/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Tightest known upper bounds for W in instances G-P-W.

   A trivial upper bound upper_/3 can be defined as:

       upper_(G, P, W) :-
               N #= G*P,
               Meet #= P - 1,
               W #= (N - 1) // Meet.

   However, for several instances, tighter upper bounds are known.
   In particular, we have the following differences:

    ?- upper(G,P,W),
       \+ upper_(G,P,W).
       G = 6, P = 5, W = 6
    ;  G = 6, P = 6, W = 3
    ;  G = 9, P = 4, W = 12
    ;  G = 10, P = 3, W = 15
    ;  false.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

upper(6,3,8).
upper(6,4,7).
upper(6,5,6).
upper(6,6,3).

upper(7,3,10).
upper(7,4,9).
upper(7,5,8).
upper(7,6,8).
upper(7,7,8).

upper(8,3,11).
upper(8,4,10).
upper(8,5,9).
upper(8,6,9).
upper(8,7,9).
upper(8,8,9).

upper(9,3,13).
upper(9,4,12).
upper(9,5,11).
upper(9,6,10).
upper(9,7,10).
upper(9,8,10).
upper(9,9,10).

upper(10,3,15).
upper(10,4,13).
upper(10,5,12).
upper(10,6,11).
upper(10,7,11).
upper(10,8,11).
upper(10,9,11).
upper(10,10,11).

/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Best solutions found so far with constraint programming.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

csp(6,3,8).
csp(6,4,7).
csp(6,5,6).
csp(6,6,3).

csp(7,3,9).
csp(7,4,7).
csp(7,5,5).
csp(7,6,4).
csp(7,7,7).

csp(8,3,10).
csp(8,4,9).
csp(8,5,6).
csp(8,6,5).
csp(8,7,4).
csp(8,8,9).

csp(9,3,11).
csp(9,4,8).
csp(9,5,6).
csp(9,6,5).
csp(9,7,4).
csp(9,8,3).
csp(9,9,3).

csp(10,3,13).
csp(10,4,9).
csp(10,5,7).
csp(10,6,6).
csp(10,7,5).
csp(10,8,4).
csp(10,9,3).
csp(10,10,3).

/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Best solutions found by local search.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

ls(6,3,8).
ls(6,4,6).
ls(6,5,6).
ls(6,6,3).

ls(7,3,9).
ls(7,4,7).
ls(7,5,5).
ls(7,6,4).
ls(7,7,3).

ls(8,3,10).
ls(8,4,8).
ls(8,5,6).
ls(8,6,5).
ls(8,7,4).
ls(8,8,4).

ls(9,3,11).
ls(9,4,8).
ls(9,5,6).
ls(9,6,5).
ls(9,7,4).
ls(9,8,3).
ls(9,9,3).

ls(10,3,13).
ls(10,4,9).
ls(10,5,7).
ls(10,6,6).
ls(10,7,5).
ls(10,8,4).
ls(10,9,3).
ls(10,10,3).

/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Best solutions found with memetic algorithm.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

ma(6,3,8).
ma(6,4,6).
ma(6,5,6).
ma(6,6,3).

ma(7,3,9).
ma(7,4,7).
ma(7,5,5).
ma(7,6,4).
ma(7,7,4).

ma(8,3,10).
ma(8,4,8).
ma(8,5,6).
ma(8,6,5).
ma(8,7,4).
ma(8,8,4).

ma(9,3,12).
ma(9,4,9).
ma(9,5,7).
ma(9,6,6).
ma(9,7,5).
ma(9,8,4).
ma(9,9,3).

ma(10,3,13).
ma(10,4,10).
ma(10,5,8).
ma(10,6,7).
ma(10,7,5).
ma(10,8,5).
ma(10,9,4).
ma(10,10,3).

/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Best solutions found with greedy randomized adaptive search.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

grasp(6,3,8).
grasp(6,4,6).
grasp(6,5,6).
grasp(6,6,3).

grasp(7,3,9).
grasp(7,4,7).
grasp(7,5,5).
grasp(7,6,4).
grasp(7,7,4).

grasp(8,3,10).
grasp(8,4,10).
grasp(8,5,6).
grasp(8,6,5).
grasp(8,7,4).
grasp(8,8,5).

grasp(9,3,12).
grasp(9,4,9).
grasp(9,5,7).
grasp(9,6,6).
grasp(9,7,5).
grasp(9,8,4).
grasp(9,9,3).

grasp(10,3,13).
grasp(10,4,10).
grasp(10,5,8).
grasp(10,6,7).
grasp(10,7,5).
grasp(10,8,5).
grasp(10,9,4).
grasp(10,10,3).

% hard_for_grasp(10,4,10).
hard_for_grasp(10,6,7).
hard_for_grasp(6,5,6).
hard_for_grasp(9,3,12).

/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Describing barplots.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

:- use_module(library(lists)).
:- use_module(library(format)).
:- use_module(library(dcgs)).

% G = number of groups per week
barplot(G) -->
        { findall(P, csp(G,P,_), Ps),
          findall(W, all(G,_,W,_), Ws0),
          sort(Ws0, Ws),
          phrase((...,[MaxW]), Ws) },
        row(Ps, G, grasp),
        row(Ps, G, ma),
        row(Ps, G, ls),
        row(Ps, G, csp),
        row(Ps, G, upper),
        "v <- rbind(grasp, ma, ls)\n",
        "colnames(v) <- c(",
        r_list(Ps),
        format_("postscript(\"g~w.ps\", width=5, height=5, page=\"special\")\n", [G]),
        format_("t <- barplot(v,yaxt=\"n\", ylab=\"number of weeks\", xlab=\"size of groups\", main=\"~w groups per week\", beside=T, ylim=c(0,~w), col=\"gray\", space=c(0.2,1))\n", [G,MaxW]),
        format_("axis(2, at=0:~w)\n", [MaxW]),
        "xs <- colMeans(t)\n",
        "for (i in 1:length(xs)) {\n\
    l <- xs[i]-1.8\n\
    r <- xs[i]+1.8\n\
    lines(c(l,r), c(csp[i],csp[i]))\n\
    lines(c(l,l), c(csp[i],csp[i]+0.2))\n\
    lines(c(r,r), c(csp[i],csp[i]+0.2))\n\
    lines(c(l,r), c(upper[i],upper[i]))\n\
    lines(c(l,l), c(upper[i],upper[i]-0.2))\n\
    lines(c(r,r), c(upper[i],upper[i]-0.2))\n}\n",
              "dev.off()\n".

%?- phrase(barplot(6), Cs), format("~s", [Cs]).

%?- grasp(7,X,Y).


row(Ps, G, What) -->
        format_("~w <- c(", [What]),
        row_(Ps, G, What).

r_list([])     --> ")\n".
r_list([L|Ls]) -->
        format_("~w", [L]),
        (   { Ls == [] } -> ")\n"
        ;   ", ", r_list(Ls)
        ).

row_([], _, _) --> [].
row_([P|Ps], G, What) -->
        { call(What, G, P, W) },
        format_("~w", [W]),
        (   { Ps == [] } -> ")\n"
        ;   ", ",
            row_(Ps, G, What)
        ).

all(G, P, W, Which) :-
        member(Which, [grasp,ma,csp,ls,upper]),
        call(Which, G, P, W).

%?- all(G, P, W, upper).

%?- upper(N,N,X).