



"""simple docstring"""






def 			_lowercase				(  __snake_case	)						->   Dict:
			__lowerCAmelCase      :  List[Any]												=       generate_pascal_triangle(__snake_case	)
			for row_idx in range(__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 			_lowercase				(  __snake_case	)						->   str:

			if not isinstance(__snake_case					,__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"	)

			__lowerCAmelCase      :  list[list[int]]												=       []
			for current_row_idx in range(__snake_case	):
						__lowerCAmelCase      :  int												=       populate_current_row(__snake_case					,__snake_case	)
						triangle.append(__snake_case	)
			return triangle


def 			_lowercase				(  __snake_case					,__snake_case	)						->   Tuple:
			__lowerCAmelCase      :  List[Any]												=       [-1] * (current_row_idx + 1)
			# first and last elements of current row are equal to 1
			__lowerCAmelCase      :  Any												=       1, 1
			for current_col_idx in range(1					,__snake_case	):
						calculate_current_element(
						    __snake_case					,__snake_case					,__snake_case					,__snake_case	)
			return current_row


def 			_lowercase				(  __snake_case					,__snake_case					,__snake_case					,__snake_case					,)						->   Optional[Any]:
			__lowerCAmelCase      :  Dict												=       triangle[current_row_idx - 1][current_col_idx - 1]
			__lowerCAmelCase      :  List[str]												=       triangle[current_row_idx - 1][current_col_idx]
			__lowerCAmelCase      :  Dict												=       above_to_left_elt + above_to_right_elt


def 			_lowercase				(  __snake_case	)						->   int:

			if not isinstance(__snake_case					,__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"	)

			__lowerCAmelCase      :  list[list[int]]												=       [[1]]

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

			return result


def 			_lowercase				(  )						->   Optional[Any]:
			from collections.abc import Callable
			from timeit import timeit

			def benchmark_a_function(__snake_case					,__snake_case	) -> None:
						__lowerCAmelCase      :  int												=       F"""{func.__name__}({value})"""
						__lowerCAmelCase      :  Optional[Any]												=       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(__snake_case					,__snake_case	)
						print()


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	benchmark()







"""simple docstring"""



from __future__ import annotations

__A		:       List[Any]  				=		[-10, -5, 0, 5, 5.1, 11, 13, 21, 3, 4, -21, -10, -5, -1, 0]
__A		:       str  				=		[-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1]



def 						lowercase    (				__snake_case				: list[float]	):
		lowercase_ : List[str]							       =   []
		lowercase_ : List[Any]							       =   len(__snake_case	)

		for i in range(__snake_case	):
				lowercase_ : float							       =   -1
				for j in range(i + 1		,					__snake_case	):
						if arr[i] < arr[j]:
								lowercase_ : List[str]							       =   arr[j]
								break
				result.append(__snake_case	)
		return result



def 						lowercase    (				__snake_case				: list[float]	):
		lowercase_ : List[str]							       =   []
		for i, outer in enumerate(__snake_case	):
				lowercase_ : float							       =   -1
				for inner in arr[i + 1 :]:
						if outer < inner:
								lowercase_ : List[Any]							       =   inner
								break
				result.append(__snake_case	)
		return result



def 						lowercase    (				__snake_case				: list[float]	):
		lowercase_ : List[str]							       =   len(__snake_case	)
		lowercase_ : list[float]							       =   []
		lowercase_ : list[float]							       =   [-1] * arr_size

		for index in reversed(range(__snake_case	)	):
				if stack:
						while stack[-1] <= arr[index]:
								stack.pop()
								if not stack:
										break
				if stack:
						lowercase_ : Optional[Any]							       =   stack[-1]
				stack.append(arr[index]	)
		return result


if __name__ == "__main__":
						from doctest import testmod
						from timeit import timeit

						testmod()
						print(next_greatest_element_slow(arr))
						print(next_greatest_element_fast(arr))
						print(next_greatest_element(arr))

						__A		:       int  				=		(
						    '''from __main__ import arr, next_greatest_element_slow, '''
						    '''next_greatest_element_fast, next_greatest_element'''
						)
						print(
						    '''next_greatest_element_slow():''',
						    timeit('''next_greatest_element_slow(arr)''', setup=setup),
						)
						print(
						    '''next_greatest_element_fast():''',
						    timeit('''next_greatest_element_fast(arr)''', setup=setup),
						)
						print(
						    '''     next_greatest_element():''',
						    timeit('''next_greatest_element(arr)''', setup=setup),
						)



