# 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.

"""

  Set covering in Google CP Solver.

  Problem from
  Katta G. Murty: 'Optimization Models for Decision Making', page 302f
  http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf

  10 senators making a committee, where there must at least be one
  representative from each group:
  group:        senators:
  southern      1 2 3 4 5
  northern      6 7 8 9 10
  liberals      2 3 8 9 10
  conservative  1 5 6 7
  democrats     3 4 5 6 7 9
  republicans   1 2 8 10

  The objective is to minimize the number of senators.

  Compare with the following models:
  * MiniZinc: http://www.hakank.org/minizinc/set_covering3_model.mzn (model)
              http://www.hakank.org/minizinc/set_covering3.mzn (data)
  * Comet   : http://www.hakank.org/comet/set_covering3.co
  * ECLiPSe : http://www.hakank.org/eclipse/set_covering3.ecl
  * SICStus : http://hakank.org/sicstus/set_covering3.pl
  * Gecode  : http://hakank.org/gecode/set_covering3.cpp


  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/

"""

from constraint_solver import pywrapcp

def main(unused_argv):

    # Create the solver.
    solver = pywrapcp.Solver('Set covering')

    #
    # data
    #
    num_groups = 6
    num_senators = 10

    # which group does a senator belong to?
    belongs = [
        [1, 1, 1, 1, 1, 0, 0, 0, 0, 0],   # 1 southern
        [0, 0, 0, 0, 0, 1, 1, 1, 1, 1],   # 2 northern
        [0, 1, 1, 0, 0, 0, 0, 1, 1, 1],   # 3 liberals
        [1, 0, 0, 0, 1, 1, 1, 0, 0, 0],   # 4 conservative
        [0, 0, 1, 1, 1, 1, 1, 0, 1, 0],   # 5 democrats
        [1, 1, 0, 0, 0, 0, 0, 1, 0, 1]    # 6 republicans
        ]


    #
    # declare variables
    #
    x = [solver.IntVar(0, 1, 'x[%i]' % i) for i in range(num_senators)]

    #
    # constraints
    #

    # number of assigned senators (to minimize)
    z = solver.Sum(x)

    # ensure that each group is covered by at least
    # one senator
    for i in range(num_groups):
        solver.Add(
            solver.SumGreaterOrEqual([x[j]*belongs[i][j]
                                      for j in range(num_senators)],
                                     1))

    objective = solver.Minimize(z, 1)

    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add(x)
    solution.AddObjective(z)

    collector = solver.LastSolutionCollector(solution)
    solver.Solve(solver.Phase(x,
                              solver.INT_VAR_DEFAULT,
                              solver.INT_VALUE_DEFAULT),
                 [collector, objective])

    print "z:", collector.ObjectiveValue(0)
    print "x:", [collector.Value(0, x[i]) for i in range(num_senators)]
    for j in range(num_senators):
        if collector.Value(0, x[j]) == 1:
            print "Senator", j+1, "belongs to these groups:",
            for i in range(num_groups):
                if belongs[i][j] == 1:
                    print i + 1,
            print

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


if __name__ == '__main__':
    main("cp sample")