# 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.

"""

  Set partition and set covering in Google CP Solver.

  Example from the Swedish book
  Lundgren, Roennqvist, Vaebrand
  'Optimeringslaera' (translation: 'Optimization theory'),
  page 408.

  * Set partition:
    We want to minimize the cost of the alternatives which covers all the
    objects, i.e. all objects must be choosen. The requirement is than an
    object may be selected _exactly_ once.

    Note: This is 1-based representation

    Alternative        Cost        Object
    1                  19           1,6
    2                  16           2,6,8
    3                  18           1,4,7
    4                  13           2,3,5
    5                  15           2,5
    6                  19           2,3
    7                  15           2,3,4
    8                  17           4,5,8
    9                  16           3,6,8
    10                 15           1,6,7

    The problem has a unique solution of z = 49 where alternatives
         3, 5, and 9
    is selected.

  * Set covering:
    If we, however, allow that an object is selected _more than one time_,
    then the solution is z = 45 (i.e. less cost than the first problem),
    and the alternatives
         4, 8, and 10
    is selected, where object 5 is selected twice (alt. 4 and 8).
    It's an unique solution as well.


 Compare with the following models:
  * MiniZinc: http://www.hakank.org/minizinc/set_covering4.mzn
  * Comet   : http://www.hakank.org/comet/set_covering4.co
  * ECLiPSe : http://www.hakank.org/eclipse/set_covering4.ecl
  * SICStus : http://www.hakank.org/sicstus/set_covering4.pl
  * Gecode  : http://www.hakank.org/gecode/set_covering4.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/

"""
from __future__ import print_function
from ortools.constraint_solver import pywrapcp


def main(set_partition=1):

  # Create the solver.
  solver = pywrapcp.Solver("Set partition and set covering")

  #
  # data
  #
  num_alternatives = 10
  num_objects = 8

  # costs for the alternatives
  costs = [19, 16, 18, 13, 15, 19, 15, 17, 16, 15]

  # the alternatives, and their objects
  a = [
      # 1 2 3 4 5 6 7 8    the objects
      [1, 0, 0, 0, 0, 1, 0, 0],  # alternative 1
      [0, 1, 0, 0, 0, 1, 0, 1],  # alternative 2
      [1, 0, 0, 1, 0, 0, 1, 0],  # alternative 3
      [0, 1, 1, 0, 1, 0, 0, 0],  # alternative 4
      [0, 1, 0, 0, 1, 0, 0, 0],  # alternative 5
      [0, 1, 1, 0, 0, 0, 0, 0],  # alternative 6
      [0, 1, 1, 1, 0, 0, 0, 0],  # alternative 7
      [0, 0, 0, 1, 1, 0, 0, 1],  # alternative 8
      [0, 0, 1, 0, 0, 1, 0, 1],  # alternative 9
      [1, 0, 0, 0, 0, 1, 1, 0]   # alternative 10
  ]

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

  #
  # constraints
  #

  # sum the cost of the choosen alternative,
  # to be minimized
  z = solver.ScalProd(x, costs)

  #
  for j in range(num_objects):
    if set_partition == 1:
      solver.Add(
          solver.SumEquality([x[i] * a[i][j]
                              for i in range(num_alternatives)],
                             1))
    else:
      solver.Add(
          solver.SumGreaterOrEqual([x[i] * a[i][j]
                                    for i in range(num_alternatives)],
                                   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[i] for i in range(num_alternatives)],
                            solver.INT_VAR_DEFAULT,
                            solver.INT_VALUE_DEFAULT),
               [collector, objective])

  print("z:", collector.ObjectiveValue(0))
  print("selected alternatives:", [i + 1 for i in range(num_alternatives)
                                   if collector.Value(0, x[i]) == 1])

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


if __name__ == "__main__":
  print("Set partition:")
  main(1)

  print("\nSet covering:")
  main(0)