
"""simple docstring"""







from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    )  ->     list[float]:







							"""simple docstring"""


							__snake_case			,   __snake_case     			=       coefficient_matrix.shape
							__snake_case			,   __snake_case     			=       constant_matrix.shape

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

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

							if rowsa != rowsa:
														__snake_case     			=       (
														    "Coefficient and constant matrices dimensions must be nxn and nx1 but "
														    F'''received {rowsa}x{colsa} and {rowsa}x{colsa}'''
														)
														raise ValueError(SCREAMING_SNAKE_CASE )

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

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

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

							__snake_case			,   __snake_case     			=       table.shape

							strictly_diagonally_dominant(SCREAMING_SNAKE_CASE )

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

							return [float(SCREAMING_SNAKE_CASE ) for i in new_val]
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     bool:







							"""simple docstring"""


							__snake_case			,   __snake_case     			=       table.shape

							__snake_case     			=       True

							for i in range(0							,    SCREAMING_SNAKE_CASE ):
														__snake_case     			=       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()


"""simple docstring"""







from __future__ import annotations

from itertools import permutations
from random import randint
from timeit import repeat
def   __UpperCamelCase   (					)  ->     tuple[list[int], int]:







							"""simple docstring"""


							__snake_case     			=       [randint(-10_00							,    10_00 ) for i in range(10 )]
							__snake_case     			=       randint(-50_00							,    50_00 )
							return (arr, r)


_SCREAMING_SNAKE_CASE	       =      make_dataset()
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE )  ->     tuple[int, ...]:







							"""simple docstring"""


							for triplet in permutations(SCREAMING_SNAKE_CASE							,    3 ):
														if sum(SCREAMING_SNAKE_CASE ) == target:
																					return tuple(sorted(SCREAMING_SNAKE_CASE ) )
							return (0, 0, 0)
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE )  ->     tuple[int, int, int]:







							"""simple docstring"""


							arr.sort()
							__snake_case     			=       len(SCREAMING_SNAKE_CASE )
							for i in range(n - 1 ):
														__snake_case			,   __snake_case     			=       i + 1, n - 1
														while left < right:
																					if arr[i] + arr[left] + arr[right] == target:
																												return (arr[i], arr[left], arr[right])
																					elif arr[i] + arr[left] + arr[right] < target:
																												left += 1
																					elif arr[i] + arr[left] + arr[right] > target:
																												right -= 1
							return (0, 0, 0)
def   __UpperCamelCase   (					)  ->     tuple[float, float]:







							"""simple docstring"""


							__snake_case     			=       "\nfrom __main__ import dataset, triplet_sum1, triplet_sum2\n"
							__snake_case     			=       "\ntriplet_sum1(*dataset)\n"
							__snake_case     			=       "\ntriplet_sum2(*dataset)\n"
							__snake_case     			=       repeat(setup=SCREAMING_SNAKE_CASE							,    stmt=SCREAMING_SNAKE_CASE							,    repeat=5							,    number=1_00_00 )
							__snake_case     			=       repeat(setup=SCREAMING_SNAKE_CASE							,    stmt=SCREAMING_SNAKE_CASE							,    repeat=5							,    number=1_00_00 )
							return (min(SCREAMING_SNAKE_CASE ), min(SCREAMING_SNAKE_CASE ))


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		_SCREAMING_SNAKE_CASE	       =      solution_times()
		print(F"""The time for naive implementation is {times[0]}.""")
		print(F"""The time for optimized implementation is {times[1]}.""")
