text: # 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.
  
  """
  
    Discrete tomography in Google CP Solver.
  
    Problem from http://eclipse.crosscoreop.com/examples/tomo.ecl.txt
    '''
    This is a little 'tomography' problem, taken from an old issue
    of Scientific American.
  
    A matrix which contains zeroes and ones gets "x-rayed" vertically and
    horizontally, giving the total number of ones in each row and column.
    The problem is to reconstruct the contents of the matrix from this
    information. Sample run:
  
    ?- go.
      0 0 7 1 6 3 4 5 2 7 0 0
   0
   0
   8      * * * * * * * *
   2      *             *
   6      *   * * * *   *
   4      *   *     *   *
   5      *   *   * *   *
   3      *   *         *
   7      *   * * * * * *
   0
   0
  
   Eclipse solution by Joachim Schimpf, IC-Parc
   '''
  
   Compare with the following models:
   * Comet: http://www.hakank.org/comet/discrete_tomography.co
   * Gecode: http://www.hakank.org/gecode/discrete_tomography.cpp
   * MiniZinc: http://www.hakank.org/minizinc/tomography.mzn
   * Tailor/Essence': http://www.hakank.org/tailor/tomography.eprime
   * SICStus: http://hakank.org/sicstus/discrete_tomography.pl
  
    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 ortools.constraint_solver import pywrapcp
  
  
  def main(row_sums="", col_sums=""):
  
    # Create the solver.
    solver = pywrapcp.Solver("n-queens")
  
    #
    # data
    #
    if row_sums == "":
      print "Using default problem instance"
      row_sums = [0, 0, 8, 2, 6, 4, 5, 3, 7, 0, 0]
      col_sums = [0, 0, 7, 1, 6, 3, 4, 5, 2, 7, 0, 0]
  
    r = len(row_sums)
    c = len(col_sums)
  
    # declare variables
    x = []
    for i in range(r):
      t = []
      for j in range(c):
        t.append(solver.IntVar(0, 1, "x[%i,%i]" % (i, j)))
      x.append(t)
    x_flat = [x[i][j] for i in range(r) for j in range(c)]
  
    #
    # constraints
    #
    [solver.Add(solver.Sum([x[i][j] for j in range(c)]) == row_sums[i])
     for i in range(r)]
    [solver.Add(solver.Sum([x[i][j] for i in range(r)]) == col_sums[j])
     for j in range(c)]
  
    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add(x_flat)
  
    # db: DecisionBuilder
    db = solver.Phase(x_flat,
                      solver.INT_VAR_SIMPLE,
                      solver.ASSIGN_MIN_VALUE)
  
    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
      print_solution(x, r, c, row_sums, col_sums)
      print
  
      num_solutions += 1
    solver.EndSearch()
  
    print
    print "num_solutions:", num_solutions
    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "WallTime:", solver.WallTime()
  
  #
  # Print solution
  #
  
  
  def print_solution(x, rows, cols, row_sums, col_sums):
    print "  ",
    for j in range(cols):
      print col_sums[j],
    print
    for i in range(rows):
      print row_sums[i],
      for j in range(cols):
        if x[i][j].Value() == 1:
          print "#",
        else:
          print ".",
      print ""
  
  
  #
  # Read a problem instance from a file
  #
  def read_problem(file):
    f = open(file, "r")
    row_sums = f.readline()
    col_sums = f.readline()
    row_sums = [int(r) for r in (row_sums.rstrip()).split(",")]
    col_sums = [int(c) for c in (col_sums.rstrip()).split(",")]
  
    return [row_sums, col_sums]
  
  if __name__ == "__main__":
    if len(sys.argv) > 1:
      file = sys.argv[1]
      print "Problem instance from", file
      [row_sums, col_sums] = read_problem(file)
      main(row_sums, col_sums)
    else:
      main()
  