


"""simple docstring"""
from __future__ import annotations

from math import pi, sqrt

def 				_snake_case      (   __snake_case							:      float						, __snake_case							:      float   ):




   """simple docstring"""







   if inductance <= 0:
      raise ValueError("""Inductance cannot be 0 or negative"""   )

   elif capacitance <= 0:
      raise ValueError("""Capacitance cannot be 0 or negative"""   )

   else:
      return (
          "Resonant frequency",
          float(1 / (2 * pi * (sqrt(inductance * capacitance   )))   ),
      )


if __name__ == "__main__":
 import doctest

 doctest.testmod()





"""simple docstring"""
def 				_snake_case      (   __snake_case							:      list[list[int]]						, __snake_case							:      int						, __snake_case							:      int						, __snake_case							:      list[int]   ):




   """simple docstring"""







   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 				_snake_case      (   __snake_case							:      list[list[int]]						, __snake_case							:      list[int]						, __snake_case							:      int   ):




   """simple docstring"""







   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	:					List[str]   =		next_ver
         # Validate created path
         if util_hamilton_cycle(__snake_case						, __snake_case						, curr_ind + 1   ):
            return True
         # Backtrack
         _lowerCamelCase	:					Tuple   =		-1
   return False





def 				_snake_case      (   __snake_case							:      list[list[int]]						, __snake_case							:      int = 0   ):




   """simple docstring"""







   _lowerCamelCase	:					Any   =		[-1] * (len(__snake_case   ) + 1)
   # initialize start and end of path with starting index
   _lowerCamelCase	:					Optional[int]   =		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 []

