as well as termination properties. So far I have not seen an approach that offers all that. While maplist/N does guarantee these properties, it is not expressible enough. We need much more than that. The property of monotonicity is very precious. It helps e.g. to diagnose failure. To illustrate this I have written a very tiny library to explain failures by generalizing a query: http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/diadem.pl

Thriller wrote: > We use ECLiPSe CLP > Here is my code for 3 * 3 square: > > /* carre(C1,C2,C3,C4,C5,C6,C7,C8,C9). */ > :- lib(ic). > > carre(C1,C2,C3,C4,C5,C6,C7,C8,C9):- > Dcarre=[C1,C2,C3,C4,C5,C6,C7,C8,C9], > Dcarre #::1..9, > alldifferent(Dcarre), > C1+C2+C3 #= C4+C5+C6, > C1+C2+C3 #= C7+C8+C9, > C1+C2+C3 #= C1+C5+C9, > C1+C2+C3 #= C3+C5+C7, > labeling(Dcarre). The ECLiPSe web site http://eclipse-clp.org/examples/ has a number of examples of this kind, including a magic square one http://eclipse-clp.org/examples/magicsquare.ecl.txt -- Joachim

On 16 nov, 17:59, YauHsienHuang <g9414002.pccu.edu...@gmail.com> wrote: > This solution seems using Prolog to write a procedural program. > > On Nov 17, 12:13=A0am, afa <neng.z...@gmail.com> wrote: > > > Here is a program in B-Prolog. This is not meant to be a solution, but > ... > > magicSquare(N) :- > > =A0 =A0 new_array(Matrix,[N,N]), > > =A0 =A0 NN is N*N, > > =A0 =A0 term_variables(Matrix,Vars), > > =A0 =A0 Vars :: 1..NN, > > =A0 =A0 Sum is NN*(NN+1)//(2*N), > > =A0 =A0 Matrix^rows @=3DRows, > > =A0 =A0 foreach(Row in Rows, sum(Row)#=3DSum), > > =A0 =A0 Matrix^columns @=3DCols, > > =A0 =A0 foreach(Col in Cols, sum(Col)#=3DSum), > > =A0 =A0 Matrix^diagonal1 @=3D Diag1, > > =A0 =A0 sum(Diag1) #=3D Sum, > > =A0 =A0 Matrix^diagonal2 @=3D Diag2, > > =A0 =A0 sum(Diag2) #=3D Sum, > > =A0 =A0 all_different(Vars), > > =A0 =A0 labeling([ffc],Vars), > > =A0 =A0 foreach(Row in Rows, writeln(Row)). > > > Cheers, > > Neng-Fa > > > This program contains too much nonstandard Hy, I'm interesting in that exercice too. Cause I wanted to know how using variable (N) instead of fixed values like square of 3x3. I Have tried your code but it doesn't works. Perhaps you need to declare a lib for that ? For example to use Vars::1..N you need ic library : :- lib(ic). But I have tried with it and I have some errors with foreach function. I don't how how it works but it seem to have a mistake. And what means the @=3D ? and the ^ ? thank you for your help to understand how i works.

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