
"""simple docstring"""

def     lowercase__						(					lowerCAmelCase				:					Dict ) ->      List[Any]:






				"""simple docstring"""




				UpperCAmelCase									=					[]
				UpperCAmelCase									=					[]
				UpperCAmelCase									=					{
				    '''^''': 3,
				    '''*''': 2,
				    '''/''': 2,
				    '''%''': 2,
				    '''+''': 1,
				    '''-''': 1,
				}  # Priority of each operator
				UpperCAmelCase									=					len(lowerCamelCase_ ) if (len(lowerCamelCase_ ) > 7) else 7

				# Print table header for output
				print(
				    'Symbol'.center(8 ) ,				'Stack'.center(lowerCamelCase_ ) ,				'Postfix'.center(lowerCamelCase_ ) ,				sep=' | ' ,				)
				print('-' * (print_width * 3 + 7) )

				for x in infix:
								if x.isalpha() or x.isdigit():
												post_fix.append(lowerCamelCase_ )  # if x is Alphabet / Digit, add it to Postfix
								elif x == "(":
												stack.append(lowerCamelCase_ )  # if x is "(" push to Stack
								elif x == ")":  # if x is ")" pop stack until "(" is encountered
												while stack[-1] != "(":
																post_fix.append(stack.pop() )  # Pop stack & add the content to Postfix
												stack.pop()
								else:
												if len(lowerCamelCase_ ) == 0:
																stack.append(lowerCamelCase_ )  # If stack is empty, push x to stack
												else:  # while priority of x is not > priority of element in the stack
																while len(lowerCamelCase_ ) > 0 and priority[x] <= priority[stack[-1]]:
																				post_fix.append(stack.pop() )  # pop stack & add to Postfix
																stack.append(lowerCamelCase_ )  # push x to stack

								print(
								    x.center(8 ) ,				(''.join(lowerCamelCase_ )).ljust(lowerCamelCase_ ) ,				(''.join(lowerCamelCase_ )).ljust(lowerCamelCase_ ) ,				sep=' | ' ,				)  # Output in tabular format

				while len(lowerCamelCase_ ) > 0:  # while stack is not empty
								post_fix.append(stack.pop() )  # pop stack & add to Postfix
								print(
								    ' '.center(8 ) ,				(''.join(lowerCamelCase_ )).ljust(lowerCamelCase_ ) ,				(''.join(lowerCamelCase_ )).ljust(lowerCamelCase_ ) ,				sep=' | ' ,				)  # Output in tabular format

				return "".join(lowerCamelCase_ )  # return Postfix as str




def     lowercase__						(					lowerCAmelCase				:					Dict ) ->      List[Any]:






				"""simple docstring"""




				UpperCAmelCase									=					list(infix[::-1] )  # reverse the infix equation

				for i in range(len(lowerCamelCase_ ) ):
								if infix[i] == "(":
												UpperCAmelCase									=					''')'''  # change "(" to ")"
								elif infix[i] == ")":
												UpperCAmelCase									=					'''('''  # change ")" to "("

				return (infix_2_postfix(''.join(lowerCamelCase_ ) ))[
				    ::-1
				]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
			SCREAMING_SNAKE_CASE_    					=						input('''\nEnter an Infix Equation = ''')  # Input an Infix equation
			SCREAMING_SNAKE_CASE_    					=						''.join(Infix.split())  # Remove spaces from the input
			print('''\n\t''', Infix, '''(Infix) -> ''', infix_2_prefix(Infix), '''(Prefix)''')





"""simple docstring"""

def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      int:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )
    if n == 0:
        return 0
    UpperCAmelCase									=					float('-inf' )
    for i in range(1 ,				n + 1 ):
        UpperCAmelCase									=					max(
            lowerCAmelCase ,				prices[i - 1] + naive_cut_rod_recursive(n - i ,				lowerCAmelCase ) )

    return max_revue




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Dict:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					[float('-inf' ) for _ in range(n + 1 )]
    return _top_down_cut_rod_recursive(lowerCAmelCase ,				lowerCAmelCase ,				lowerCAmelCase )




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ,				lowerCAmelCase				:					list ) ->      int:






    """simple docstring"""




    if max_rev[n] >= 0:
        return max_rev[n]
    elif n == 0:
        return 0
    else:
        UpperCAmelCase									=					float('-inf' )
        for i in range(1 ,				n + 1 ):
            UpperCAmelCase									=					max(
                lowerCAmelCase ,				prices[i - 1] + _top_down_cut_rod_recursive(n - i ,				lowerCAmelCase ,				lowerCAmelCase ) ,				)

        UpperCAmelCase									=					max_revenue

    return max_rev[n]




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Optional[int]:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )

    # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
    # length 0.
    UpperCAmelCase									=					[float('-inf' ) for _ in range(n + 1 )]
    UpperCAmelCase									=					0

    for i in range(1 ,				n + 1 ):
        UpperCAmelCase									=					max_rev[i]
        for j in range(1 ,				i + 1 ):
            UpperCAmelCase									=					max(lowerCAmelCase ,				prices[j - 1] + max_rev[i - j] )

        UpperCAmelCase									=					max_revenue_i

    return max_rev[n]




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Union[str, Any]:






    """simple docstring"""




    if n < 0:
        UpperCAmelCase									=					F"n must be greater than or equal to 0. Got n = {n}"
        raise ValueError(lowerCAmelCase )

    if n > len(lowerCAmelCase ):
        UpperCAmelCase									=					(
            'Each integral piece of rod must have a corresponding price. '
            F"Got n = {n} but length of prices = {len(lowerCAmelCase )}"
        )
        raise ValueError(lowerCAmelCase )




def     lowercase__						(					) ->      Optional[int]:






    """simple docstring"""




    UpperCAmelCase									=					[6, 10, 12, 15, 20, 23]
    UpperCAmelCase									=					len(lowerCAmelCase )

    # the best revenue comes from cutting the rod into 6 pieces, each
    # of length 1 resulting in a revenue of 6 * 6 = 36.
    UpperCAmelCase									=					36

    UpperCAmelCase									=					top_down_cut_rod(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					bottom_up_cut_rod(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					naive_cut_rod_recursive(lowerCAmelCase ,				lowerCAmelCase )

    assert expected_max_revenue == max_rev_top_down
    assert max_rev_top_down == max_rev_bottom_up
    assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
   main()



