/*

  Furniture moving (scheduling) in Picat.

  From Marriott & Stukey: "Programming with constraints", page  112f

  One result:
     Sp Sc Sb  St
    [0, 0, 30, 45]

  Where the values are the start time for each task:
   Starts with piano time 0  : 3 persons  (30 min)
               chair time 0  : 1 person   (10 min)
               bed   time 30 : 3 persons  (15 min)
               table time 45 : 2 persons  (15 min)

   0       10   15    30      45      60

   piano --------------|bed---|       
   piano --------------|       table----|
   piano --------------|bed---|
   chair --|            bed---|table----| 

  There are many other solutions...


  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.


main => go.

go =>
        L = findall([Sp, Sc, Sb, St], move([Sp, Sc, Sb, St])),
        NumSolutions = length(L),
        writef("start_times: %w\n", L),
        writef("number_of_solutions: %d\n", NumSolutions).

go2 =>
        L = findall([Sp, Sc, Sb, St], move2([Sp, Sc, Sb, St])),
        NumSolutions = length(L),
        writef("start_times: %w\n", L),
        writef("number_of_solutions: %d\n", NumSolutions).



% Minimize end time
go3 =>
        move3.



move([Sp, Sc, Sb, St]) =>

        NumPersons :: 0..3,
        
        Sp :: 0..30, % piano: 60 - 30 
        Sc :: 0..50, % chair: 60 - 10
        Sb :: 0..45, % bed  : 60 - 15
        St :: 0..45, % table: 60 - 15
        
        Duration = [30,10,15,15],
        MenNeeded = [3,1,3,2],
        cumulative([Sp, Sc, Sb, St], Duration, MenNeeded, NumPersons),


        % to get the end time of the tasks
        SpEnd #= Sp + 30,
        ScEnd #= Sc + 10,
        SbEnd #= Sb + 15,
        StEnd #= St + 15,

        Vars = [Sp,Sc,Sb,St] ++ NumPersons,

        % get all solutions
        % NumPersons = 3,
        solve(Vars),

        writeln([piano=(Sp,SpEnd), chair=(Sc,ScEnd), 
                 bed=(Sb,SbEnd), table=(St,StEnd), 
                 num=NumPersons]).
        
        

move2(X) =>
        N = 4,
        X = new_list(N),
        X :: 0..60,
        NumPersons :: 0..3,
        
        Duration = [30,10,15,15],
        MenNeeded = [3,1,3,2],
        cumulative(X, Duration, MenNeeded, NumPersons),


        % to get the end time of the tasks
        End = new_list(N),
        End :: 0..60,
        foreach(I in 1..N) End[I] #= X[I]+Duration[I] end,

        Vars = X ++ End ++ [NumPersons],

        solve([ff,updown],Vars),

        writeln([X, persons=NumPersons]).

%
% Minimize the end time (min span)
%
move3 =>
        N = 4,
        X = new_list(N),
        X :: 0..60,
        NumPersons :: 0..3,
        
        Duration = [30,10,15,15],
        MenNeeded = [3,1,3,2],
        cumulative(X, Duration, MenNeeded, NumPersons),


        % to get the end time of the tasks
        End = new_list(N),
        End :: 0..60,
        foreach(I in 1..N) End[I] #= X[I]+Duration[I] end,

        Vars = X ++ End ++ [NumPersons],

        EndTime #= max(End),
        solve([$min(EndTime),ff,down],Vars),

        writeln([X, persons=NumPersons,endTime=EndTime]).