






snake_case__      :	List[Any]       	=      {
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase):
			UpperCamelCase_									=     set()
			# keep track of all the paths to be checked
			UpperCamelCase_									=     [[start]]

			# return path if start is goal
			if start == goal:
						return [start]

			# keeps looping until all possible paths have been checked
			while queue:
						# pop the first path from the queue
						UpperCamelCase_									=     queue.pop(0)
						# get the last node from the path
						UpperCamelCase_									=     path[-1]
						if node not in explored:
									UpperCamelCase_									=     graph[node]
									# go through all neighbour nodes, construct a new path and
									# push it into the queue
									for neighbour in neighbours:
												UpperCamelCase_									=     list(__lowercase)
												new_path.append(__lowercase)
												queue.append(__lowercase)
												# return path if neighbour is goal
												if neighbour == goal:
															return new_path

												# mark node as explored
									explored.add(__lowercase)

    # in case there's no path between the 2 nodes
			return []






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase):
			if not graph or start not in graph or target not in graph:
						return -1
			if start == target:
						return 0
			UpperCamelCase_									=     [start]
			UpperCamelCase_									=     set(__lowercase)
			# Keep tab on distances from `start` node.
			UpperCamelCase_									=     {start: 0, target: -1}
			while queue:
						UpperCamelCase_									=     queue.pop(0)
						if node == target:
									UpperCamelCase_									=     (
									    dist[node] if dist[target] == -1 else min(dist[target]    ,      dist[node])
									)
						for adjacent in graph[node]:
									if adjacent not in visited:
												visited.add(__lowercase)
												queue.append(__lowercase)
												UpperCamelCase_									=     dist[node] + 1
			return dist[target]


if __name__ == "__main__":
	print(bfs_shortest_path(demo_graph, """G""", """D"""))  # returns ['G', 'C', 'A', 'B', 'D']
	print(bfs_shortest_path_distance(demo_graph, """G""", """D"""))  # returns 4













from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def     _snake_case    (__lowercase    ,      __lowercase    ,      __lowercase = "x"    ,      __lowercase = 10**-10    ,      __lowercase = 1    ,      ):
   UpperCamelCase_									=     symbols(__lowercase)
   UpperCamelCase_									=     lambdify(__lowercase    ,      __lowercase)
   UpperCamelCase_									=     lambdify(__lowercase    ,      diff(__lowercase    ,      __lowercase))

   UpperCamelCase_									=     starting_point

   while True:
      if diff_function(__lowercase) != 0:
         UpperCamelCase_									=     prev_guess - multiplicity * func(__lowercase) / diff_function(
             __lowercase)
      else:
         raise ZeroDivisionError('Could not find root') from None

      # Precision is checked by comparing the difference of consecutive guesses
      if abs(next_guess - prev_guess) < precision:
         return next_guess

      UpperCamelCase_									=     next_guess


# Let's Execute
if __name__ == "__main__":
 # Find root of trigonometric function
 # Find value of pi
 print(f'The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}')

 # Find root of polynomial
 # Find fourth Root of 5
 print(f'The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}')

 # Find value of e
 print(
     """The root of log(y) - 1 = 0 is """,
     f'{newton_raphson("log(y) - 1", 2, variable="y")}',
 )

 # Exponential Roots
 print(
     """The root of exp(x) - 1 = 0 is""",
     f'{newton_raphson("exp(x) - 1", 1_0, precision=0.005)}',
 )

 # Find root of cos(x)
 print(f'The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}')





