


from bisect import bisect
from itertools import accumulate

def 	lowerCAmelCase__			(      a__:		Any      ,  a__:		int      ,  a__:		List[str]      ,  a__:		Tuple	)  ->		Any:


							'''simple docstring'''





							_UpperCAmelCase					=      sorted(zip(a__      ,  a__	)      ,  key=lambda a__	: x[0] / x[1]      ,  reverse=a__	)
							_UpperCAmelCase		,	_UpperCAmelCase					=      [i[0] for i in r], [i[1] for i in r]
							_UpperCAmelCase					=      list(accumulate(a__	)	)
							_UpperCAmelCase					=      bisect(a__      ,  a__	)
							return (
							    0
							    if k == 0
							    else sum(vl[:k]	) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
							    if k != n
							    else sum(vl[:k]	)
							)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




from __future__ import annotations

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

def 	lowerCAmelCase__			(      a__:		NDArray[floataa]      ,  a__:		NDArray[floataa]      ,  a__:		list[int]      ,  a__:		int      ,  )  ->		list[float]:


							'''simple docstring'''





							_UpperCAmelCase		,	_UpperCAmelCase					=      coefficient_matrix.shape
							_UpperCAmelCase		,	_UpperCAmelCase					=      constant_matrix.shape

							if rowsa != colsa:
														_UpperCAmelCase					=      F'''Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'''
														raise ValueError(a__	)

							if colsa != 1:
														_UpperCAmelCase					=      F'''Constant matrix must be nx1 but received {rowsa}x{colsa}'''
														raise ValueError(a__	)

							if rowsa != rowsa:
														_UpperCAmelCase					=      (
														    '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:
														_UpperCAmelCase					=      (
														    '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'	)

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

							_UpperCAmelCase		,	_UpperCAmelCase					=      table.shape

							strictly_diagonally_dominant(a__	)

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

							return [float(a__	) for i in new_val]

def 	lowerCAmelCase__			(      a__:		NDArray[floataa]	)  ->		bool:


							'''simple docstring'''





							_UpperCAmelCase		,	_UpperCAmelCase					=      table.shape

							_UpperCAmelCase					=      True

							for i in range(0      ,  a__	):
														_UpperCAmelCase					=      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()
