





from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray





def    __UpperCamelCase      (    a,     a,     a,     a,     ) ->list[float]:
					lowerCamelCase__    ,		lowerCamelCase__       =       coefficient_matrix.shape
					lowerCamelCase__    ,		lowerCamelCase__       =       constant_matrix.shape

					if rowsa != colsa:
										lowerCamelCase__       =       f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
										raise ValueError(a)

					if colsa != 1:
										lowerCamelCase__       =       f"Constant matrix must be nx1 but received {rowsa}x{colsa}"
										raise ValueError(a)

					if rowsa != rowsa:
										lowerCamelCase__       =       (
										    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
										    f"received {rowsa}x{colsa} and {rowsa}x{colsa}"
										)
										raise ValueError(a)

					if len(a) != rowsa:
										lowerCamelCase__       =       (
										    "Number of initial values must be equal to number of rows in coefficient "
										    f"matrix but received {len(a)} and {rowsa}"
										)
										raise ValueError(a)

					if iterations <= 0:
										raise ValueError("Iterations must be at least 1")

					lowerCamelCase__       =       np.concatenate(
					    (coefficient_matrix, constant_matrix),     axis=1)

					lowerCamelCase__    ,		lowerCamelCase__       =       table.shape

					strictly_diagonally_dominant(a)

					# Iterates the whole matrix for given number of times
					for _ in range(a):
										lowerCamelCase__       =       []
										for row in range(a):
															lowerCamelCase__       =       0
															for col in range(a):
																				if col == row:
																									lowerCamelCase__       =       table[row][col]
																				elif col == cols - 1:
																									lowerCamelCase__       =       table[row][col]
																				else:
																									temp += (-1) * table[row][col] * init_val[col]
															lowerCamelCase__       =       (temp + val) / denom
															new_val.append(a)
										lowerCamelCase__       =       new_val

					return [float(a) for i in new_val]





def    __UpperCamelCase      (    a) ->bool:
					lowerCamelCase__    ,		lowerCamelCase__       =       table.shape

					lowerCamelCase__       =       True

					for i in range(0,     a):
										lowerCamelCase__       =       0
										for j in range(0,     cols - 1):
															if i == j:
																				continue
															else:
																				total += table[i][j]

										if table[i][i] <= total:
															raise ValueError("Coefficient matrix is not strictly diagonally dominant")

					return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
						import doctest

						doctest.testmod()








from multiprocessing import Lock, Pipe, Process

# lock used to ensure that two processes do not access a pipe at the same time
A_												=     Lock()





def    __UpperCamelCase      (    a,     a,     a,     a,     a,     a,     a) ->Optional[int]:
					global process_lock

					# we perform n swaps since after n swaps we know we are sorted
					# we *could* stop early if we are sorted already, but it takes as long to
					# find out we are sorted as it does to sort the list with this algorithm
					for i in range(0,     10):
										if (i + position) % 2 == 0 and r_send is not None:
															# send your value to your right neighbor
															process_lock.acquire()
															r_send[1].send(a)
															process_lock.release()

															# receive your right neighbor's value
															process_lock.acquire()
															lowerCamelCase__       =       rr_cv[0].recv()
															process_lock.release()

															# take the lower value since you are on the left
															lowerCamelCase__       =       min(a,     a)
										elif (i + position) % 2 != 0 and l_send is not None:
															# send your value to your left neighbor
															process_lock.acquire()
															l_send[1].send(a)
															process_lock.release()

															# receive your left neighbor's value
															process_lock.acquire()
															lowerCamelCase__       =       lr_cv[0].recv()
															process_lock.release()

															# take the higher value since you are on the right
															lowerCamelCase__       =       max(a,     a)
    # after all swaps are performed, send the values back to main
					result_pipe[1].send(a)





def    __UpperCamelCase      (    a) ->Optional[Any]:
					lowerCamelCase__       =       []
					lowerCamelCase__       =       []
					# initialize the list of pipes where the values will be retrieved
					for _ in arr:
										result_pipe.append(Pipe())
					# creates the processes
					# the first and last process only have one neighbor so they are made outside
					# of the loop
					lowerCamelCase__       =       Pipe()
					lowerCamelCase__       =       Pipe()
					process_array_.append(
					    Process(
					        target=a,     args=(0, arr[0], None, temp_rs, None, temp_rr, result_pipe[0]),     ))
					lowerCamelCase__       =       temp_rs
					lowerCamelCase__       =       temp_rr

					for i in range(1,     len(a) - 1):
										lowerCamelCase__       =       Pipe()
										lowerCamelCase__       =       Pipe()
										process_array_.append(
										    Process(
										        target=a,     args=(i, arr[i], temp_ls, temp_rs, temp_lr, temp_rr, result_pipe[i]),     ))
										lowerCamelCase__       =       temp_rs
										lowerCamelCase__       =       temp_rr

					process_array_.append(
					    Process(
					        target=a,     args=(
					            len(a) - 1,
					            arr[len(a) - 1],
					            temp_ls,
					            None,
					            temp_lr,
					            None,
					            result_pipe[len(a) - 1],
					        ),     ))

					# start the processes
					for p in process_array_:
										p.start()

					# wait for the processes to end and write their values to the list
					for p in range(0,     len(a)):
										lowerCamelCase__       =       result_pipe[p][0].recv()
										process_array_[p].join()
					return arr





def    __UpperCamelCase      (    ) ->List[Any]:
					lowerCamelCase__       =       list(range(10,     0,     -1))
					print("Initial List")
					print(*a)
					lowerCamelCase__       =       odd_even_transposition(a)
					print("Sorted List\n")
					print(*a)


if __name__ == "__main__":
						main()

