#
# Sudoku puzzle solver by by Luigi Poderico (www.poderico.it).
#
from constraint import *

problem = Problem()

# Define the variables: 9 rows of 9 variables rangin in 1...9
for i in range(1, 10) :
    problem.addVariables(range(i*10+1, i*10+10), range(1, 10))

# Each row has different values
for i in range(1, 10) :
    problem.addConstraint(AllDifferentConstraint(), range(i*10+1, i*10+10))

# Each colum has different values
for i in range(1, 10) :
    problem.addConstraint(AllDifferentConstraint(), range(10+i, 100+i, 10))

# Each 3x3 box has different values
problem.addConstraint(AllDifferentConstraint(), [11,12,13,21,22,23,31,32,33])
problem.addConstraint(AllDifferentConstraint(), [41,42,43,51,52,53,61,62,63])
problem.addConstraint(AllDifferentConstraint(), [71,72,73,81,82,83,91,92,93])

problem.addConstraint(AllDifferentConstraint(), [14,15,16,24,25,26,34,35,36])
problem.addConstraint(AllDifferentConstraint(), [44,45,46,54,55,56,64,65,66])
problem.addConstraint(AllDifferentConstraint(), [74,75,76,84,85,86,94,95,96])

problem.addConstraint(AllDifferentConstraint(), [17,18,19,27,28,29,37,38,39])
problem.addConstraint(AllDifferentConstraint(), [47,48,49,57,58,59,67,68,69])
problem.addConstraint(AllDifferentConstraint(), [77,78,79,87,88,89,97,98,99])

# Some value is given.
initValue = [[0, 9, 0, 7, 0, 0, 8, 6, 0],
             [0, 3, 1, 0, 0, 5, 0, 2, 0],
             [8, 0, 6, 0, 0, 0, 0, 0, 0],
             [0, 0, 7, 0, 5, 0, 0, 0, 6],
             [0, 0, 0, 3, 0, 7, 0, 0, 0],
             [5, 0, 0, 0, 1, 0, 7, 0, 0],
             [0, 0, 0, 0, 0, 0, 1, 0, 9],
             [0, 2, 0, 6, 0, 0, 0, 5, 0],
             [0, 5, 4, 0, 0, 8, 0, 7, 0]]

for i in range(1, 10) :
    for j in range(1, 10):
        if initValue[i-1][j-1] !=0 :
            problem.addConstraint(lambda var, val=initValue[i-1][j-1]:
                                  var==val, (i*10+j,))

# Get the solutions.
solutions = problem.getSolutions()

# Print the solutions
for solution in solutions:
    for i in range(1, 10):
        for j in range(1, 10):
            index = i*10+j
            print solution[index],
        print
    print