(!****************************************************************
   CP example problems
   ===================

   file probeac2001_nary.mos
   `````````````````````````
   Euler knight tour problem implemented with user-defined
   binary constraints.
   -- n-ary formulation version --

   *** This model cannot be run with a Community Licence 
       for the default data instance ***

   (c) 2008 Artelys S.A. and Fair Isaac Corporation
       Creation: May 2005, rev. Jul. 2022
*****************************************************************!)
model "Euler Knight Moves"
 uses "kalis"

 parameters
  S = 8                                  ! No. of rows/columns
 end-parameters

 N:= S * S                               ! Total number of cells
 setparam("KALIS_DEFAULT_LB", 0)
 setparam("KALIS_DEFAULT_UB", N-1)

 forward function valid_knight_move(vals: cptuple, s: integer): boolean

 declarations
  PATH = 1..N                            ! Cells on the board
  pos: array(PATH) of cpvar              ! Position p in tour
  propagation : integer                  ! Alg choice: 0, 1, or 2
 end-declarations

! Selecting the propagation algorithm for the generic nary constraint
 propagation := 0

! Setting names of decision variables
 forall(i in PATH) setname(pos(i), "Position"+i)

! Fix the start position
 pos(1) = 0

! Each cell is visited once
 all_different(pos, KALIS_GEN_ARC_CONSISTENCY)

! The knight's path obeys the chess rules for valid knight moves
 forall(i in 1..N-1)
  generic_nary_constraint({pos(i), pos(i+1)}, ->valid_knight_move,propagation,S)
 generic_nary_constraint({pos(N), pos(1)}, ->valid_knight_move,propagation,S)

! Setting enumeration parameters
 cp_set_branching(probe_assign_var(KALIS_SMALLEST_MIN,
                  KALIS_MAX_TO_MIN, pos, 14))

! Search for up to NBSOL solutions
 solct:= 0
 if not cp_find_next_sol then
  writeln("No solution")
 else
  writeln(pos)
 end-if

! **** Test whether the move from a to b is admissible ****
 function valid_knight_move(vals: cptuple, s: integer): boolean
  declarations
   xa,ya,xb,yb,delta_x,delta_y: integer
   a,b : integer
  end-declarations
  ! Current position data
  a := getelt(vals,1)  ! 1 : pos(i)
  b := getelt(vals,2)  ! 2 : pos(i+1)

  xa := a div s
  ya := a mod s
  xb := b div s
  yb := b mod s
  delta_x := abs(xa-xb)
  delta_y := abs(ya-yb)
  returned := (delta_x<=2) and (delta_y<=2) and (delta_x+delta_y=3)
 end-function

end-model