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step_function_sample_sat

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/sat/step_function_sample_sat.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/ortools/sat/samples/step_function_sample_sat.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python

%pip install ortools

Implements a step function.

python

from ortools.sat.python import cp_model


class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
    """Print intermediate solutions."""

    def __init__(self, variables: list[cp_model.IntVar]):
        cp_model.CpSolverSolutionCallback.__init__(self)
        self.__variables = variables

    def on_solution_callback(self) -> None:
        for v in self.__variables:
            print(f"{v}={self.value(v)}", end=" ")
        print()


def step_function_sample_sat():
    """Encode the step function."""

    # Model.
    model = cp_model.CpModel()

    # Declare our primary variable.
    x = model.new_int_var(0, 20, "x")

    # Create the expression variable and implement the step function
    # Note it is not defined for x == 2.
    #
    #        -               3
    # -- --      ---------   2
    #                        1
    #      -- ---            0
    # 0 ================ 20
    #
    expr = model.new_int_var(0, 3, "expr")

    # expr == 0 on [5, 6] U [8, 10]
    b0 = model.new_bool_var("b0")
    model.add_linear_expression_in_domain(
        x, cp_model.Domain.from_intervals([(5, 6), (8, 10)])
    ).only_enforce_if(b0)
    model.add(expr == 0).only_enforce_if(b0)

    # expr == 2 on [0, 1] U [3, 4] U [11, 20]
    b2 = model.new_bool_var("b2")
    model.add_linear_expression_in_domain(
        x, cp_model.Domain.from_intervals([(0, 1), (3, 4), (11, 20)])
    ).only_enforce_if(b2)
    model.add(expr == 2).only_enforce_if(b2)

    # expr == 3 when x == 7
    b3 = model.new_bool_var("b3")
    model.add(x == 7).only_enforce_if(b3)
    model.add(expr == 3).only_enforce_if(b3)

    # At least one bi is true. (we could use an exactly one constraint).
    model.add_bool_or(b0, b2, b3)

    # Search for x values in increasing order.
    model.add_decision_strategy([x], cp_model.CHOOSE_FIRST, cp_model.SELECT_MIN_VALUE)

    # Create a solver and solve with a fixed search.
    solver = cp_model.CpSolver()

    # Force the solver to follow the decision strategy exactly.
    solver.parameters.search_branching = cp_model.FIXED_SEARCH
    # Enumerate all solutions.
    solver.parameters.enumerate_all_solutions = True

    # Search and print out all solutions.
    solution_printer = VarArraySolutionPrinter([x, expr])
    solver.solve(model, solution_printer)


step_function_sample_sat()