


'''simple docstring'''





from math import exp


def 					a__    (				UpperCamelCase_	:			Union[str, Any]	):
   return 8 * x - 2 * exp(-x	)


def 					a__    (				UpperCamelCase_	:			str,      UpperCamelCase_	:			Tuple,      UpperCamelCase_	:			Any	):
   UpperCAmelCase__  :str            =			lower_bound
   UpperCAmelCase__  :str            =			upper_bound
   for _ in range(0,      UpperCamelCase_	):
      UpperCAmelCase__  :Optional[Any]            =			xa, xa - (f(UpperCamelCase_	) * (xa - xa)) / (f(UpperCamelCase_	) - f(UpperCamelCase_	))
   return xa


if __name__ == "__main__":
    print(F'''Example: {secant_method(1, 3, 2)}''')







'''simple docstring'''





import heapq


def 					a__    (				UpperCamelCase_	:			Dict,      UpperCamelCase_	:			Tuple,      UpperCamelCase_	:			Dict	):
   UpperCAmelCase__  :List[Any]            =			[(0, start)]  # cost from start node,end node
   UpperCAmelCase__  :Optional[int]            =			set()
   while heap:
      ((UpperCAmelCase__)      ,	(UpperCAmelCase__))  :Optional[Any]            =			heapq.heappop(UpperCamelCase_	)
      if u in visited:
         continue
      visited.add(UpperCamelCase_	)
      if u == end:
         return cost
      for v, c in graph[u]:
         if v in visited:
            continue
         UpperCAmelCase__  :int            =			cost + c
         heapq.heappush(UpperCamelCase_,      (next_item, v)	)
   return -1


__lowerCamelCase       				=	{
    '''A''': [['''B''', 2], ['''C''', 5]],
    '''B''': [['''A''', 2], ['''D''', 3], ['''E''', 1], ['''F''', 1]],
    '''C''': [['''A''', 5], ['''F''', 3]],
    '''D''': [['''B''', 3]],
    '''E''': [['''B''', 4], ['''F''', 3]],
    '''F''': [['''C''', 3], ['''E''', 3]],
}
__lowerCamelCase       				=	{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''F''', 3]],
    '''F''': [],
}
__lowerCamelCase       				=	{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}

__lowerCamelCase       				=	dijkstra(G, '''E''', '''C''')
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

__lowerCamelCase       				=	dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 3 --> F == 3

__lowerCamelCase       				=	dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
    import doctest

    doctest.testmod()



