


import unittest

import numpy as np
def       _a			(				SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE = None						,    ):


  """simple docstring"""




  lowercase__						=				np.shape(SCREAMING_SNAKE_CASE					)
  lowercase__						=				np.shape(SCREAMING_SNAKE_CASE					)
  lowercase__						=				np.shape(SCREAMING_SNAKE_CASE					)

  if shape_a[0] != shape_b[0]:
    lowercase__						=				(
        '''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(SCREAMING_SNAKE_CASE					)

  if shape_b[1] != shape_c[1]:
    lowercase__						=				(
        '''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(SCREAMING_SNAKE_CASE					)

  lowercase__						=				pseudo_inv
  if a_inv is None:
    try:
      lowercase__						=				np.linalg.inv(SCREAMING_SNAKE_CASE					)
    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 	_a							(      unittest.TestCase      ):

       def 				lowerCamelCase_			(							self:     Union[str, Any]							)      ->       None:





         """simple docstring"""







         lowercase__						=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
         lowercase__						=				np.array([[0, 3], [3, 0], [2, 3]]							)
         lowercase__						=				np.array([[2, 1], [6, 3]]							)

         lowercase__						=				schur_complement(UpperCamelCase_   ,						UpperCamelCase_   ,						UpperCamelCase_							)

         lowercase__						=				np.block([[a, b], [b.T, c]]							)

         lowercase__						=				np.linalg.det(UpperCamelCase_							)
         lowercase__						=				np.linalg.det(UpperCamelCase_							)
         lowercase__						=				np.linalg.det(UpperCamelCase_							)

         self.assertAlmostEqual(UpperCamelCase_   ,						det_a * det_s							)

       def 				lowerCamelCase_			(							self:     int							)      ->       None:





         """simple docstring"""







         lowercase__						=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
         lowercase__						=				np.array([[0, 3], [3, 0], [2, 3]]							)
         lowercase__						=				np.array([[2, 1], [6, 3]]							)

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


       def 				lowerCamelCase_			(							self:     Tuple							)      ->       None:





         """simple docstring"""







         lowercase__						=				np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
         lowercase__						=				np.array([[0, 3], [3, 0], [2, 3]]							)
         lowercase__						=				np.array([[2, 1, 3], [6, 3, 5]]							)

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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   unittest.main()






from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass


@dataclass
class 	_a							:
							_lowercase     :      int
							_lowercase     :      TreeNode | None  				=			None
							_lowercase     :      TreeNode | None  				=			None
lowerCAmelCase	=							namedtuple('CoinsDistribResult', 'moves excess')
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		if root is None:
				return 0

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

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

		def count_coins(SCREAMING_SNAKE_CASE					) -> int:
				if node is None:
						return 0

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

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

		# Main calculation
		def get_distrib(SCREAMING_SNAKE_CASE					) -> CoinsDistribResult:

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

				lowercase__					,		lowercase__						=				get_distrib(node.left					)
				lowercase__					,		lowercase__						=				get_distrib(node.right					)

				lowercase__						=				1 - left_distrib_excess
				lowercase__						=				1 - right_distrib_excess

				lowercase__						=				(
				    left_distrib_moves
				    + right_distrib_moves
				    + abs(SCREAMING_SNAKE_CASE					)
				    + abs(SCREAMING_SNAKE_CASE					)
				)
				lowercase__						=				node.data - coins_to_left - coins_to_right

				return CoinsDistribResult(SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE					)

		return get_distrib(SCREAMING_SNAKE_CASE					)[0]


if __name__ == "__main__":
			import doctest

			doctest.testmod()


