057: Killer Sudoku

# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""

  Killer Sudoku in Google CP Solver.

  http://en.wikipedia.org/wiki/Killer_Sudoku
  '''
  Killer sudoku (also killer su doku, sumdoku, sum doku, addoku, or
  samunamupure) is a puzzle that combines elements of sudoku and kakuro.
  Despite the name, the simpler killer sudokus can be easier to solve
  than regular sudokus, depending on the solver's skill at mental arithmetic;
  the hardest ones, however, can take hours to crack.

  ...

  The objective is to fill the grid with numbers from 1 to 9 in a way that
  the following conditions are met:

    * Each row, column, and nonet contains each number exactly once.
    * The sum of all numbers in a cage must match the small number printed
      in its corner.
    * No number appears more than once in a cage. (This is the standard rule
      for killer sudokus, and implies that no cage can include more
      than 9 cells.)

  In 'Killer X', an additional rule is that each of the long diagonals
  contains each number once.
  '''

  Here we solve the problem from the Wikipedia page, also shown here
  http://en.wikipedia.org/wiki/File:Killersudoku_color.svg

  The output is:
    2 1 5 6 4 7 3 9 8
    3 6 8 9 5 2 1 7 4
    7 9 4 3 8 1 6 5 2
    5 8 6 2 7 4 9 3 1
    1 4 2 5 9 3 8 6 7
    9 7 3 8 1 6 4 2 5
    8 2 1 7 3 9 5 4 6
    6 5 9 4 2 8 7 1 3
    4 3 7 1 6 5 2 8 9


  Compare with the following models:
  * Comet   : http://www.hakank.org/comet/killer_sudoku.co
  * MiniZinc: http://www.hakank.org/minizinc/killer_sudoku.mzn
  * SICStus: http://www.hakank.org/sicstus/killer_sudoku.pl
  * ECLiPSE: http://www.hakank.org/eclipse/killer_sudoku.ecl
  * Gecode: http://www.hakank.org/gecode/killer_sudoku.cpp


  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
"""

import sys

from constraint_solver import pywrapcp

#
# Ensure that the sum of the segments
# in cc == res
#
def calc(cc, x, res):

    solver = x.values()[0].solver()

    # sum the numbers
    solver.Add(solver.Sum([x[i[0]-1,i[1]-1] for i in cc]) == res)



def main():

    # Create the solver.
    solver = pywrapcp.Solver('Killer Sudoku')

    #
    # data
    #

    # size of matrix
    n = 9

    # For a better view of the problem, see
    #  http://en.wikipedia.org/wiki/File:Killersudoku_color.svg

    # hints
    #    [sum, [segments]]
    # Note: 1-based
    problem = [
            [ 3, [[1,1], [1,2]]],
            [15, [[1,3], [1,4], [1,5]]],
            [22, [[1,6], [2,5], [2,6], [3,5]]],
            [ 4, [[1,7], [2,7]]],
            [16, [[1,8], [2,8]]],
            [15, [[1,9], [2,9], [3,9], [4,9]]],
            [25, [[2,1], [2,2], [3,1], [3,2]]],
            [17, [[2,3], [2,4]]],
            [ 9, [[3,3], [3,4], [4,4]]],
            [ 8, [[3,6], [4,6],[5,6]]],
            [20, [[3,7], [3,8],[4,7]]],
            [ 6, [[4,1], [5,1]]],
            [14, [[4,2], [4,3]]],
            [17, [[4,5], [5,5],[6,5]]],
            [17, [[4,8], [5,7],[5,8]]],            
            [13, [[5,2], [5,3],[6,2]]],
            [20, [[5,4], [6,4],[7,4]]],
            [12, [[5,9], [6,9]]],
            [27, [[6,1], [7,1],[8,1],[9,1]]],
            [ 6, [[6,3], [7,2],[7,3]]],
            [20, [[6,6], [7,6], [7,7]]],
            [ 6, [[6,7], [6,8]]],
            [10, [[7,5], [8,4],[8,5],[9,4]]],
            [14, [[7,8], [7,9],[8,8],[8,9]]],
            [ 8, [[8,2], [9,2]]],
            [16, [[8,3], [9,3]]],
            [15, [[8,6], [8,7]]],
            [13, [[9,5], [9,6],[9,7]]],
            [17, [[9,8], [9,9]]]]

    #
    # variables
    #

    # the set
    x = {}
    for i in range(n):
        for j in range(n):
            x[i,j] = solver.IntVar(1, n, 'x[%i,%i]' % (i,j))

    x_flat = [x[i,j] for i in range(n) for j in range(n)]

    #
    # constraints
    #

    # all rows and columns must be unique
    for i in range(n):
        row = [x[i,j] for j in range(n)]
        solver.Add(solver.AllDifferent(row))

        col = [x[j,i] for j in range(n)]
        solver.Add(solver.AllDifferent(col))

    # cells
    for i in range(2):
        for j in range(2):
            cell = [x[r,c]
                    for r in range(i*3,i*3+3)
                    for c in range(j*3,j*3+3)]
            solver.Add(solver.AllDifferent(cell));

    # calculate the segments
    for (res, segment) in problem:
        calc(segment, x, res)


    #
    # search and solution
    #
    db = solver.Phase(x_flat,
                 solver.INT_VAR_DEFAULT,
                 solver.INT_VALUE_DEFAULT)

    solver.NewSearch(db)

    num_solutions = 0
    while solver.NextSolution():
        for i in range(n):
            for j in range(n):
                print x[i,j].Value(),
            print

        print
        num_solutions += 1

    solver.EndSearch()

    print
    print "num_solutions:", num_solutions
    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "WallTime:", solver.WallTime()


if __name__ == '__main__':
    main()