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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 from Steven Skiena, The Stony Brook Algorithm Repository
  http://www.cs.sunysb.edu/~algorith/files/set-cover.shtml
  '''
  Input Description: A set of subsets S_1, ..., S_m of the
  universal set U = {1,...,n}.

  Problem: What is the smallest subset of subsets T subset S such
  that \cup_{t_i in T} t_i = U?
  '''
  Data is from the pictures INPUT/OUTPUT.

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

#
# data
#
num_sets = 7
num_elements = 12
belongs = [
    # 1 2 3 4 5 6 7 8 9 0 1 2  elements
    [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],  # Set 1
    [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],  # 2
    [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0],  # 3
    [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0],  # 4
    [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0],  # 5
    [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0],  # 6
    [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  # 7
]

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

# number of choosen sets
z = solver.IntVar(0, num_sets * 2, 'z')

# total number of elements in the choosen sets
tot_elements = solver.IntVar(0, num_sets * num_elements)

#
# constraints
#
solver.Add(z == solver.Sum(x))

# all sets must be used
for j in range(num_elements):
  s = solver.Sum([belongs[i][j] * x[i] for i in range(num_sets)])
  solver.Add(s >= 1)

# number of used elements
solver.Add(tot_elements == solver.Sum([
    x[i] * belongs[i][j] for i in range(num_sets) for j in range(num_elements)
]))

# objective
objective = solver.Minimize(z, 1)

#
# search and result
#
db = solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)

solver.NewSearch(db, [objective])

num_solutions = 0
while solver.NextSolution():
  num_solutions += 1
  print('z:', z.Value())
  print('tot_elements:', tot_elements.Value())
  print('x:', [x[i].Value() for i in range(num_sets)])

solver.EndSearch()

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