


"""simple docstring"""



from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class 					__magic_name__		:
       __A			:      int
       __A			:      TreeNode | None        =   None
       __A			:      TreeNode | None        =   None







UpperCAmelCase      		=			namedtuple('''CoinsDistribResult''', '''moves excess''')






def       lowerCamelCase					(a_						:TreeNode | None)     ->							int:

       if root is None:
              return 0

       # Validation
       def count_nodes(a_						:TreeNode | None) -> int:
              if node is None:
                     return 0

              return count_nodes(node.left) + count_nodes(node.right) + 1

       def count_coins(a_						:TreeNode | None) -> int:
              if node is None:
                     return 0

              return count_coins(node.left) + count_coins(node.right) + node.data

       if count_nodes(a_) != count_coins(a_):
              raise ValueError('''The nodes number should be same as the number of coins''')

       # Main calculation
       def get_distrib(a_						:TreeNode | None) -> CoinsDistribResult:

              if node is None:
                     return CoinsDistribResult(0				,				1)

              lowercase							,  lowercase		:List[Any]       							=				get_distrib(node.left)
              lowercase							,  lowercase		:List[str]       							=				get_distrib(node.right)

              lowercase		:str       							=				1 - left_distrib_excess
              lowercase		:List[str]       							=				1 - right_distrib_excess

              lowercase		:Any       							=				(
                  left_distrib_moves
                  + right_distrib_moves
                  + abs(a_)
                  + abs(a_)
              )
              lowercase		:Tuple       							=				node.data - coins_to_left - coins_to_right

              return CoinsDistribResult(a_				,				a_)

       return get_distrib(a_)[0]


if __name__ == "__main__":
 import doctest

 doctest.testmod()





"""simple docstring"""



import unittest

import numpy as np






def       lowerCamelCase					(a_						:np.ndarray				,				a_						:np.ndarray				,				a_						:np.ndarray				,				a_						:np.ndarray | None = None				,				)     ->							np.ndarray:
       lowercase		:str       							=				np.shape(a_)
       lowercase		:Dict       							=				np.shape(a_)
       lowercase		:Optional[int]       							=				np.shape(a_)

       if shape_a[0] != shape_b[0]:
              lowercase		:List[str]       							=				(
                  '''Expected the same number of rows for A and B. '''
                  F"""Instead found A of size {shape_a} and B of size {shape_b}"""
              )
              raise ValueError(a_)

       if shape_b[1] != shape_c[1]:
              lowercase		:List[str]       							=				(
                  '''Expected the same number of columns for B and C. '''
                  F"""Instead found B of size {shape_b} and C of size {shape_c}"""
              )
              raise ValueError(a_)

       lowercase		:Optional[Any]       							=				pseudo_inv
       if a_inv is None:
              try:
                     lowercase		:int       							=				np.linalg.inv(a_)
              except np.linalg.LinAlgError:
                     raise ValueError(
                         '''Input matrix A is not invertible. Cannot compute Schur complement.''')

       return mat_c - mat_b.T @ a_inv @ mat_b
class 					__magic_name__		(			unittest.TestCase     ):






       def  __snake_case						(   self  :    int				):

              '''simple docstring'''






              lowercase		:Dict       							=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]				)
              lowercase		:List[str]       							=				np.array([[0, 3], [3, 0], [2, 3]]				)
              lowercase		:List[str]       							=				np.array([[2, 1], [6, 3]]				)

              lowercase		:Any       							=				schur_complement(snake_case__  ,     snake_case__  ,     snake_case__				)

              lowercase		:int       							=				np.block([[a, b], [b.T, c]]				)

              lowercase		:Tuple       							=				np.linalg.det(snake_case__				)
              lowercase		:Any       							=				np.linalg.det(snake_case__				)
              lowercase		:List[Any]       							=				np.linalg.det(snake_case__				)

              self.assertAlmostEqual(snake_case__  ,     det_a * det_s				)






       def  __snake_case						(   self  :    Optional[int]				):

              '''simple docstring'''






              lowercase		:Union[str, Any]       							=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]				)
              lowercase		:Union[str, Any]       							=				np.array([[0, 3], [3, 0], [2, 3]]				)
              lowercase		:List[str]       							=				np.array([[2, 1], [6, 3]]				)

              with self.assertRaises(snake_case__				):
                     schur_complement(snake_case__  ,     snake_case__  ,     snake_case__				)







       def  __snake_case						(   self  :    List[Any]				):

              '''simple docstring'''






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

              with self.assertRaises(snake_case__				):
                     schur_complement(snake_case__  ,     snake_case__  ,     snake_case__				)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()

