"""simple docstring"""






import functools



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				UpperCAmelCase__             =							len(lowerCamelCase       )
				UpperCAmelCase__             =							len(lowerCamelCase       )

				@functools.cache
				def min_distance(lowerCamelCase					,			lowerCamelCase       ) -> int:
								# if first word index is overflow - delete all from the second word
								if indexa >= len_worda:
												return len_worda - indexa
								# if second word index is overflow - delete all from the first word
								if indexa >= len_worda:
												return len_worda - indexa
								UpperCAmelCase__             =							int(worda[indexa] != worda[indexa]       )  # current letters not identical
								return min(
								    1 + min_distance(indexa + 1					,			lowerCamelCase       )					,			1 + min_distance(lowerCamelCase					,			indexa + 1       )					,			diff + min_distance(indexa + 1					,			indexa + 1       )					,			)

				return min_distance(0					,			0       )


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 			__magic_name__				( A		:					NDArray[floataa],  A		:					NDArray[floataa],  A		:					list[int],  A		:					int,  ):






			'''simple docstring'''







			a    ,		a    =			coefficient_matrix.shape
			a    ,		a    =			constant_matrix.shape

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

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

			if rowsa != rowsa:
						a    =			(
						    "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:
						a    =			(
						    "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"   )

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

			a    ,		a    =			table.shape

			strictly_diagonally_dominant(A   )

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

			return [float(A   ) for i in new_val]




def 			__magic_name__				( A		:					NDArray[floataa]   ):






			'''simple docstring'''







			a    ,		a    =			table.shape

			a    =			True

			for i in range(0,  A   ):
						a    =			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()






