Sudoku (CP model)

• The model sudoku_ka.mos solves a given Sudoku grid by Constraint Programming.

(!****************************************************************
   CP example problems
   ===================
   
   file sudoku2_ka.mos
   ``````````````````
   Sudoku puzzle - data read from file.

   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, Aug. 2005, rev. Jan. 2018
*****************************************************************!)

model "sudoku (Kalis)"
 uses "kalis", "mmsystem"

 parameters
  DATAFILE = "sudokug290705.dat"
 end-parameters

 forward procedure print_solution(numsol: integer)
 
 setparam("kalis_default_lb", 1); setparam("kalis_default_ub", 9)
                                     ! Default variable bounds

 declarations
  XS = {'A','B','C','D','E','F','G','H','I'}
  YS = 1..9
  VALUE: dynamic array(XS,YS) of integer
  v: array(XS,YS) of cpvar
 end-declarations
    
 initializations from "Data/"+DATAFILE
  VALUE
 end-initializations

! Fix variables to the given values 
 forall(x in XS, y in YS | exists(VALUE(x,y))) v(x,y) = VALUE(x,y)   
    
 starttime:=gettime

! All-different values in rows 
 forall(y in YS) all_different( union(x in XS) {v(x,y)})

! All-different values in columns
 forall(x in XS) all_different(union(y in YS) {v(x,y)})

! All-different values in 3x3 squares
 forall(i in 0..2) do
  all_different(union(x in {'A','B','C'}, y in {1+3*i,2+3*i,3+3*i}) {v(x,y)})
  all_different(union(x in {'D','E','F'}, y in {1+3*i,2+3*i,3+3*i}) {v(x,y)})
  all_different(union(x in {'G','H','I'}, y in {1+3*i,2+3*i,3+3*i}) {v(x,y)})
 end-do  

 cp_show_prob

! Solve the problem
 solct:= 0
 while (cp_find_next_sol) do
  solct+=1
  print_solution(solct)
 end-do
 
 cp_show_stats
 writeln("Number of solutions: ", solct)  
 writeln("Total time: ", gettime-starttime)

!****************************************************************
! Solution printing
 procedure print_solution(numsol: integer)
  writeln("Solution ", numsol)
  write("   "); forall(x in XS) write(x," "); writeln
  forall(y in YS) do
   write(y, ": ")
   forall(x in XS) write(v(x,y)," ")
   writeln
  end-do
  returned:=true
 end-procedure
    
end-model