


import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format="%(message)s")

def       lowercase_		(		_A			:    np.ndarray						):

      """simple docstring"""




      return input_array.reshape((input_array.size, 1)						)

def       lowercase_		(		_A			:    np.ndarray    ,					_A			:    np.ndarray    ,					_A			:    int						):

      """simple docstring"""




      lowerCamelCase__		:				List[Any]    =  np.nan
      for i in range(_A						):
            lowerCamelCase__		:				List[Any]    =  features[:, labels == i]
            lowerCamelCase__		:				str    =  data.mean(1						)
            # Centralize the data of class i
            lowerCamelCase__		:				List[str]    =  data - column_reshape(_A						)
            if i > 0:
                  # If covariance_sum is not None
                  covariance_sum += np.dot(_A    ,					centered_data.T						)
            else:
                  # If covariance_sum is np.nan (i.e. first loop)
                  lowerCamelCase__		:				Tuple    =  np.dot(_A    ,					centered_data.T						)

      return covariance_sum / features.shape[1]

def       lowercase_		(		_A			:    np.ndarray    ,					_A			:    np.ndarray    ,					_A			:    int						):

      """simple docstring"""




      lowerCamelCase__		:				Optional[int]    =  features.mean(1						)
      lowerCamelCase__		:				Optional[int]    =  np.nan
      for i in range(_A						):
            lowerCamelCase__		:				str    =  features[:, labels == i]
            lowerCamelCase__		:				List[str]    =  data.shape[1]
            lowerCamelCase__		:				Any    =  data.mean(1						)
            if i > 0:
                  # If covariance_sum is not None
                  covariance_sum += device_data * np.dot(
                      column_reshape(_A						) - column_reshape(_A						)    ,					(column_reshape(_A						) - column_reshape(_A						)).T    ,					)
            else:
                  # If covariance_sum is np.nan (i.e. first loop)
                  lowerCamelCase__		:				Optional[int]    =  device_data * np.dot(
                      column_reshape(_A						) - column_reshape(_A						)    ,					(column_reshape(_A						) - column_reshape(_A						)).T    ,					)

      return covariance_sum / features.shape[1]

def       lowercase_		(		_A			:    np.ndarray    ,					_A			:    int						):

      """simple docstring"""




      if features.any():
            lowerCamelCase__		:				List[Any]    =  features.mean(1						)
            # Center the dataset
            lowerCamelCase__		:				str    =  features - np.reshape(_A    ,					(data_mean.size, 1)						)
            lowerCamelCase__		:				Dict    =  np.dot(_A    ,					centered_data.T						) / features.shape[1]
            lowerCamelCase__    ,   lowerCamelCase__		:				List[Any]    =  np.linalg.eigh(_A						)
            # Take all the columns in the reverse order (-1), and then takes only the first
            lowerCamelCase__		:				List[Any]    =  eigenvectors[:, ::-1][:, 0:dimensions]
            # Project the database on the new space
            lowerCamelCase__		:				Dict    =  np.dot(filtered_eigenvectors.T    ,					_A						)
            logging.info("Principal Component Analysis computed"						)

            return projected_data
      else:
            logging.basicConfig(level=logging.ERROR    ,					format="%(message)s"    ,					force=_A						)
            logging.error("Dataset empty"						)
            raise AssertionError

def       lowercase_		(		_A			:    np.ndarray    ,					_A			:    np.ndarray    ,					_A			:    int    ,					_A			:    int						):

      """simple docstring"""




      assert classes > dimensions

      # Check if features have been already loaded
      if features.any:
            lowerCamelCase__    ,   lowerCamelCase__		:				Dict    =  eigh(
                covariance_between_classes(_A    ,					_A    ,					_A						)    ,					covariance_within_classes(_A    ,					_A    ,					_A						)    ,					)
            lowerCamelCase__		:				int    =  eigenvectors[:, ::-1][:, :dimensions]
            lowerCamelCase__    ,   lowerCamelCase__    ,   lowerCamelCase__		:				Union[str, Any]    =  np.linalg.svd(_A						)
            lowerCamelCase__		:				Optional[int]    =  svd_matrix[:, 0:dimensions]
            lowerCamelCase__		:				Dict    =  np.dot(filtered_svd_matrix.T    ,					_A						)
            logging.info("Linear Discriminant Analysis computed"						)

            return projected_data
      else:
            logging.basicConfig(level=logging.ERROR    ,					format="%(message)s"    ,					force=_A						)
            logging.error("Dataset empty"						)
            raise AssertionError

def       lowercase_		(		):

      """simple docstring"""




      lowerCamelCase__		:				int    =  np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]						)
      lowerCamelCase__		:				List[str]    =  np.array([0, 0, 0, 1, 1]						)
      lowerCamelCase__		:				str    =  2
      lowerCamelCase__		:				Dict    =  2

      # Assert that the function raises an AssertionError if dimensions > classes
      with pytest.raises(_A						) as error_info:
            lowerCamelCase__		:				Tuple    =  linear_discriminant_analysis(
                _A    ,					_A    ,					_A    ,					_A						)
            if isinstance(_A    ,					np.ndarray						):
                  raise AssertionError(
                      "Did not raise AssertionError for dimensions > classes"						)
            assert error_info.type is AssertionError

def       lowercase_		(		):

      """simple docstring"""




      lowerCamelCase__		:				Tuple    =  np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]						)
      lowerCamelCase__		:				str    =  2
      lowerCamelCase__		:				int    =  np.array([[6.92_820_323, 8.66_025_404, 10.39_230_485], [3.0, 3.0, 3.0]]						)

      with pytest.raises(_A						) as error_info:
            lowerCamelCase__		:				Optional[int]    =  principal_component_analysis(_A    ,					_A						)
            if not np.allclose(_A    ,					_A						):
                  raise AssertionError
            assert error_info.type is AssertionError


if __name__ == "__main__":
    import doctest

    doctest.testmod()






from collections import defaultdict

def       lowercase_		(		_A			:    int						):

      """simple docstring"""




      lowerCamelCase__		:				Union[str, Any]    =  1
      lowerCamelCase__		:				Dict    =  True
      for v in tree[start]:
            if v not in visited:
                  ret += dfs(_A						)
      if ret % 2 == 0:
            cuts.append(_A						)
      return ret

def       lowercase_		(		):

      """simple docstring"""




      dfs(1						)


if __name__ == "__main__":
    A,  A      :    Tuple		=					10, 9
    A      :    int		=					defaultdict(list)
    A      :    dict[int, bool]		=					{}
    A      :    list[int]		=					[]
    A      :    List[str]		=					0
    A      :    Tuple		=					[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
    for u, v in edges:
        tree[u].append(v)
        tree[v].append(u)
    even_tree()
    print(len(cuts) - 1)


