



"""simple docstring"""







from __future__ import annotations

from typing import Any






class       UpperCamelCase__			:

			"""simple docstring"""


			def __init__(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__ = 0		)      ->	None:
				A__							,							A__											=					row, column
				A__											=					[[default_value for c in range(SCREAMING_SNAKE_CASE__		)] for r in range(SCREAMING_SNAKE_CASE__		)]


			def __str__(      self		)      ->	str:
				A__											=					f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

				# Make string identifier
				A__											=					0
				for row_vector in self.array:
					for obj in row_vector:
						A__											=					max(SCREAMING_SNAKE_CASE__						,	len(str(SCREAMING_SNAKE_CASE__		)		)		)
				A__											=					f"""%{max_element_length}s"""

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

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


			def __repr__(      self		)      ->	str:
				return str(self		)


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


			def __getitem__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Any:
				assert self.validate_indicies(SCREAMING_SNAKE_CASE__		)
				return self.array[loc[0]][loc[1]]


			def __setitem__(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	None:
				assert self.validate_indicies(SCREAMING_SNAKE_CASE__		)
				A__											=					value


			def __add__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Matrix:
				assert isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)
				assert self.row == another.row and self.column == another.column

				# Add
				A__											=					Matrix(self.row						,	self.column		)
				for r in range(self.row		):
					for c in range(self.column		):
						A__											=					self[r, c] + another[r, c]
				return result


			def __neg__(      self		)      ->	Matrix:
				A__											=					Matrix(self.row						,	self.column		)
				for r in range(self.row		):
					for c in range(self.column		):
						A__											=					-self[r, c]
				return result


			def __sub__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Matrix:
				return self + (-another)


			def __mul__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Matrix:

				if isinstance(SCREAMING_SNAKE_CASE__						,	(int, float)		):  # Scalar multiplication
					A__											=					Matrix(self.row						,	self.column		)
					for r in range(self.row		):
						for c in range(self.column		):
							A__											=					self[r, c] * another
					return result
				elif isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		):  # Matrix multiplication
					assert self.column == another.row
					A__											=					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__											=					f"""Unsupported type given for another ({type(SCREAMING_SNAKE_CASE__		)})"""
					raise TypeError(SCREAMING_SNAKE_CASE__		)


			def   snake_case__	(      self		)      ->	Matrix:
				A__											=					Matrix(self.column						,	self.row		)
				for r in range(self.row		):
					for c in range(self.column		):
						A__											=					self[r, c]
				return result







			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	Any:
				assert isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		) and isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)
				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__											=					v.transpose()
				A__											=					(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       _lowerCamelCase				(							)	-> None:






				"""simple docstring"""





				A__											=					Matrix(3,	3,	0     )
				for i in range(3     ):
					A__											=					1
				print(F"""a^(-1) is {ainv}"""     )
				# u, v
				A__											=					Matrix(3,	1,	0     )
				A__							,							A__							,							A__											=					1, 2, -3
				A__											=					Matrix(3,	1,	0     )
				A__							,							A__							,							A__											=					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(UpperCAmelCase_,	UpperCAmelCase_     )}"""     )

			def       _lowerCamelCase				(							)	-> None:






				"""simple docstring"""





				import doctest

				doctest.testmod()




			testa()








'''simple docstring'''






from __future__ import annotations

import time

import numpy as np

lowercase				=[8, 5, 9, 7]
lowercase				=[
    [2, 0, 1, 1],
    [0, 1, 2, 1],
    [4, 0, 0, 3],
    [0, 2, 1, 0],
    [1, 0, 3, 0],
]
lowercase				=[
    [3, 2, 1, 4],
    [0, 2, 5, 2],
    [5, 1, 0, 5],
    [1, 5, 3, 0],
    [3, 0, 3, 3],
]






class    __magic_name__				:






       def __init__(     self    ,				snake_case    ,				snake_case    ,				snake_case    ,				)		->    None:




          '''simple docstring'''
          _UpperCAmelCase  :  Optional[Any]				       =claim_vector
          _UpperCAmelCase  :  Optional[int]				       =allocated_resources_table
          _UpperCAmelCase  :  int				       =maximum_claim_table






       def      lowerCAmelCase						(     self)		->    list[int]:




          '''simple docstring'''
          return [
              sum(p_item[i] for p_item in self.__allocated_resources_table)
              for i in range(len(self.__allocated_resources_table[0]))
          ]






       def      lowerCAmelCase						(     self)		->    list[int]:




          '''simple docstring'''
          return np.array(self.__claim_vector) - np.array(
              self.__processes_resource_summation())






       def      lowerCAmelCase						(     self)		->    list[list[int]]:




          '''simple docstring'''
          return [
              list(np.array(self.__maximum_claim_table[i]) - np.array(snake_case))
              for i, allocated_resource in enumerate(self.__allocated_resources_table)
          ]






       def      lowerCAmelCase						(     self)		->    dict[int, list[int]]:




          '''simple docstring'''
          return {self.__need().index(snake_case): i for i in self.__need()}






       def      lowerCAmelCase						(     self    ,				**snake_case)		->    None:




          '''simple docstring'''
          _UpperCAmelCase  :  Any				       =self.__need()
          _UpperCAmelCase  :  str				       =self.__allocated_resources_table
          _UpperCAmelCase  :  Dict				       =self.__available_resources()
          _UpperCAmelCase  :  Tuple				       =self.__need_index_manager()
          for kw, val in kwargs.items():
             if kw and val is True:
                self.__pretty_data()
          print('_' * 5_0 + '\n')
          while need_list:
             _UpperCAmelCase  :  Any				       =False
             for each_need in need_list:
                _UpperCAmelCase  :  Any				       =True
                for index, need in enumerate(snake_case):
                   if need > available_resources[index]:
                      _UpperCAmelCase  :  Optional[int]				       =False
                      break
                if execution:
                   _UpperCAmelCase  :  Union[str, Any]				       =True
                   # get the original index of the process from ind_ctrl db
                   for original_need_index, need_clone in need_index_manager.items():
                      if each_need == need_clone:
                         _UpperCAmelCase  :  List[str]				       =original_need_index
                   print(f"Process {process_number + 1} is executing.")
                   # remove the process run from stack
                   need_list.remove(snake_case)
                   # update available/freed resources stack
                   _UpperCAmelCase  :  Any				       =np.array(snake_case) + np.array(
                       alloc_resources_table[process_number])
                   print(
                       'Updated available resource stack for processes: '
                       + ' '.join([str(snake_case) for x in available_resources]))
                   break
             if safe:
                print('The process is in a safe state.\n')
             else:
                print('System in unsafe state. Aborting...\n')
                break






       def      lowerCAmelCase						(     self)		->    Dict:




          '''simple docstring'''
          print(' ' * 9 + 'Allocated Resource Table')
          for item in self.__allocated_resources_table:
             print(
                 f"P{self.__allocated_resources_table.index(snake_case) + 1}"
                 + ' '.join(f"{it:>8}" for it in item)
                 + '\n')
          print(' ' * 9 + 'System Resource Table')
          for item in self.__maximum_claim_table:
             print(
                 f"P{self.__maximum_claim_table.index(snake_case) + 1}"
                 + ' '.join(f"{it:>8}" for it in item)
                 + '\n')
          print(
              'Current Usage by Active Processes: '
              + ' '.join(str(snake_case) for x in self.__claim_vector))
          print(
              'Initial Available Resources:       '
              + ' '.join(str(snake_case) for x in self.__available_resources()))
          time.sleep(1)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

