code: def test_add_random_inputs(direction: StudyDirection) -> None:
      n_additional_trials = 3
      dummy_value = -1
      distributions = {
          "bacon": CategoricalDistribution((0, 1, 2)),
          "egg": FloatDistribution(1, 10),
          "spam": IntDistribution(1, 10),
      }
  
      trials_before = [
          create_trial(
              params={"bacon": 0, "egg": 1, "spam": 10},
              distributions=distributions,
              value=1.0,
          ),
      ]
      p = _preprocessing.AddRandomInputs(
          n_additional_trials=n_additional_trials,
          dummy_value=dummy_value,
      )
      trials_after = p.apply(trials_before, direction)
  
      assert (
          len(trials_after) == len(trials_before) + n_additional_trials
      )
      assert trials_before[0] == trials_after[0]
      for t in trials_after[1:]:
          assert t.value == dummy_value
          assert t.distributions == distributions
          assert set(t.params.keys()) == set(distributions.keys())
  
          for name, distribution in distributions.items():
              assert distribution._contains(t.params[name])
  
file_path: optuna/tests/terminator_tests/improvement_tests/test_preprocessing.py
imports: from __future__ import annotations
  from unittest import mock
  import numpy
  import pytest
  from optuna.distributions import CategoricalDistribution
  from optuna.distributions import FloatDistribution
  from optuna.distributions import IntDistribution
  from optuna.study._study_direction import StudyDirection
  from optuna.terminator.improvement import _preprocessing
  from optuna.trial import create_trial
  from optuna.trial import FrozenTrial
label_desc: Use image node_id 8 for calling a global function with example usage: test_add_random_inputs(direction) without return types