


"""simple docstring"""
import timeit




class   lowercase__							:





   def __init__(       self			,      SCREAMING_SNAKE_CASE)     ->     Tuple:
      if isinstance(SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE):  # Initializes a matrix identical to the one provided.
         _lowerCamelCase  :				List[str]      =		arg
         _lowerCamelCase  :				List[str]      =		len(SCREAMING_SNAKE_CASE)
      else:  # Initializes a square matrix of the given size and set values to zero.
         _lowerCamelCase  :				List[Any]      =		arg
         _lowerCamelCase  :				Union[str, Any]      =		[[0 for _ in range(self.n)] for _ in range(self.n)]





   def __mul__(       self			,      SCREAMING_SNAKE_CASE)     ->     Optional[Any]:
      _lowerCamelCase  :				List[Any]      =		Matrix(self.n)
      for i in range(self.n):
         for j in range(self.n):
            for k in range(self.n):
               matrix.t[i][j] += self.t[i][k] * b.t[k][j]
      return matrix







def 							_snake_case			(      __snake_case       :			Union[str, Any]	,   __snake_case       :			List[Any]      ):




   """simple docstring"""







   _lowerCamelCase  :				List[Any]      =		Matrix([[1, 0], [0, 1]]      )
   while b > 0:
      if b & 1:
         matrix *= a
      a *= a
      b >>= 1
   return matrix

def 							_snake_case			(      __snake_case       :			List[str]	,   __snake_case       :			str	,   __snake_case       :			List[Any]      ):




   """simple docstring"""







   if n == 1:
      return fa
   elif n == 2:
      return fa
   _lowerCamelCase  :				Any      =		Matrix([[1, 1], [1, 0]]      )
   _lowerCamelCase  :				List[str]      =		modular_exponentiation(__snake_case	,   n - 2      )
   return fa * matrix.t[0][0] + fa * matrix.t[0][1]

def 							_snake_case			(      __snake_case       :			int	,   __snake_case       :			Optional[int]	,   __snake_case       :			List[Any]      ):




   """simple docstring"""







   if n == 1:
      return fa
   elif n == 2:
      return fa

   _lowerCamelCase  :				Optional[Any]      =		fa
   _lowerCamelCase  :				int      =		fa
   n -= 2

   while n > 0:
      _lowerCamelCase      ,						_lowerCamelCase  :				Tuple      =		fn_a + fn_a, fn_a
      n -= 1

   return fn_a

def 							_snake_case			(      ):




   """simple docstring"""







   _lowerCamelCase  :				List[str]      =		"""
from random import randint
from __main__ import fibonacci_with_matrix_exponentiation
"""
   _lowerCamelCase  :				int      =		"""fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)"""
   _lowerCamelCase  :				Tuple      =		timeit.timeit(setup=__snake_case	,   stmt=__snake_case	,   number=100      )
   print("""With matrix exponentiation the average execution time is """	,   exec_time / 100      )
   return exec_time

def 							_snake_case			(      ):




   """simple docstring"""







   _lowerCamelCase  :				Dict      =		"""
from random import randint
from __main__ import simple_fibonacci
"""
   _lowerCamelCase  :				Optional[int]      =		"""simple_fibonacci(randint(1,70000), 1, 1)"""
   _lowerCamelCase  :				List[Any]      =		timeit.timeit(setup=__snake_case	,   stmt=__snake_case	,   number=100      )
   print(
       """Without matrix exponentiation the average execution time is """	,   exec_time / 100      )
   return exec_time

def 							_snake_case			(      ):




   """simple docstring"""







   matrix_exponentiation_time()
   simple_fibonacci_time()


if __name__ == "__main__":
 main()





"""simple docstring"""
def 							_snake_case			(      __snake_case       :			str	,   __snake_case       :			str	,   __snake_case       :			int	,   __snake_case       :			int	,   __snake_case       :			int	,   __snake_case       :			int	,   ):




   """simple docstring"""







   _lowerCamelCase  :				Optional[Any]      =		list(__snake_case      )
   _lowerCamelCase  :				Optional[int]      =		list(__snake_case      )
   _lowerCamelCase  :				Union[str, Any]      =		len(__snake_case      )
   _lowerCamelCase  :				Optional[int]      =		len(__snake_case      )

   _lowerCamelCase  :				List[str]      =		[
       [0 for _ in range(len_destination_seq + 1      )] for _ in range(len_source_seq + 1      )
   ]
   _lowerCamelCase  :				List[Any]      =		[
       ["""0""" for _ in range(len_destination_seq + 1      )] for _ in range(len_source_seq + 1      )
   ]

   for i in range(1	,   len_source_seq + 1      ):
      _lowerCamelCase  :				Optional[Any]      =		i * delete_cost
      _lowerCamelCase  :				Any      =		F'D{source_seq[i - 1]:c}'

   for i in range(1	,   len_destination_seq + 1      ):
      _lowerCamelCase  :				Dict      =		i * insert_cost
      _lowerCamelCase  :				List[str]      =		F'I{destination_seq[i - 1]:c}'

   for i in range(1	,   len_source_seq + 1      ):
      for j in range(1	,   len_destination_seq + 1      ):
         if source_seq[i - 1] == destination_seq[j - 1]:
            _lowerCamelCase  :				Union[str, Any]      =		costs[i - 1][j - 1] + copy_cost
            _lowerCamelCase  :				Tuple      =		F'C{source_seq[i - 1]:c}'
         else:
            _lowerCamelCase  :				Tuple      =		costs[i - 1][j - 1] + replace_cost
            _lowerCamelCase  :				List[str]      =		F'R{source_seq[i - 1]:c}' + str(destination_seq[j - 1]      )

         if costs[i - 1][j] + delete_cost < costs[i][j]:
            _lowerCamelCase  :				Any      =		costs[i - 1][j] + delete_cost
            _lowerCamelCase  :				Any      =		F'D{source_seq[i - 1]:c}'

         if costs[i][j - 1] + insert_cost < costs[i][j]:
            _lowerCamelCase  :				Dict      =		costs[i][j - 1] + insert_cost
            _lowerCamelCase  :				Union[str, Any]      =		F'I{destination_seq[j - 1]:c}'

   return costs, ops

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




   """simple docstring"""







   if i == 0 and j == 0:
      return []
   else:
      if ops[i][j][0] == "C" or ops[i][j][0] == "R":
         _lowerCamelCase  :				List[Any]      =		assemble_transformation(__snake_case	,   i - 1	,   j - 1      )
         seq.append(ops[i][j]      )
         return seq
      elif ops[i][j][0] == "D":
         _lowerCamelCase  :				Optional[Any]      =		assemble_transformation(__snake_case	,   i - 1	,   __snake_case      )
         seq.append(ops[i][j]      )
         return seq
      else:
         _lowerCamelCase  :				str      =		assemble_transformation(__snake_case	,   __snake_case	,   j - 1      )
         seq.append(ops[i][j]      )
         return seq


if __name__ == "__main__":
 UpperCAmelCase ,     UpperCAmelCase   =	compute_transform_tables("""Python""", """Algorithms""", -1, 1, 2, 2)

 UpperCAmelCase   =	len(operations)
 UpperCAmelCase   =	len(operations[0])
 UpperCAmelCase   =	assemble_transformation(operations, m - 1, n - 1)

 UpperCAmelCase   =	list("""Python""")
 UpperCAmelCase   =	0
 UpperCAmelCase   =	0

 with open("""min_cost.txt""", """w""") as file:
  for op in sequence:
   print("""""".join(string))

   if op[0] == "C":
    file.write("""%-16s""" % """Copy %c""" % op[1])
    file.write("""\t\t\t""" + """""".join(string))
    file.write("""\r\n""")

    cost -= 1
   elif op[0] == "R":
    UpperCAmelCase   =	op[2]

    file.write("""%-16s""" % ("""Replace %c""" % op[1] + """ with """ + str(op[2])))
    file.write("""\t\t""" + """""".join(string))
    file.write("""\r\n""")

    cost += 1
   elif op[0] == "D":
    string.pop(i)

    file.write("""%-16s""" % """Delete %c""" % op[1])
    file.write("""\t\t\t""" + """""".join(string))
    file.write("""\r\n""")

    cost += 2
   else:
    string.insert(i, op[1])

    file.write("""%-16s""" % """Insert %c""" % op[1])
    file.write("""\t\t\t""" + """""".join(string))
    file.write("""\r\n""")

    cost += 2

   i += 1

  print("""""".join(string))
  print("""Cost: """, cost)

  file.write("""\r\nMinimum cost: """ + str(cost))

