






'''simple docstring'''



from queue import PriorityQueue
from typing import Any

import numpy as np



def  __UpperCAmelCase						(					SCREAMING_SNAKE_CASE__:						dict,       SCREAMING_SNAKE_CASE__:						str,       SCREAMING_SNAKE_CASE__:						set,       SCREAMING_SNAKE_CASE__:						set,       SCREAMING_SNAKE_CASE__:						dict,       SCREAMING_SNAKE_CASE__:						dict,       SCREAMING_SNAKE_CASE__:						PriorityQueue,       SCREAMING_SNAKE_CASE__:						dict,       SCREAMING_SNAKE_CASE__:						float | int,       )	->      float | int:

   """simple docstring"""
   for nxt, d in graph[v]:
      if nxt in visited_forward:
         continue
      __a					  =     cst_fwd.get(SCREAMING_SNAKE_CASE__,       np.inf     )
      __a					  =     cst_fwd[v] + d
      if new_cost_f < old_cost_f:
         queue.put((new_cost_f, nxt)     )
         __a					  =     new_cost_f
         __a					  =     v
      if nxt in visited_backward:
         if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
            __a					  =     cst_fwd[v] + d + cst_bwd[nxt]
   return shortest_distance



def  __UpperCAmelCase						(					SCREAMING_SNAKE_CASE__:						str,       SCREAMING_SNAKE_CASE__:						str,       SCREAMING_SNAKE_CASE__:						dict,       SCREAMING_SNAKE_CASE__:						dict     )	->      int:

   """simple docstring"""
   __a					  =     -1

   __a					  =     set()
   __a					  =     set()
   __a					  =     {source: 0}
   __a					  =     {destination: 0}
   __a					  =     {source: None}
   __a					  =     {destination: None}
   __a					  =     PriorityQueue()
   __a					  =     PriorityQueue()

   __a					  =     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():
      __a  ,      __a					  =     queue_forward.get()
      visited_forward.add(SCREAMING_SNAKE_CASE__     )

      __a  ,      __a					  =     queue_backward.get()
      visited_backward.add(SCREAMING_SNAKE_CASE__     )

      __a					  =     pass_and_relaxation(
          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__,       )

      __a					  =     pass_and_relaxation(
          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__,       )

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

   if shortest_distance != np.inf:
      __a					  =     shortest_distance
   return shortest_path_distance


__UpperCamelCase   :							Dict         =   {
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""G""", 2]],
    """F""": [],
    """G""": [["""F""", 1]],
}
__UpperCamelCase   :							int         =   {
    """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'''



from __future__ import annotations

from typing import TypedDict
class 				__SCREAMING_SNAKE_CASE							(				_lowerCAmelCase  ):
      __a	       =42
      __a	       =42







def  __UpperCAmelCase						(					SCREAMING_SNAKE_CASE__:						str     )	->      list[str]:

   """simple docstring"""
   if not isinstance(SCREAMING_SNAKE_CASE__,       SCREAMING_SNAKE_CASE__     ):
      raise TypeError('The parameter s type must be str.'     )

   return [s[i:] + s[:i] for i in range(len(SCREAMING_SNAKE_CASE__     )     )]



def  __UpperCAmelCase						(					SCREAMING_SNAKE_CASE__:						str     )	->      BWTTransformDict:

   """simple docstring"""
   if not isinstance(SCREAMING_SNAKE_CASE__,       SCREAMING_SNAKE_CASE__     ):
      raise TypeError('The parameter s type must be str.'     )
   if not s:
      raise ValueError('The parameter s must not be empty.'     )

   __a					  =     all_rotations(SCREAMING_SNAKE_CASE__     )
   rotations.sort()  # sort the list of rotations in alphabetically order
   # make a string composed of the last char of each rotation
   __a					  =     {
       "bwt_string": "".join([word[-1] for word in rotations]     ),
       "idx_original_string": rotations.index(SCREAMING_SNAKE_CASE__     ),
   }
   return response



def  __UpperCAmelCase						(					SCREAMING_SNAKE_CASE__:						str,       SCREAMING_SNAKE_CASE__:						int     )	->      str:

   """simple docstring"""
   if not isinstance(SCREAMING_SNAKE_CASE__,       SCREAMING_SNAKE_CASE__     ):
      raise TypeError('The parameter bwt_string type must be str.'     )
   if not bwt_string:
      raise ValueError('The parameter bwt_string must not be empty.'     )
   try:
      __a					  =     int(SCREAMING_SNAKE_CASE__     )
   except ValueError:
      raise TypeError(
          'The parameter idx_original_string type must be int or passive'
          ' of cast to int.'     )
   if idx_original_string < 0:
      raise ValueError('The parameter idx_original_string must not be lower than 0.'     )
   if idx_original_string >= len(SCREAMING_SNAKE_CASE__     ):
      raise ValueError(
          'The parameter idx_original_string must be lower than' ' len(bwt_string).'     )

   __a					  =     [''] * len(SCREAMING_SNAKE_CASE__     )
   for _ in range(len(SCREAMING_SNAKE_CASE__     )     ):
      for i in range(len(SCREAMING_SNAKE_CASE__     )     ):
         __a					  =     bwt_string[i] + ordered_rotations[i]
      ordered_rotations.sort()
   return ordered_rotations[idx_original_string]


if __name__ == "__main__":
 __UpperCamelCase   :							Any         =   """Provide a string that I will generate its BWT transform: """
 __UpperCamelCase   :							Dict         =   input(entry_msg).strip()
 __UpperCamelCase   :							Optional[int]         =   bwt_transform(s)
 print(
     f"""Burrows Wheeler transform for string '{s}' results """
     f"""in '{result["bwt_string"]}'"""
 )
 __UpperCamelCase   :							Dict         =   reverse_bwt(result["""bwt_string"""], result["""idx_original_string"""])
 print(
     f"""Reversing Burrows Wheeler transform for entry '{result["bwt_string"]}' """
     f"""we get original string '{original_string}'"""
 )