ortools-clone/python/fill_a_pix.py

# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.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.

"""

  Fill-a-Pix problem in Google CP Solver.

  From http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/basiclogic
  '''
  Each puzzle consists of a grid containing clues in various places. The
  object is to reveal a hidden picture by painting the squares around each
  clue so that the number of painted squares, including the square with
  the clue, matches the value of the clue.
  '''

  http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules
  '''
  Fill-a-Pix is a Minesweeper-like puzzle based on a grid with a pixilated
  picture hidden inside. Using logic alone, the solver determines which
  squares are painted and which should remain empty until the hidden picture
  is completely exposed.
  '''

  Fill-a-pix History:
  http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/history


  Compare with the following models:
  * MiniZinc: http://www.hakank.org/minizinc/fill_a_pix.mzn
  * SICStus Prolog: http://www.hakank.org/sicstus/fill_a_pix.pl
  * ECLiPSe: http://hakank.org/eclipse/fill_a_pix.ecl
  * Gecode: http://hakank.org/gecode/fill_a_pix.cpp

  And see the Minesweeper model:
  * http://www.hakank.org/google_or_tools/minesweeper.py


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


# Puzzle 1 from
# http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules
default_n = 10
X = -1
default_puzzle = [
    [X,X,X,X,X,X,X,X,0,X],
    [X,8,8,X,2,X,0,X,X,X],
    [5,X,8,X,X,X,X,X,X,X],
    [X,X,X,X,X,2,X,X,X,2],
    [1,X,X,X,4,5,6,X,X,X],
    [X,0,X,X,X,7,9,X,X,6],
    [X,X,X,6,X,X,9,X,X,6],
    [X,X,6,6,8,7,8,7,X,5],
    [X,4,X,6,6,6,X,6,X,4],
    [X,X,X,X,X,X,3,X,X,X]
    ]


def main(puzzle='', n=''):

    # Create the solver.
    solver = pywrapcp.Solver('Fill-a-Pix')

    #
    # data
    #

    # Set default problem
    if puzzle == '':
        puzzle = default_puzzle
        n = default_n
    else:
        print 'n:', n

    # for the neighbors of 'this' cell
    S = [-1,0,1]

    # print problem instance
    print 'Problem:'
    for i in range(n):
        for j in range(n):
            if puzzle[i][j] == X:
                sys.stdout.write('.')
            else:
                sys.stdout.write(str(puzzle[i][j]))
        print
    print

    #
    # declare variables
    #
    pict = {}
    for i in range(n):
        for j in range(n):
            pict[(i,j)] = solver.IntVar(0,1, 'pict %i %i' % (i, j))

    pict_flat = [pict[i,j] for i in range(n) for j in range(n)]

    #
    # constraints
    #
    for i in range(n):
        for j in range(n):
            if puzzle[i][j] > X:
                # this cell is the sum of all the surrounding cells
                solver.Add(
                    puzzle[i][j] == solver.Sum([pict[i+a,j+b]
                                       for a in S for b in S
                                       if i + a >=0 and
                                          j + b >=0 and
                                          i + a < n  and
                                          j + b < n
                                       ])
                    )

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

    solver.NewSearch(db)
    num_solutions = 0
    print "Solution:"
    while solver.NextSolution():
        num_solutions += 1
        for i in range(n):
            row = [str(pict[i,j].Value()) for j in range(n)]
            for j in range(n):
                if row[j] == '0':
                    row[j] = ' '
                else:
                    row[j] = '#'
            print "".join(row)
        print

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


#
# Read a problem instance from a file
#
def read_problem(file):
    f = open(file, 'r')
    n = int(f.readline())
    puzzle = []
    for i in range(n):
        x = f.readline()
        row = [0]*n
        for j in range(n):
            if x[j] == '.':
                tmp = -1
            else:
                tmp = int(x[j])
            row[j] = tmp
        puzzle.append(row)
    return [puzzle, n]


if __name__ == '__main__':
    if len(sys.argv) > 1:
        file = sys.argv[1]
        print 'Problem instance from', file
        [puzzle, n] = read_problem(file)
        main(puzzle, n)
    else:
        main()