code: def test_iforest_average_path_length():
      # It tests non-regression for #8549 which used the wrong formula
      # for average path length, strictly for the integer case
      # Updated to check average path length when input is <= 2 (issue #11839)
      result_one = (
          2.0 * (np.log(4.0) + np.euler_gamma) - 2.0 * 4.0 / 5.0
      )
      result_two = (
          2.0 * (np.log(998.0) + np.euler_gamma) - 2.0 * 998.0 / 999.0
      )
      assert_allclose(_average_path_length([0]), [0.0])
      assert_allclose(_average_path_length([1]), [0.0])
      assert_allclose(_average_path_length([2]), [1.0])
      assert_allclose(_average_path_length([5]), [result_one])
      assert_allclose(_average_path_length([999]), [result_two])
      assert_allclose(
          _average_path_length(np.array([1, 2, 5, 999])),
          [0.0, 1.0, result_one, result_two],
      )
      # _average_path_length is increasing
      avg_path_length = _average_path_length(np.arange(5))
      assert_array_equal(avg_path_length, np.sort(avg_path_length))
  
imports: import warnings
  from unittest.mock import Mock, patch
  import numpy
  import pytest
  from sklearn.datasets import load_diabetes, load_iris, make_classification
  from sklearn.ensemble import IsolationForest
  from sklearn.ensemble._iforest import _average_path_length
  from sklearn.metrics import roc_auc_score
  from sklearn.model_selection import ParameterGrid, train_test_split
  from sklearn.utils import check_random_state
  from sklearn.utils._testing import assert_allclose, assert_array_almost_equal, assert_array_equal, ignore_warnings
  from sklearn.utils.fixes import CSC_CONTAINERS, CSR_CONTAINERS
label_desc: Use image node_id 11 for calling a global function with example usage: test_iforest_average_path_length() without return types