


def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      )->						None:




      """simple docstring"""

      snake_case_ =   generate_pascal_triangle(SCREAMING_SNAKE_CASE      )
      for row_idx in range(SCREAMING_SNAKE_CASE      ):
            # Print left spaces
            for _ in range(num_rows - row_idx - 1      ):
                  print(end=''' '''      )
            # Print row values
            for col_idx in range(row_idx + 1      ):
                  if col_idx != row_idx:
                        print(triangle[row_idx][col_idx]      ,      end=''' '''      )
                  else:
                        print(triangle[row_idx][col_idx]      ,      end=''''''      )
            print()






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      )->						list[list[int]]:




      """simple docstring"""

      if not isinstance(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ):
            raise TypeError('''The input value of \'num_rows\' should be \'int\''''      )

      if num_rows == 0:
            return []
      elif num_rows < 0:
            raise ValueError(
                '''The input value of \'num_rows\' should be greater than or equal to 0'''      )

      snake_case_ =   []
      for current_row_idx in range(SCREAMING_SNAKE_CASE      ):
            snake_case_ =   populate_current_row(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )
            triangle.append(SCREAMING_SNAKE_CASE      )
      return triangle






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )->						list[int]:




      """simple docstring"""

      snake_case_ =   [-1] * (current_row_idx + 1)
      # first and last elements of current row are equal to 1
      snake_case_ ,					snake_case_ =   1, 1
      for current_col_idx in range(1      ,      SCREAMING_SNAKE_CASE      ):
            calculate_current_element(
                SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )
      return current_row






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ,      )->						None:




      """simple docstring"""

      snake_case_ =   triangle[current_row_idx - 1][current_col_idx - 1]
      snake_case_ =   triangle[current_row_idx - 1][current_col_idx]
      snake_case_ =   above_to_left_elt + above_to_right_elt






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      )->						list[list[int]]:




      """simple docstring"""

      if not isinstance(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ):
            raise TypeError('''The input value of \'num_rows\' should be \'int\''''      )

      if num_rows == 0:
            return []
      elif num_rows < 0:
            raise ValueError(
                '''The input value of \'num_rows\' should be greater than or equal to 0'''      )

      snake_case_ =   [[1]]

      for row_index in range(1      ,      SCREAMING_SNAKE_CASE      ):
            snake_case_ =   [0] + result[-1] + [0]
            snake_case_ =   row_index + 1
            # Calculate the number of distinct elements in a row
            snake_case_ =   sum(divmod(SCREAMING_SNAKE_CASE      ,      2      )      )
            snake_case_ =   [
                temp_row[i - 1] + temp_row[i] for i in range(1      ,      distinct_elements + 1      )
            ]
            snake_case_ =   row_first_half[: (row_index + 1) // 2]
            row_second_half.reverse()
            snake_case_ =   row_first_half + row_second_half
            result.append(SCREAMING_SNAKE_CASE      )

      return result






def  __lowerCAmelCase					()->						None:




      """simple docstring"""

      from collections.abc import Callable
      from timeit import timeit

      def benchmark_a_function(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ) -> None:
            snake_case_ =   f'''{func.__name__}({value})'''
            snake_case_ =   timeit(f'''__main__.{call}'''      ,      setup='''import __main__'''      )
            # print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
            print(f'''{call:38} -- {timing:.4f} seconds'''      )

      for value in range(15      ):  # (1, 7, 14):
            for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
                  benchmark_a_function(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )
            print()


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   benchmark()



import copy
import re







class lowerCAmelCase_		:

 '''simple docstring'''

 __snake_case				=						"hp"
 __snake_case				=						{}
 __snake_case				=						None



 @classmethod
 def 		UpperCamelCase__  (			cls	,   _UpperCAmelCase	,   _UpperCAmelCase      ):
       snake_case_ =   prefix
       snake_case_ =   defaults
       cls.build_naming_info()



 @staticmethod
 def 		UpperCamelCase__  (			_UpperCAmelCase	,   _UpperCAmelCase      ):
       if len(_UpperCAmelCase      ) == 0:
             return ""
       snake_case_ =   None
       if any(char.isdigit() for char in word      ):
             raise Exception(F'''Parameters should not contain numbers: \'{word}\' contains a number'''      )
       if word in info["short_word"]:
             return info["short_word"][word]
       for prefix_len in range(1	,   len(_UpperCAmelCase      ) + 1      ):
             snake_case_ =   word[:prefix_len]
             if prefix in info["reverse_short_word"]:
                   continue
             else:
                   snake_case_ =   prefix
                   break

       if short_word is None:
             # Paranoid fallback
             def int_to_alphabetic(_UpperCAmelCase      ):
                   snake_case_ =   ''''''
                   while integer != 0:
                         snake_case_ =   chr(ord('''A'''      ) + integer % 10      ) + s
                         integer //= 10
                   return s

             snake_case_ =   0
             while True:
                   snake_case_ =   word + '''#''' + int_to_alphabetic(_UpperCAmelCase      )
                   if sword in info["reverse_short_word"]:
                         continue
                   else:
                         snake_case_ =   sword
                         break

       snake_case_ =   short_word
       snake_case_ =   word
       return short_word



 @staticmethod
 def 		UpperCamelCase__  (			_UpperCAmelCase	,   _UpperCAmelCase      ):
       snake_case_ =   param_name.split('''_'''      )

       snake_case_ =   [TrialShortNamer.shortname_for_word(_UpperCAmelCase	,   _UpperCAmelCase      ) for word in words]

       # We try to create a separatorless short name, but if there is a collision we have to fallback
       # to a separated short name
       snake_case_ =   ['''''', '''_''']

       for separator in separators:
             snake_case_ =   separator.join(_UpperCAmelCase      )
             if shortname not in info["reverse_short_param"]:
                   snake_case_ =   shortname
                   snake_case_ =   param_name
                   return shortname

       return param_name



 @staticmethod
 def 		UpperCamelCase__  (			_UpperCAmelCase	,   _UpperCAmelCase      ):
       snake_case_ =   TrialShortNamer.shortname_for_key(_UpperCAmelCase	,   _UpperCAmelCase      )
       snake_case_ =   short_name
       snake_case_ =   param_name



 @classmethod
 def 		UpperCamelCase__  (			cls      ):
       if cls.NAMING_INFO is not None:
             return

       snake_case_ =   {
           '''short_word''': {},
           '''reverse_short_word''': {},
           '''short_param''': {},
           '''reverse_short_param''': {},
       }

       snake_case_ =   list(cls.DEFAULTS.keys()      )

       for k in field_keys:
             cls.add_new_param_name(_UpperCAmelCase	,   _UpperCAmelCase      )

       snake_case_ =   info



 @classmethod
 def 		UpperCamelCase__  (			cls	,   _UpperCAmelCase      ):
       cls.build_naming_info()
       assert cls.PREFIX is not None
       snake_case_ =   [copy.copy(cls.PREFIX      )]

       for k, v in params.items():
             if k not in cls.DEFAULTS:
                   raise Exception(F'''You should provide a default value for the param name {k} with value {v}'''      )
             if v == cls.DEFAULTS[k]:
                   # The default value is not added to the name
                   continue

             snake_case_ =   cls.NAMING_INFO['''short_param'''][k]

             if isinstance(_UpperCAmelCase	,   _UpperCAmelCase      ):
                   snake_case_ =   1 if v else 0

             snake_case_ =   '''''' if isinstance(_UpperCAmelCase	,   (int, float)      ) else '''-'''
             snake_case_ =   F'''{key}{sep}{v}'''
             name.append(_UpperCAmelCase      )

       return "_".join(_UpperCAmelCase      )





 @classmethod
 def 		UpperCamelCase__  (			cls	,   _UpperCAmelCase      ):
       snake_case_ =   repr[len(cls.PREFIX      ) + 1 :]
       if repr == "":
             snake_case_ =   []
       else:
             snake_case_ =   repr.split('''_'''      )

       snake_case_ =   {}

       for value in values:
             if "-" in value:
                   snake_case_ ,					snake_case_ =   value.split('''-'''      )
             else:
                   snake_case_ =   re.sub('''[0-9.]'''	,   ''''''	,   _UpperCAmelCase      )
                   snake_case_ =   float(re.sub('''[^0-9.]'''	,   ''''''	,   _UpperCAmelCase      )      )

             snake_case_ =   cls.NAMING_INFO['''reverse_short_param'''][p_k]

             snake_case_ =   p_v

       for k in cls.DEFAULTS:
             if k not in parameters:
                   snake_case_ =   cls.DEFAULTS[k]

       return parameters