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overlapping_intervals_sample_sat

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

First, you must install ortools package in this colab.

python

%pip install ortools

Code sample to demonstrates how to detect if two intervals overlap.

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 overlapping_interval_sample_sat():
    """Create the overlapping Boolean variables and enumerate all states."""
    model = cp_model.CpModel()

    horizon = 7

    # First interval.
    start_var_a = model.new_int_var(0, horizon, "start_a")
    duration_a = 3
    end_var_a = model.new_int_var(0, horizon, "end_a")
    unused_interval_var_a = model.new_interval_var(
        start_var_a, duration_a, end_var_a, "interval_a"
    )

    # Second interval.
    start_var_b = model.new_int_var(0, horizon, "start_b")
    duration_b = 2
    end_var_b = model.new_int_var(0, horizon, "end_b")
    unused_interval_var_b = model.new_interval_var(
        start_var_b, duration_b, end_var_b, "interval_b"
    )

    # a_after_b Boolean variable.
    a_after_b = model.new_bool_var("a_after_b")
    model.add(start_var_a >= end_var_b).only_enforce_if(a_after_b)
    model.add(start_var_a < end_var_b).only_enforce_if(~a_after_b)

    # b_after_a Boolean variable.
    b_after_a = model.new_bool_var("b_after_a")
    model.add(start_var_b >= end_var_a).only_enforce_if(b_after_a)
    model.add(start_var_b < end_var_a).only_enforce_if(~b_after_a)

    # Result Boolean variable.
    a_overlaps_b = model.new_bool_var("a_overlaps_b")

    # Option a: using only clauses
    model.add_bool_or(a_after_b, b_after_a, a_overlaps_b)
    model.add_implication(a_after_b, ~a_overlaps_b)
    model.add_implication(b_after_a, ~a_overlaps_b)

    # Option b: using an exactly one constraint.
    # model.add_exactly_one(a_after_b, b_after_a, a_overlaps_b)

    # Search for start values in increasing order for the two intervals.
    model.add_decision_strategy(
        [start_var_a, start_var_b],
        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([start_var_a, start_var_b, a_overlaps_b])
    solver.solve(model, solution_printer)


overlapping_interval_sample_sat()