




def 						SCREAMING_SNAKE_CASE__ (   lowercase					)  ->       list[list]:
   snake_case				:    List[Any]           =	current_set.copy()
   for row_index, row in enumerate(lowercase					):
      snake_case				:    List[Any]           =	row[0]
      for column_index, column in enumerate(lowercase					):
         if magnitude == 0:
            snake_case				:    int           =	column
            continue
         snake_case				:    Tuple           =	column / magnitude
    # Subtract to cancel term
   snake_case				:    int           =	current_set[0]
   snake_case				:    Any           =	[first_row]
   snake_case				:    Optional[Any]           =	current_set[1::]
   for row in current_set:
      snake_case				:    Union[str, Any]           =	[]
      # If first term is 0, it is already in form we want, so we preserve it
      if row[0] == 0:
         final_set.append(lowercase					)
         continue
      for column_index in range(len(lowercase					)					):
         temp_row.append(first_row[column_index] - row[column_index]					)
      final_set.append(lowercase					)
   # Create next recursion iteration set
   if len(final_set[0]					) != 3:
      snake_case				:    Optional[int]           =	final_set[0]
      snake_case				:    List[Any]           =	[]
      snake_case				:    Optional[Any]           =	[]
      for row in final_set[1::]:
         current_first_column.append(row[0]					)
         next_iteration.append(row[1::]					)
      snake_case				:    Union[str, Any]           =	simplify(lowercase					)
      for i in range(len(lowercase					)					):
         resultant[i].insert(0						,current_first_column[i]					)
      resultant.insert(0						,lowercase					)
      snake_case				:    Tuple           =	resultant
   return final_set




def 						SCREAMING_SNAKE_CASE__ (   lowercase					)  ->       list:
   if len(lowercase					) == 0:
      raise IndexError("""solve_simultaneous() requires n lists of length n+1"""					)
   snake_case				:    Optional[Any]           =	len(lowercase					) + 1
   if any(len(lowercase					) != _length for item in equations					):
      raise IndexError("""solve_simultaneous() requires n lists of length n+1"""					)
   for row in equations:
      if any(not isinstance(lowercase						,(int, float)					) for column in row					):
         raise ValueError("""solve_simultaneous() requires lists of integers"""					)
   if len(lowercase					) == 1:
      return [equations[0][-1] / equations[0][0]]
   snake_case				:    Tuple           =	equations.copy()
   if any(0 in row for row in data_set					):
      snake_case				:    int           =	data_set.copy()
      snake_case				:    Optional[Any]           =	[]
      for row_index, row in enumerate(lowercase					):
         if 0 not in row:
            snake_case				:    Union[str, Any]           =	data_set.pop(lowercase					)
            break
      if not full_row:
         raise ValueError("""solve_simultaneous() requires at least 1 full equation"""					)
      data_set.insert(0						,lowercase					)
   snake_case				:    int           =	data_set.copy()
   snake_case				:    List[str]           =	simplify(lowercase					)
   snake_case				:    Any           =	simplified[::-1]
   snake_case				:    list           =	[]
   for row in simplified:
      snake_case				:    Any           =	row[-1]
      if not solutions:
         if row[-2] == 0:
            solutions.append(0					)
            continue
         solutions.append(current_solution / row[-2]					)
         continue
      snake_case				:    Any           =	row.copy()[: len(lowercase					) - 1 :]
      while temp_row[0] == 0:
         temp_row.pop(0					)
      if len(lowercase					) == 0:
         solutions.append(0					)
         continue
      snake_case				:    int           =	temp_row[1::]
      snake_case				:    Union[str, Any]           =	temp_row[::-1]
      for column_index, column in enumerate(lowercase					):
         current_solution -= column * solutions[column_index]
      solutions.append(lowercase					)
   snake_case				:    Dict           =	[]
   for item in solutions:
      final.append(float(round(lowercase						,5					)					)					)
   return final[::-1]


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       lowerCamelCase	:	Any				=   [
           [2, 1, 1, 1, 1, 4],
           [1, 2, 1, 1, 1, 5],
           [1, 1, 2, 1, 1, 6],
           [1, 1, 1, 2, 1, 7],
           [1, 1, 1, 1, 2, 8],
       ]
       print(solve_simultaneous(eq))
       print(solve_simultaneous([[4, 2]]))











# using dfs for finding eulerian path traversal




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase						,lowercase						,lowercase=None					)  ->       Any:
   snake_case				:    Union[str, Any]           =	(path or []) + [u]
   for v in graph[u]:
      if visited_edge[u][v] is False:
         snake_case     , snake_case				:    int           =	True, True
         snake_case				:    List[Any]           =	dfs(lowercase						,lowercase						,lowercase						,lowercase					)
   return path




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase					)  ->       Tuple:
   snake_case				:    Union[str, Any]           =	0
   snake_case				:    Union[str, Any]           =	-1
   for i in range(lowercase					):
      if i not in graph.keys():
         continue
      if len(graph[i]					) % 2 == 1:
         odd_degree_nodes += 1
         snake_case				:    str           =	i
   if odd_degree_nodes == 0:
      return 1, odd_node
   if odd_degree_nodes == 2:
      return 2, odd_node
   return 3, odd_node




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase					)  ->       List[str]:
   snake_case				:    Tuple           =	[[False for _ in range(max_node + 1					)] for _ in range(max_node + 1					)]
   snake_case     , snake_case				:    Any           =	check_circuit_or_path(lowercase						,lowercase					)
   if check == 3:
      print("""graph is not Eulerian"""					)
      print("""no path"""					)
      return
   snake_case				:    str           =	1
   if check == 2:
      snake_case				:    Optional[int]           =	odd_node
      print("""graph has a Euler path"""					)
   if check == 1:
      print("""graph has a Euler cycle"""					)
   snake_case				:    Dict           =	dfs(lowercase						,lowercase						,lowercase					)
   print(lowercase					)




def 						SCREAMING_SNAKE_CASE__ (   )  ->       Optional[Any]:
   snake_case				:    Union[str, Any]           =	{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
   snake_case				:    Optional[int]           =	{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
   snake_case				:    Optional[int]           =	{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
   snake_case				:    List[Any]           =	{1: [2, 3], 2: [1, 3], 3: [1, 2]}
   snake_case				:    Tuple           =	{
       1: [],
       2: []
       # all degree is zero
   }
   snake_case				:    Tuple           =	10
   check_euler(lowercase						,lowercase					)
   check_euler(lowercase						,lowercase					)
   check_euler(lowercase						,lowercase					)
   check_euler(lowercase						,lowercase					)
   check_euler(lowercase						,lowercase					)


if __name__ == "__main__":
       main()





