






def       __lowerCAmelCase      (						__snake_case					, __snake_case					, __snake_case					, __snake_case       ):

     # 1. Validate that path exists between current and next vertices
     if graph[path[curr_ind - 1]][next_ver] == 0:
          return False

     # 2. Validate that next vertex is not already in path
     return not any(vertex == next_ver for vertex in path       )





def       __lowerCAmelCase      (						__snake_case					, __snake_case					, __snake_case       ):

     # Base Case
     if curr_ind == len(__snake_case       ):
          # return whether path exists between current and starting vertices
          return graph[path[curr_ind - 1]][path[0]] == 1

     # Recursive Step
     for next_ver in range(0					, len(__snake_case       )       ):
          if valid_connection(__snake_case					, __snake_case					, __snake_case					, __snake_case       ):
               # Insert current vertex  into path as next transition
               __lowerCAmelCase								=					next_ver
               # Validate created path
               if util_hamilton_cycle(__snake_case					, __snake_case					, curr_ind + 1       ):
                    return True
               # Backtrack
               __lowerCAmelCase								=					-1
     return False





def       __lowerCAmelCase      (						__snake_case					, __snake_case = 0       ):
     __lowerCAmelCase								=					[-1] * (len(__snake_case       ) + 1)
     # initialize start and end of path with starting index
     __lowerCAmelCase								=					__lowerCAmelCase								=					start_index
     # evaluate and if we find answer return path either return empty array
     return path if util_hamilton_cycle(__snake_case					, __snake_case					, 1       ) else []












from __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
lowerCamelCase			:					int         =	1.0_5457_1817E-34  # unit of ℏ : J * s

lowerCamelCase			:					Union[str, Any]         =	3E8  # unit of c : m * s^-1





def       __lowerCAmelCase      (						__snake_case					, __snake_case					, __snake_case       ):

     if (force, area, distance).count(0       ) != 1:
          raise ValueError("One and only one argument must be 0"       )
     if force < 0:
          raise ValueError("Magnitude of force can not be negative"       )
     if distance < 0:
          raise ValueError("Distance can not be negative"       )
     if area < 0:
          raise ValueError("Area can not be negative"       )
     if force == 0:
          __lowerCAmelCase								=					(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
              240 * (distance) ** 4
          )
          return {"force": force}
     elif area == 0:
          __lowerCAmelCase								=					(240 * force * (distance) ** 4) / (
              REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
          )
          return {"area": area}
     elif distance == 0:
          __lowerCAmelCase								=					(
              (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
          ) ** (1 / 4)
          return {"distance": distance}
     raise ValueError("One and only one argument must be 0"       )


# Run doctest
if __name__ == "__main__":
 import doctest

 doctest.testmod()






