#!/usr/bin/env python3
# Copyright 2010-2022 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
#
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# distributed under the License is distributed on an "AS IS" BASIS,
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"""Code sample that encodes the product of two Boolean variables."""


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 implications.
    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.parameters.enumerate_all_solutions = True
    solver.Solve(model, solution_printer)


BooleanProductSampleSat()
