
def      lowerCamelCase__       (       __lowerCAmelCase						:						list[list[int | float]]       ):




			"""simple docstring"""


			lowerCAmelCase_      			=			len(__lowerCAmelCase       )
			lowerCAmelCase_      			=			len(matrix[0]       )
			lowerCAmelCase_      			=			min(__lowerCAmelCase					,							__lowerCAmelCase       )

			for row in range(__lowerCAmelCase       ):
						# Check if diagonal element is not zero
						if matrix[row][row] != 0:
									# Eliminate all the elements below the diagonal
									for col in range(row + 1					,							__lowerCAmelCase       ):
												lowerCAmelCase_      			=			matrix[col][row] / matrix[row][row]
												for i in range(__lowerCAmelCase					,							__lowerCAmelCase       ):
															matrix[col][i] -= multiplier * matrix[row][i]
						else:
									# Find a non-zero diagonal element to swap rows
									lowerCAmelCase_      			=			True
									for i in range(row + 1					,							__lowerCAmelCase       ):
												if matrix[i][row] != 0:
															lowerCAmelCase_			,						lowerCAmelCase_      			=			matrix[i], matrix[row]
															lowerCAmelCase_      			=			False
															break
									if reduce:
												rank -= 1
												for i in range(__lowerCAmelCase       ):
															lowerCAmelCase_      			=			matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
									row -= 1

			return rank


if __name__ == "__main__":
			import doctest

			doctest.testmod()





import math





class 			_lowerCAmelCase      :




				def __init__(      self       ,       _UpperCamelCase=0  )       ->   Tuple:  # a graph with Node 0,1,...,N-1
							lowerCAmelCase_      			=			n
							lowerCAmelCase_      			=			[
							    [math.inf for j in range(0       ,       _UpperCamelCase  )] for i in range(0       ,       _UpperCamelCase  )
							]  # adjacency matrix for weight
							lowerCAmelCase_      			=			[
							    [math.inf for j in range(0       ,       _UpperCamelCase  )] for i in range(0       ,       _UpperCamelCase  )
							]  # dp[i][j] stores minimum distance from i to j




				def   __a		(      self       ,       _UpperCamelCase       ,       _UpperCamelCase       ,       _UpperCamelCase  )       ->   List[Any]:
							lowerCAmelCase_      			=			w




				def   __a		(      self  )       ->   List[str]:
							for k in range(0       ,       self.n  ):
										for i in range(0       ,       self.n  ):
													for j in range(0       ,       self.n  ):
																lowerCAmelCase_      			=			min(self.dp[i][j]       ,       self.dp[i][k] + self.dp[k][j]  )




				def   __a		(      self       ,       _UpperCamelCase       ,       _UpperCamelCase  )       ->   Dict:
							return self.dp[u][v]


if __name__ == "__main__":
			_A     =  Graph(5)
			graph.add_edge(0, 2, 9)
			graph.add_edge(0, 4, 10)
			graph.add_edge(1, 3, 5)
			graph.add_edge(2, 3, 7)
			graph.add_edge(3, 0, 10)
			graph.add_edge(3, 1, 2)
			graph.add_edge(3, 2, 1)
			graph.add_edge(3, 4, 6)
			graph.add_edge(4, 1, 3)
			graph.add_edge(4, 2, 4)
			graph.add_edge(4, 3, 9)
			graph.floyd_warshall()
			graph.show_min(1, 4)
			graph.show_min(0, 3)



