





'''simple docstring'''




from __future__ import annotations






def        _lowerCAmelCase			(  __snake_case  : str ,							__snake_case  : list[str] | None = None			)     ->     list[list[str]]:
     __A						: Any      =       word_bank or []
     # create a table
     __A						: int      =       len(__snake_case			) + 1

     __A						: list[list[list[str]]]      =       []
     for _ in range(__snake_case			):
          table.append([]			)
     # seed value
     __A						: Tuple      =       [[]]  # because empty string has empty combination

     # iterate through the indices
     for i in range(__snake_case			):
          # condition
          if table[i] != []:
               for word in word_bank:
                    # slice condition
                    if target[i : i + len(__snake_case			)] == word:
                         __A						: list[list[str]]      =       [
                             [word, *way] for way in table[i]
                         ]
                         # adds the word to every combination the current position holds
                         # now,push that combination to the table[i+len(word)]
                         table[i + len(__snake_case			)] += new_combinations

    # combinations are in reverse order so reverse for better output
     for combination in table[len(__snake_case			)]:
          combination.reverse()

     return table[len(__snake_case			)]


if __name__ == "__main__":
  print(all_construct('''jwajalapa''', ['''jwa''', '''j''', '''w''', '''a''', '''la''', '''lapa''']))
  print(all_construct('''rajamati''', ['''s''', '''raj''', '''amat''', '''raja''', '''ma''', '''i''', '''t''']))
  print(
      all_construct(
          '''hexagonosaurus''',
          ['''h''', '''ex''', '''hex''', '''ag''', '''ago''', '''ru''', '''auru''', '''rus''', '''go''', '''no''', '''o''', '''s'''],
      )
  )






'''simple docstring'''




from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403






def        _lowerCAmelCase			(  __snake_case  : str ,							__snake_case  : complex ,							__snake_case  : str = "x" ,							__snake_case  : float = 10**-10 ,							__snake_case  : int = 1 ,							)     ->     complex:
     __A						: int      =       symbols(__snake_case			)
     __A						: Tuple      =       lambdify(__snake_case ,							__snake_case			)
     __A						: Any      =       lambdify(__snake_case ,							diff(__snake_case ,							__snake_case			)			)

     __A						: str      =       starting_point

     while True:
          if diff_function(__snake_case			) != 0:
               __A						: Optional[Any]      =       prev_guess - multiplicity * func(__snake_case			) / diff_function(
                   __snake_case			)
          else:
               raise ZeroDivisionError('Could not find root'			) from None

          # Precision is checked by comparing the difference of consecutive guesses
          if abs(next_guess - prev_guess			) < precision:
               return next_guess

          __A						: Dict      =       next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(f"""The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}""")

  # Find root of polynomial
  # Find fourth Root of 5
  print(f"""The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5j)}""")

  # Find value of e
  print(
      '''The root of log(y) - 1 = 0 is ''',
      f"""{newton_raphson("log(y) - 1", 2, variable="y")}""",
  )

  # Exponential Roots
  print(
      '''The root of exp(x) - 1 = 0 is''',
      f"""{newton_raphson("exp(x) - 1", 10, precision=0.005)}""",
  )

  # Find root of cos(x)
  print(f"""The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}""")