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# Copyright 2010-2018 Google LLC
# 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.
"""Code sample that encodes the product of two Boolean variables."""

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

from ortools.sat.python import cp_model


def BooleanProductSampleSat():
    """Encoding of the product of two Boolean variables.

  p == x * y, which is the same as p <=> x and y
  """
    model = cp_model.CpModel()
    x = model.NewBoolVar('x')
    y = model.NewBoolVar('y')
    p = model.NewBoolVar('p')

    # x and y implies p, rewrite as not(x and y) or p
    model.AddBoolOr([x.Not(), y.Not(), p])

    # p implies x and y, expanded into two implication
    model.AddImplication(p, x)
    model.AddImplication(p, y)

    # Create a solver and solve.
    solver = cp_model.CpSolver()
    solution_printer = cp_model.VarArraySolutionPrinter([x, y, p])
    solver.SearchForAllSolutions(model, solution_printer)


BooleanProductSampleSat()