
def   lowerCAmelCase_						(					_snake_case      :  Tuple      ,   _snake_case      :  str   )				->		Optional[Any]:







	'''simple docstring'''


	print("\nThe shortest path matrix using Floyd Warshall algorithm\n"   )
	for i in range(_snake_case   ):
		for j in range(_snake_case   ):
			if dist[i][j] != float("inf"   ):
				print(int(dist[i][j]   )      ,   end="\t"   )
			else:
				print("INF"      ,   end="\t"   )
		print()






def   lowerCAmelCase_						(					_snake_case      :  Tuple      ,   _snake_case      :  List[Any]   )				->		Tuple:







	'''simple docstring'''


	__magic_name__		:		Dict	   =     [[float("inf"   ) for _ in range(_snake_case   )] for _ in range(_snake_case   )]

	for i in range(_snake_case   ):
		for j in range(_snake_case   ):
			__magic_name__		:		List[Any]	   =     graph[i][j]

			# check vertex k against all other vertices (i, j)
	for k in range(_snake_case   ):
		# looping through rows of graph array
		for i in range(_snake_case   ):
			# looping through columns of graph array
			for j in range(_snake_case   ):
				if (
				    dist[i][k] != float("inf"   )
				    and dist[k][j] != float("inf"   )
				    and dist[i][k] + dist[k][j] < dist[i][j]
				):
					__magic_name__		:		str	   =     dist[i][k] + dist[k][j]

	_print_dist(_snake_case      ,   _snake_case   )
	return dist, v


if __name__ == "__main__":
				snake_case :		List[str]							      =  int(input("Enter number of vertices: "))
				snake_case :		Dict							      =  int(input("Enter number of edges: "))

				snake_case :		Any							      =  [[float("inf") for i in range(v)] for j in range(v)]

				for i in range(v):
								snake_case :		Optional[int]							      =  0.0

								# src and dst are indices that must be within the array size graph[e][v]
								# failure to follow this will result in an error
				for i in range(e):
								print("\nEdge ", i + 1)
								snake_case :		Union[str, Any]							      =  int(input("Enter source:"))
								snake_case :		List[str]							      =  int(input("Enter destination:"))
								snake_case :		Union[str, Any]							      =  float(input("Enter weight:"))
								snake_case :		Tuple							      =  weight

				floyd_warshall(graph, v)

				# Example Input
				# Enter number of vertices: 3
				# Enter number of edges: 2

				# # generated graph from vertex and edge inputs
				# [[inf, inf, inf], [inf, inf, inf], [inf, inf, inf]]
				# [[0.0, inf, inf], [inf, 0.0, inf], [inf, inf, 0.0]]

				# specify source, destination and weight for edge #1
				# Edge  1
				# Enter source:1
				# Enter destination:2
				# Enter weight:2

				# specify source, destination and weight for edge #2
				# Edge  2
				# Enter source:2
				# Enter destination:1
				# Enter weight:1

				# # Expected Output from the vertice, edge and src, dst, weight inputs!!
				# 0		INF	INF
				# INF	0	2
				# INF	1	0


def   lowerCAmelCase_						(					_snake_case      :  list[list[int | float]]   )				->		int:







	'''simple docstring'''


	__magic_name__		:		Any	   =     len(_snake_case   )
	__magic_name__		:		Optional[Any]	   =     len(matrix[0]   )
	__magic_name__		:		Union[str, Any]	   =     min(_snake_case      ,   _snake_case   )

	for row in range(_snake_case   ):
		# 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      ,   _snake_case   ):
				__magic_name__		:		Optional[Any]	   =     matrix[col][row] / matrix[row][row]
				for i in range(_snake_case      ,   _snake_case   ):
					matrix[col][i] -= multiplier * matrix[row][i]
		else:
			# Find a non-zero diagonal element to swap rows
			__magic_name__		:		str	   =     True
			for i in range(row + 1      ,   _snake_case   ):
				if matrix[i][row] != 0:
					__magic_name__   ,    __magic_name__		:		List[str]	   =     matrix[i], matrix[row]
					__magic_name__		:		Union[str, Any]	   =     False
					break
			if reduce:
				rank -= 1
				for i in range(_snake_case   ):
					__magic_name__		:		Any	   =     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()
