:- use_module(library(clpfd)).

solve(N) :-
   latin_square(N,Square),
   maplist(writeln,Square).

latin_square(N,Square) :-
   length(Square,N),            % Square = [[X11,...,X1N],...,[XN1,...,XNN]]
   maplist(same_length(Square),Square), %
   append(Square,AllVars),
   AllVars ins 1..N,
   maplist(all_different,Square),   % All different in a row.
   transpose(Square,TSquare),       % All different in a column.
   maplist(all_different,TSquare),  %
   labeling([ff],AllVars).


diagonal_to_lst([[H]],[H]).
diagonal_to_lst([[H|_]|T],[H|L]) :-
   maplist(tail,T,T1),
   diagonal_to_lst(T1,L).

tail([_|T],T).


:- use_module(library(clpfd)).
solve(N) :-
   latin_square(N,Square),
   maplist(writeln,Square).

latin_square(N,Square) :-
   length(Square,N),            % Square = [[X11,...,X1N],...,[XN1,...,XNN]]
   maplist(same_length(Square),Square), %
   append(Square,AllVars),
   AllVars ins 1..N,
   maplist(all_different,Square),   % All different in a row.
   transpose(Square,TSquare),       % All different in a column.
   maplist(all_different,TSquare),  %
   labeling([ff],AllVars).

:- use_module(library(clpfd)).

mrok(Sol) :-
   Vars = [M,R,O,K,C,I,E,N,S1,C1],
   Sol = sol(m:M,r:R,o:O,k:K,c:C,i:I,e:E,n:N,s1:S1,c1:C1),
   Vars ins 0..9,
   all_different(Vars),
   M #\= 0, C #\= 0,
   (M*1000 + R*100 + O*10 + K) *
   (M*1000 + R*100 + O*10 + K) #=
   C*10000000 + I*1000000 + E*100000 + M*10000 + N*1000 + O*100 + S1*10 + C1,
   labeling([ff],Vars).

:- use_module(library(clpfd)).

%zadanie z książki ze stronki meissnera 152 strona
visit(sol(fs:FS, hs:HS, j:J, m:M, t:T)) :-
   Vars = [FS, HS, J, M, T],
   Vars ins 0..1,
   HS #<== FS,
   M #\/ J,
   FS #\ T,
   T #<==> J,
   M #==> (J #/\ HS),
   labeling([ff],Vars).


:- use_module(library(clpfd)).
equations2(sol(a:A, b:B, c:C, d:D, e:E, f:F, g:G)) :-
   Vars = [A, B, C, D, E, F, G],
   Vars ins 1..10,

   all_different(Vars),
   B + G #= D,
   B + C #= A,
   C + E + G #= F,
   D #< A #==> C #= 2,
   D #>= A #==> E #= 2,
   sum(Vars,#=,Sum),
   labeling([min(Sum),ff],Vars).

%dwuwymiarowa dystrybucja
equations21(sol(a:A, b:B, c:C, d:D, e:E, f:F, g:G)) :-
   Vars = [A, B, C, D, E, F, G],
   Vars ins 1..10,
   all_different(Vars),
   B + G #= D,
   B + C #= A,
   C + E + G #= F,
   D #< A #==> C #= 2,
   D #>= A #==> E #= 2,
   Sum in 7..70,
   labeling([ff],[Sum]),
   sum(Vars,#=,Sum),
   labeling([ff],Vars).
%dwuwymiarowa dystrybucja

%
%   Let V(G) be a set of vertices of the graph G, let N(v)
%   be a set of all neighbours of the vertex v in V, and
%   let a coloring be any assignment of the form V -> Colors,
%   where Colors = {1,2,3,...}. Find a coloring, which uses
%   a minimal number of colors, such that all sums of colors
%   of N(v) for every vertex v are pairvise distinct.
%   coloring([[2,3,4,5],[1,3],[1,2,4],[1,3,5],[1,4]],L).
%

:- use_module(library(clpfd)).

coloring2(Graph,Coloring) :-
    length(Graph,N),
    length(Coloring,N),
    length(Tints,N),
    Cn in 1..N,
    labeling([ff], [Cn]),
    Coloring ins 1..Cn,
    constr(Graph,Coloring,Tints),
    all_different(Tints),
    labeling([ff], Tints).

constr(Graph,Coloring,Tints) :-
    maplist(vert_sum(Coloring),Graph,Tints).

vert_sum(VertexColoring,VertNeighInds, VertSum) :-
    maplist(ind_to_vert(VertexColoring),VertNeighInds,VertNeighs),
    sum(VertNeighs, #=, VertSum).

ind_to_vert(VertexColoring,VertI,Vert) :-
    nth1(VertI,VertexColoring,Vert).

:- use_module(library(clpfd)).
fraction(sol(a:A, b:B, c:C, d:D, e:E, f:F, g:G, h:H, i:I), Test1, Test2) :-
    statistics(inferences, Test1),
    Vars = [A, B, C, D, E, F, G, H, I],
    all_different(Vars),
    Vars ins 1..9,
    DD = [BC, EF, HI],
    DD ins 1..81,
    BC #= 10*B + C,
    EF #= 10*E + F,
    HI #= 10*H + I,
    A*EF*HI + D*BC*HI + G*BC*EF #= BC*EF*HI,
    A*EF #>= D*BC,
    D*HI #>= G*EF,

    3*A #>= BC,
    3*G #=< HI,
    labeling([ff, bisect], Vars),
    statistics(inferences, Test2).
%oz version 3.2