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# Copyright 2018 Gergo Rozner
# 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.
"""Solve the magic sequence problem with the CP-SAT solver."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from ortools.sat.python import cp_model


"""Magic sequence problem."""
n = 100
values = range(n)

model = cp_model.CpModel()

x = [model.NewIntVar(0, n, 'x%i' % i) for i in values]

for k in values:
  tmp_array = []
  for i in values:
    tmp_var = model.NewBoolVar('')
    model.Add(x[i] == k).OnlyEnforceIf(tmp_var)
    model.Add(x[i] != k).OnlyEnforceIf(tmp_var.Not())
    tmp_array.append(tmp_var)
  model.Add(sum(tmp_array) == x[k])

# Redundant constraint.
model.Add(sum(x) == n)

solver = cp_model.CpSolver()
# No solution printer, this problem has only 1 solution.
solver.parameters.log_search_progress = True
solver.Solve(model)
print(solver.ResponseStats())
for k in values:
  print('x[%i] = %i ' % (k, solver.Value(x[k])), end='')
print()