from functools import reduce;

#------------------------------------------------------------------------------#

def printSolutions(solutions):
    print('*'*26);
    for sol in solutions:
        ix=1;
        for cell in sol:
            print(cell[1][0],end='  ');
            if ix==9:
                print('');
                ix=1;
            else: ix+=1;
        # end for
        print('*'*26);
    # end for
# end def

#------------------------------------------------------------------------------#

Range9=range(1,10);
allCells=[(i,k) for i in Range9 for k in Range9];

def getIntialList(inputList): # No test of input data!
    problemList=[(cell,nb)
                 for (cell,nb) in zip(allCells,inputList)
                 if nb>0];
    initialList=[((i,k),list(Range9))
                 for i in Range9
                 for k in Range9];
    return [reduce(adjustCell,problemList,sp)
            for sp in initialList];

def adjustCell(sp,pp):
    def areBlocked(a,b): return (a-1)//3==(b-1)//3;
    ((i,k),val)=pp;
    ((m,n),vList)=sp;
    if (i,k)==(m,n): return ((m,n),[val]);
    elif ((i==m) or (k==n) or
          (areBlocked(i,m) and areBlocked(k,n))):
        return ((m,n),[v for v in vList if v!=val]);
    else: return sp;

def adjustCells(sol,pp):
    return [adjustCell(sp,pp) for sp in sol];

def generateAll(solutionsList,cell):
    return [adjustCells(sol,(cell,val))
                for sol in solutionsList
                for val in dict(sol)[cell]];

def solveSudoku(inputList):
    return reduce(generateAll,allCells,
                  [getIntialList(inputList)]);

#------------------------------------------------------------------------------#
#------------------------------------------------------------------------------#
if __name__ == '__main__':
    print('\n# Beginning Test ...\n');
#------------------------------------------------------------------------------#
    
    #           1  2  3  4  5  6  7  8  9
    inputList =[0, 5, 0, 0, 6, 0, 0, 0, 1]; # 1
    inputList+=[0, 0, 4, 8, 0, 0, 0, 7, 0]; # 2
    inputList+=[8, 0, 0, 0, 0, 0, 0, 5, 2]; # 3
    inputList+=[2, 0, 0, 0, 5, 7, 0, 3, 0]; # 4
    inputList+=[0, 0, 0, 0, 0, 0, 0, 0, 0]; # 5
    inputList+=[0, 3, 0, 6, 9, 0, 0, 0, 5]; # 6
    inputList+=[7, 9, 0, 0, 0, 0, 0, 0, 8]; # 7
    inputList+=[0, 1, 0, 0, 0, 6, 5, 0, 0]; # 8
    inputList+=[5, 0, 0, 0, 3, 0, 0, 6, 0]; # 9
    
    solutions=solveSudoku(inputList);

    printSolutions(solutions);
    print('\nAnzahl: ',len(solutions));

#------------------------------------------------------------------------------#
#------------------------------------------------------------------------------#
    print('\n# Finished Test.\n');
# end if main