


from queue import PriorityQueue
from typing import Any

import numpy as np
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	):


 for nxt, d in graph[v]:
  if nxt in visited_forward:
   continue
  __lowerCamelCase		:							List[Any]		 =						cst_fwd.get(__UpperCamelCase      ,	np.inf						)
  __lowerCamelCase		:							Optional[Any]		 =						cst_fwd[v] + d
  if new_cost_f < old_cost_f:
   queue.put((new_cost_f, nxt)						)
   __lowerCamelCase		:							str		 =						new_cost_f
   __lowerCamelCase		:							str		 =						v
  if nxt in visited_backward:
   if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
    __lowerCamelCase		:							List[Any]		 =						cst_fwd[v] + d + cst_bwd[nxt]
 return shortest_distance
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__						):
 __lowerCamelCase		:							str		 =						-1

 __lowerCamelCase		:							Tuple		 =						set()
 __lowerCamelCase		:							List[Any]		 =						set()
 __lowerCamelCase		:							int		 =						{source: 0}
 __lowerCamelCase		:							int		 =						{destination: 0}
 __lowerCamelCase		:							Optional[Any]		 =						{source: None}
 __lowerCamelCase		:							Any		 =						{destination: None}
 __lowerCamelCase		:							List[Any]		 =						PriorityQueue()
 __lowerCamelCase		:							Union[str, Any]		 =						PriorityQueue()

 __lowerCamelCase		:							str		 =						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[str]		 =						queue_forward.get()
  visited_forward.add(__UpperCamelCase						)

  __lowerCamelCase ,					__lowerCamelCase		:							str		 =						queue_backward.get()
  visited_backward.add(__UpperCamelCase						)

  __lowerCamelCase		:							Any		 =						pass_and_relaxation(
      __UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	)

  __lowerCamelCase		:							str		 =						pass_and_relaxation(
      __UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	__UpperCamelCase      ,	)

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

 if shortest_distance != np.inf:
  __lowerCamelCase		:							Tuple		 =						shortest_distance
 return shortest_path_distance


lowercase_	   =     {
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
lowercase_	   =     {
    '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()





def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__						):
 __lowerCamelCase		:							str		 =						0
 __lowerCamelCase		:							Tuple		 =						len(SCREAMING_SNAKE_CASE__						)

 for i in range(n - 1						):
  for j in range(i + 1      ,	SCREAMING_SNAKE_CASE__						):
   if arr[i] > arr[j]:
    num_inversions += 1

 return num_inversions
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__						):
 if len(SCREAMING_SNAKE_CASE__						) <= 1:
  return arr, 0
 __lowerCamelCase		:							Optional[int]		 =						len(SCREAMING_SNAKE_CASE__						) // 2
 __lowerCamelCase		:							Union[str, Any]		 =						arr[0:mid]
 __lowerCamelCase		:							List[Any]		 =						arr[mid:]

 __lowerCamelCase ,					__lowerCamelCase		:							Any		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							List[str]		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							Dict		 =						_count_cross_inversions(SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__						)

 __lowerCamelCase		:							List[str]		 =						inversion_p + inversions_q + cross_inversions
 return c, num_inversions
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__						):
 __lowerCamelCase		:							Optional[int]		 =						[]
 __lowerCamelCase		:							List[Any]		 =						0
 while i < len(SCREAMING_SNAKE_CASE__						) and j < len(SCREAMING_SNAKE_CASE__						):
  if p[i] > q[j]:
   # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
   # These are all inversions. The claim emerges from the
   # property that P is sorted.
   num_inversion += len(SCREAMING_SNAKE_CASE__						) - i
   r.append(q[j]						)
   j += 1
  else:
   r.append(p[i]						)
   i += 1

 if i < len(SCREAMING_SNAKE_CASE__						):
  r.extend(p[i:]						)
 else:
  r.extend(q[j:]						)

 return r, num_inversion
def 				UpperCamelCase__					(  ):
 __lowerCamelCase		:							Optional[int]		 =						[10, 2, 1, 5, 5, 2, 11]

 # this arr has 8 inversions:
 # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

 __lowerCamelCase		:							Optional[Any]		 =						count_inversions_bf(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							Optional[Any]		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)

 assert num_inversions_bf == num_inversions_recursive == 8

 print('number of inversions = '      ,	SCREAMING_SNAKE_CASE__						)

 # testing an array with zero inversion (a sorted arr_1)

 arr_a.sort()
 __lowerCamelCase		:							Optional[Any]		 =						count_inversions_bf(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							int		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)

 assert num_inversions_bf == num_inversions_recursive == 0
 print('number of inversions = '      ,	SCREAMING_SNAKE_CASE__						)

 # an empty list should also have zero inversions
 __lowerCamelCase		:							List[str]		 =						[]
 __lowerCamelCase		:							Dict		 =						count_inversions_bf(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							Dict		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)

 assert num_inversions_bf == num_inversions_recursive == 0
 print('number of inversions = '      ,	SCREAMING_SNAKE_CASE__						)


if __name__ == "__main__":
       main()

