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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.
"""

  Subset sum problem in Google CP Solver.

  From Katta G. Murty: 'Optimization Models for Decision Making', page 340
  http://ioe.engin.umich.edu/people/fac/books/murty/opti_model/junior-7.pdf
  '''
  Example 7.8.1

  A bank van had several bags of coins, each containing either
  16, 17, 23, 24, 39, or 40 coins. While the van was parked on the
  street, thieves stole some bags. A total of 100 coins were lost.
  It is required to find how many bags were stolen.
  '''

  Compare with the following models:
  * Comet: http://www.hakank.org/comet/subset_sum.co
  * ECLiPSE: http://www.hakank.org/eclipse/subset_sum.ecl
  * Gecode: http://www.hakank.org/gecode/subset_sum.cpp
  * MiniZinc: http://www.hakank.org/minizinc/subset_sum.mzn
  * Tailor/Essence': http://www.hakank.org/tailor/subset_sum.py
  * SICStus: http://hakank.org/sicstus/subset_sum.pl

  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
import sys
from ortools.constraint_solver import pywrapcp


def subset_sum(solver, values, total):
  n = len(values)
  x = [solver.IntVar(0, n) for i in range(n)]
  ss = solver.IntVar(0, n)

  solver.Add(ss == solver.Sum(x))
  solver.Add(total == solver.ScalProd(x, values))

  return x, ss



# Create the solver.
solver = pywrapcp.Solver("n-queens")

#
# data
#
print("coins:", coins)
print("total:", total)
print()

#
# declare variables
#

#
# constraints
#
x, ss = subset_sum(solver, coins, total)

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

# db: DecisionBuilder
db = solver.Phase(x, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)

solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
  print("ss:", ss.Value())
  print("x: ", [x[i].Value() for i in range(len(x))])
  print()
  num_solutions += 1
solver.EndSearch()

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

coins = [16, 17, 23, 24, 39, 40]
total = 100