

'''simple docstring'''






from __future__ import annotations

import time

import numpy as np

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






class 			lowercase_	:




  """simple docstring"""




  def __init__(      self   :     Optional[Any]					,lowercase__   :     list[int]					,lowercase__   :     list[list[int]]					,lowercase__   :     list[list[int]]					,):
   __lowercase							  = claim_vector
   __lowercase							  = allocated_resources_table
   __lowercase							  = maximum_claim_table






  def 					SCREAMING_SNAKE_CASE      (      self   :     Tuple			):
   return [
       sum(p_item[i] for p_item in self.__allocated_resources_table			)
       for i in range(len(self.__allocated_resources_table[0]			)			)
   ]






  def 					SCREAMING_SNAKE_CASE      (      self   :     str			):
   return np.array(self.__claim_vector			) - np.array(
       self.__processes_resource_summation()			)






  def 					SCREAMING_SNAKE_CASE      (      self   :     Union[str, Any]			):
   return [
       list(np.array(self.__maximum_claim_table[i]			) - np.array(lowercase__			)			)
       for i, allocated_resource in enumerate(self.__allocated_resources_table			)
   ]






  def 					SCREAMING_SNAKE_CASE      (      self   :     Any			):
   return {self.__need().index(lowercase__			): i for i in self.__need()}






  def 					SCREAMING_SNAKE_CASE      (      self   :     List[str]					,**lowercase__   :     List[Any]			):
   __lowercase							  = self.__need()
   __lowercase							  = self.__allocated_resources_table
   __lowercase							  = self.__available_resources()
   __lowercase							  = 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:
    __lowercase							  = False
    for each_need in need_list:
     __lowercase							  = True
     for index, need in enumerate(lowercase__			):
      if need > available_resources[index]:
       __lowercase							  = False
       break
     if execution:
      __lowercase							  = 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:
        __lowercase							  = original_need_index
      print(F"Process {process_number + 1} is executing."			)
      # remove the process run from stack
      need_list.remove(lowercase__			)
      # update available/freed resources stack
      __lowercase							  = np.array(lowercase__			) + np.array(
          alloc_resources_table[process_number]			)
      print(
          '''Updated available resource stack for processes: '''
          + ''' '''.join([str(lowercase__			) 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 					SCREAMING_SNAKE_CASE      (      self   :     Optional[int]			):
   print(''' ''' * 9 + '''Allocated Resource Table'''			)
   for item in self.__allocated_resources_table:
    print(
        F"P{self.__allocated_resources_table.index(lowercase__			) + 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(lowercase__			) + 1}"
        + ''' '''.join(F"{it:>8}" for it in item			)
        + '''\n'''			)
   print(
       '''Current Usage by Active Processes: '''
       + ''' '''.join(str(lowercase__			) for x in self.__claim_vector			)			)
   print(
       '''Initial Available Resources:       '''
       + ''' '''.join(str(lowercase__			) for x in self.__available_resources()			)			)
   time.sleep(1			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()





"""simple docstring"""




from math import isclose, sqrt


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float ,			SCREAMING_SNAKE_CASE_		:				float  )   ->						tuple[float, float, float]:
						SCREAMING_SNAKE_CASE													=					point_y / 4 / point_x
						SCREAMING_SNAKE_CASE													=					2 * normal_gradient / (1 + normal_gradient * normal_gradient)
						SCREAMING_SNAKE_CASE													=					(1 - normal_gradient * normal_gradient) / (
						    1 + normal_gradient * normal_gradient
						)
						SCREAMING_SNAKE_CASE													=					(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

						# to find the next point, solve the simultaeneous equations:
						# y^2 + 4x^2 = 100
						# y - b = m * (x - a)
						# ==> A x^2 + B x + C = 0
						SCREAMING_SNAKE_CASE													=					outgoing_gradient**2 + 4
						SCREAMING_SNAKE_CASE													=					2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
						SCREAMING_SNAKE_CASE													=					(point_y - outgoing_gradient * point_x) ** 2 - 1_00

						SCREAMING_SNAKE_CASE													=					(
						    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
						) / (2 * quadratic_term)
						SCREAMING_SNAKE_CASE													=					(
						    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term  )
						) / (2 * quadratic_term)

						# two solutions, one of which is our input point
						SCREAMING_SNAKE_CASE													=					x_minus if isclose(SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_  ) else x_plus
						SCREAMING_SNAKE_CASE													=					point_y + outgoing_gradient * (next_x - point_x)

						return next_x, next_y, outgoing_gradient


def     lowercase			(SCREAMING_SNAKE_CASE_		:				float = 1.4 ,			SCREAMING_SNAKE_CASE_		:				float = -9.6  )   ->						int:
						SCREAMING_SNAKE_CASE													=					0
						SCREAMING_SNAKE_CASE													=					first_x_coord
						SCREAMING_SNAKE_CASE													=					first_y_coord
						SCREAMING_SNAKE_CASE													=					(10.1 - point_y) / (0.0 - point_x)

						while not (-0.01 <= point_x <= 0.01 and point_y > 0):
												SCREAMING_SNAKE_CASE							,				SCREAMING_SNAKE_CASE							,				SCREAMING_SNAKE_CASE													=					next_point(SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_ ,			SCREAMING_SNAKE_CASE_  )
												num_reflections += 1

						return num_reflections


if __name__ == "__main__":
	print(f'''{solution() = }''')


