

from __future__ import annotations

from typing import Any






class      lowerCamelCase_      :




	def __init__(     self						:     str					,      __A						:     int					,      __A						:     int					,      __A						:     float = 0							):
		__A :			Optional[Any]		    =			row, column
		__A :			Dict		    =			[[default_value for c in range(__A							)] for r in range(__A							)]




	def __str__(     self						:     List[Any]							):
		__A :			Dict		    =			F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

		# Make string identifier
		__A :			Optional[int]		    =			0
		for row_vector in self.array:
			for obj in row_vector:
				__A :			Optional[int]		    =			max(__A					,      len(str(__A							)							)							)
		__A :			str		    =			F"""%{max_element_length}s"""

		# Make string and return
		def single_line(__A						:     list[float]							) -> str:
			nonlocal string_format_identifier
			__A :			Union[str, Any]		    =			"""["""
			line += ", ".join(string_format_identifier % (obj,) for obj in row_vector							)
			line += "]"
			return line

		s += "\n".join(single_line(__A							) for row_vector in self.array							)
		return s




	def __repr__(     self						:     Optional[int]							):
		return str(self							)




	def        lowerCAmelCase_       (     self						:     Dict					,      __A						:     tuple[int, int]							):

		if not (isinstance(__A					,      (list, tuple)							) and len(__A							) == 2):
			return False
		elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
			return False
		else:
			return True




	def __getitem__(     self						:     int					,      __A						:     tuple[int, int]							):
		assert self.validate_indicies(__A							)
		return self.array[loc[0]][loc[1]]




	def __setitem__(     self						:     List[str]					,      __A						:     tuple[int, int]					,      __A						:     float							):
		assert self.validate_indicies(__A							)
		__A :			Optional[int]		    =			value




	def __add__(     self						:     Any					,      __A						:     Matrix							):
		assert isinstance(__A					,      __A							)
		assert self.row == another.row and self.column == another.column

		# Add
		__A :			Union[str, Any]		    =			Matrix(self.row					,      self.column							)
		for r in range(self.row							):
			for c in range(self.column							):
				__A :			List[Any]		    =			self[r, c] + another[r, c]
		return result




	def __neg__(     self						:     Tuple							):
		__A :			Tuple		    =			Matrix(self.row					,      self.column							)
		for r in range(self.row							):
			for c in range(self.column							):
				__A :			List[Any]		    =			-self[r, c]
		return result




	def __sub__(     self						:     Optional[int]					,      __A						:     Matrix							):
		return self + (-another)




	def __mul__(     self						:     List[Any]					,      __A						:     int | float | Matrix							):

		if isinstance(__A					,      (int, float)							):  # Scalar multiplication
			__A :			Optional[int]		    =			Matrix(self.row					,      self.column							)
			for r in range(self.row							):
				for c in range(self.column							):
					__A :			Tuple		    =			self[r, c] * another
			return result
		elif isinstance(__A					,      __A							):  # Matrix multiplication
			assert self.column == another.row
			__A :			Dict		    =			Matrix(self.row					,      another.column							)
			for r in range(self.row							):
				for c in range(another.column							):
					for i in range(self.column							):
						result[r, c] += self[r, i] * another[i, c]
			return result
		else:
			__A :			Optional[int]		    =			F"""Unsupported type given for another ({type(__A							)})"""
			raise TypeError(__A							)




	def        lowerCAmelCase_       (     self						:     str							):
		__A :			Any		    =			Matrix(self.column					,      self.row							)
		for r in range(self.row							):
			for c in range(self.column							):
				__A :			str		    =			self[r, c]
		return result




	def        lowerCAmelCase_       (     self						:     Union[str, Any]					,      __A						:     Matrix					,      __A						:     Matrix							):
		assert isinstance(__A					,      __A							) and isinstance(__A					,      __A							)
		assert self.row == self.column == u.row == v.row  # u, v should be column vector
		assert u.column == v.column == 1  # u, v should be column vector

		# Calculate
		__A :			List[str]		    =			v.transpose()
		__A :			Tuple		    =			(v_t * self * u)[0, 0] + 1
		if numerator_factor == 0:
			return None  # It's not invertable
		return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":
			def 							__SCREAMING_SNAKE_CASE     (   )					->				None:
				__A :			Tuple		    =			Matrix(3			,3			,0       )
				for i in range(3       ):
					__A :			Any		    =			1
				print(f"""a^(-1) is {ainv}"""       )
				# u, v
				__A :			Dict		    =			Matrix(3			,1			,0       )
				__A :			Union[str, Any]		    =			1, 2, -3
				__A :			str		    =			Matrix(3			,1			,0       )
				__A :			Tuple		    =			4, -2, 5
				print(f"""u is {u}"""       )
				print(f"""v is {v}"""       )
				print(f"""uv^T is {u * v.transpose()}"""       )
				# Sherman Morrison
				print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(_lowerCamelCase			,_lowerCamelCase       )}"""       )
			def 							__SCREAMING_SNAKE_CASE     (   )					->				None:
				import doctest

				doctest.testmod()







			testa()












'''simple docstring'''






from __future__ import annotations

import math







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase ) ->				int:



			"""simple docstring"""


			if depth < 0:
						raise ValueError("""Depth cannot be less than 0""" )

			if not scores:
						raise ValueError("""Scores cannot be empty""" )

			if depth == height:
						return scores[node_index]

			return (
			    max(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			    if is_max
			    else min(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			)







def 					_a						(       ) ->				None:



			"""simple docstring"""


			__snake_case					:      Union[str, Any]							      =     [90, 23, 6, 33, 21, 65, 123, 3_4423]
			__snake_case					:      Optional[int]							      =     math.log(len(_lowerCamelCase )    ,	2 )
			print(F'''Optimal value : {minimax(0    ,	0    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )}''' )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()


