




'''simple docstring'''





def      __a     (       _UpperCamelCase:   list[list]   )						->			list[list]:

     """simple docstring"""




     _snake_case							=				current_set.copy()
     for row_index, row in enumerate(_UpperCamelCase   ):
          _snake_case							=				row[0]
          for column_index, column in enumerate(_UpperCamelCase   ):
               if magnitude == 0:
                    _snake_case							=				column
                    continue
               _snake_case							=				column / magnitude
    # Subtract to cancel term
     _snake_case							=				current_set[0]
     _snake_case							=				[first_row]
     _snake_case							=				current_set[1::]
     for row in current_set:
          _snake_case							=				[]
          # If first term is 0, it is already in form we want, so we preserve it
          if row[0] == 0:
               final_set.append(_UpperCamelCase   )
               continue
          for column_index in range(len(_UpperCamelCase   )   ):
               temp_row.append(first_row[column_index] - row[column_index]   )
          final_set.append(_UpperCamelCase   )
     # Create next recursion iteration set
     if len(final_set[0]   ) != 3:
          _snake_case							=				final_set[0]
          _snake_case							=				[]
          _snake_case							=				[]
          for row in final_set[1::]:
               current_first_column.append(row[0]   )
               next_iteration.append(row[1::]   )
          _snake_case							=				simplify(_UpperCamelCase   )
          for i in range(len(_UpperCamelCase   )   ):
               resultant[i].insert(0 ,						current_first_column[i]   )
          resultant.insert(0 ,						_UpperCamelCase   )
          _snake_case							=				resultant
     return final_set





def      __a     (       _UpperCamelCase:   list[list]   )						->			list:

     """simple docstring"""




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


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   UpperCamelCase_						:      List[str]       =						[
       [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]]))








'''simple docstring'''





from __future__ import annotations

from typing import Any





def      __a     (       _UpperCamelCase:   list[Any]   )						->			None:

     """simple docstring"""




     create_state_space_tree(_UpperCamelCase ,						[] ,						0   )





def      __a     (       _UpperCamelCase:   list[Any] ,						_UpperCamelCase:   list[Any] ,						_UpperCamelCase:   int   )						->			None:

     """simple docstring"""




     if index == len(_UpperCamelCase   ):
          print(_UpperCamelCase   )
          return

     create_state_space_tree(_UpperCamelCase ,						_UpperCamelCase ,						index + 1   )
     current_subsequence.append(sequence[index]   )
     create_state_space_tree(_UpperCamelCase ,						_UpperCamelCase ,						index + 1   )
     current_subsequence.pop()


if __name__ == "__main__":
   UpperCamelCase_						:      list[Any]       =						[3, 1, 2, 4]
   generate_all_subsequences(seq)

   seq.clear()
   seq.extend(['''A''', '''B''', '''C'''])
   generate_all_subsequences(seq)


