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# SUDOKU, Number Placement Puzzle 

# Written in pymprog by Yingjie Lan <ylan@umd.edu>



"""Sudoku, also known as Number Place, is a logic-based placement

   puzzle. The aim of the canonical puzzle is to enter a numerical

   digit from 1 through 9 in each cell of a 9x9 grid made up of 3x3

   subgrids (called "regions"), starting with various digits given in

   some cells (the "givens"). Each row, column, and region must contain

   only one instance of each numeral.



   (From Wikipedia, the free encyclopedia.)



   This example will provide a sample Super Sudoku:

   in addition to satisfying all the requirements 

   of Sudoku, Super Sudoku also requires that the

   elements in each diagonal must be distinct."""



from pymprog import *        # Import the module

beginModel("ssudoku")

I = xrange(1,10)

J = xrange(1,10)

K = xrange(1,10)

T = iprod(I,J,K) #create Indice tuples

#x[i,j,k] = 1 means cell [i,j] is assigned number k 

x = var(T, 'x', bool) #binary vars

#each cell must be assigned exactly one number

st([sum(x[i,j,k] for k in K)==1 for i in I for j in J], 'cell')

#cells in the same row must be assigned distinct numbers

st([sum(x[i,j,k] for j in J)==1 for i in I for k in K], 'row') 

#cells in the same column must be assigned distinct numbers

st([sum(x[i,j,k] for i in I)==1 for j in J for k in K], 'col')

#cells in the same region must be assigned distinct numbers

st([sum(x[i,j,k] for i in range(r,r+3) for j in range(c, c+3))==1

 for r in range(1,10,3) for c in range(1,10,3) for k in K],'reg')



#cells in \-diagonal

st([sum(x[i,i,k] for i in I)==1 for k in K])



#cells in /-diagonal

st([sum(x[i,10-i,k] for i in I)==1 for k in K])



#there is no need for an objective function here



solvopt(integer='advanced') #use advanced B&B

solve()



for i in I:

   if i in range(1,10,3):

      print " +-------+-------+-------+"

   print '',

   for j in J:

      if j in range(1,10,3): print "|",

      print "%g"%sum(x[i,j,k].primal*k for k in K),

      if j==9: print "|"

   if i == 9:

      print " +-------+-------+-------+"