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# 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 covering in Google CP Solver.

  Example 9.1-2, page 354ff, from
  Taha 'Operations Research - An Introduction'
  Minimize the number of security telephones in street
  corners on a campus.

  Compare with the following models:
  * MiniZinc: http://www.hakank.org/minizinc/set_covering2.mzn
  * Comet   : http://www.hakank.org/comet/set_covering2.co
  * ECLiPSe : http://www.hakank.org/eclipse/set_covering2.ecl
  * SICStus: http://hakank.org/sicstus/set_covering2.pl
  * Gecode: http://hakank.org/gecode/set_covering2.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



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

#
# data
#
n = 8  # maximum number of corners
num_streets = 11  # number of connected streets

# corners of each street
# Note: 1-based (handled below)
corner = [[1, 2], [2, 3], [4, 5], [7, 8], [6, 7], [2, 6], [1, 6], [4, 7],
          [2, 4], [5, 8], [3, 5]]

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

#
# constraints
#

# number of telephones, to be minimized
z = solver.Sum(x)

# ensure that all corners are covered
for i in range(num_streets):
  # also, convert to 0-based
  solver.Add(solver.SumGreaterOrEqual([x[j - 1] for j in corner[i]], 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(n)])

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