

"""simple docstring"""

from queue import PriorityQueue
from typing import Any

import numpy as np



def       SCREAMING_SNAKE_CASE							( lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					)			->						float | int:
 for nxt, d in graph[v]:
  if nxt in visited_forward:
   continue
  lowerCAmelCase__   :				List[str] 			=				cst_fwd.get(lowercase__					,					np.inf   )
  lowerCAmelCase__   :				Union[str, Any] 			=				cst_fwd[v] + d
  if new_cost_f < old_cost_f:
   queue.put((new_cost_f, nxt)   )
   lowerCAmelCase__   :				Union[str, Any] 			=				new_cost_f
   lowerCAmelCase__   :				List[str] 			=				v
  if nxt in visited_backward:
   if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
    lowerCAmelCase__   :				Optional[Any] 			=				cst_fwd[v] + d + cst_bwd[nxt]
 return shortest_distance



def       SCREAMING_SNAKE_CASE							( lowercase__					,					lowercase__					,					lowercase__					,					lowercase__   )			->						int:
 lowerCAmelCase__   :				str 			=				-1

 lowerCAmelCase__   :				Any 			=				set()
 lowerCAmelCase__   :				Union[str, Any] 			=				set()
 lowerCAmelCase__   :				List[Any] 			=				{source: 0}
 lowerCAmelCase__   :				List[str] 			=				{destination: 0}
 lowerCAmelCase__   :				Union[str, Any] 			=				{source: None}
 lowerCAmelCase__   :				str 			=				{destination: None}
 lowerCAmelCase__   :				PriorityQueue[Any] 			=				PriorityQueue()
 lowerCAmelCase__   :				PriorityQueue[Any] 			=				PriorityQueue()

 lowerCAmelCase__   :				Optional[Any] 			=				np.inf

 queue_forward.put((0, source)   )
 queue_backward.put((0, destination)   )

 if source == destination:
  return 0

 while not queue_forward.empty() and not queue_backward.empty():
  lowerCAmelCase__			,						lowerCAmelCase__   :				List[Any] 			=				queue_forward.get()
  visited_forward.add(lowercase__   )

  lowerCAmelCase__			,						lowerCAmelCase__   :				Tuple 			=				queue_backward.get()
  visited_backward.add(lowercase__   )

  lowerCAmelCase__   :				str 			=				pass_and_relaxation(
      lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					)

  lowerCAmelCase__   :				Dict 			=				pass_and_relaxation(
      lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					lowercase__					,					)

  if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
   break

 if shortest_distance != np.inf:
  lowerCAmelCase__   :				Any 			=				shortest_distance
 return shortest_path_distance


_UpperCamelCase		     =    {
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""G""", 2]],
    """F""": [],
    """G""": [["""F""", 1]],
}
_UpperCamelCase		     =    {
    """B""": [["""E""", 1]],
    """C""": [["""B""", 1]],
    """D""": [["""C""", 1]],
    """F""": [["""D""", 1], ["""G""", 1]],
    """E""": [[None, np.inf]],
    """G""": [["""E""", 2]],
}

if __name__ == "__main__":
    import doctest

    doctest.testmod()









"""simple docstring"""

def       SCREAMING_SNAKE_CASE							( lowercase__   )			->						float:
 return 1_0 - x * x



def       SCREAMING_SNAKE_CASE							( lowercase__					,					lowercase__   )			->						float:
 # Bolzano theory in order to find if there is a root between a and b
 if equation(lowercase__   ) * equation(lowercase__   ) >= 0:
  raise ValueError("Wrong space!"   )

 lowerCAmelCase__   :				Union[str, Any] 			=				a
 while (b - a) >= 0.01:
  # Find middle point
  lowerCAmelCase__   :				int 			=				(a + b) / 2
  # Check if middle point is root
  if equation(lowercase__   ) == 0.0:
   break
  # Decide the side to repeat the steps
  if equation(lowercase__   ) * equation(lowercase__   ) < 0:
   lowerCAmelCase__   :				str 			=				c
  else:
   lowerCAmelCase__   :				List[str] 			=				c
 return c


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    print(bisection(-2, 5))
    print(bisection(0, 6))






