
"""simple docstring"""

import sys




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






				"""simple docstring"""




				UpperCAmelCase									=					len(lowercase__ )
				UpperCAmelCase									=					[[0 for x in range(lowercase__ )] for x in range(lowercase__ )]
				UpperCAmelCase									=					[[0 for x in range(lowercase__ )] for x in range(lowercase__ )]

				for chain_length in range(2 ,				lowercase__ ):
								for a in range(1 ,				n - chain_length + 1 ):
												UpperCAmelCase									=					a + chain_length - 1

												UpperCAmelCase									=					sys.maxsize
												for c in range(lowercase__ ,				lowercase__ ):
																UpperCAmelCase									=					(
																    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
																)
																if cost < matrix[a][b]:
																				UpperCAmelCase									=					cost
																				UpperCAmelCase									=					c
				return matrix, sol




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






				"""simple docstring"""




				if i == j:
								print('A' + str(lowercase__ ) ,				end=' ' )
				else:
								print('(' ,				end=' ' )
								print_optiomal_solution(lowercase__ ,				lowercase__ ,				optimal_solution[i][j] )
								print_optiomal_solution(lowercase__ ,				optimal_solution[i][j] + 1 ,				lowercase__ )
								print(')' ,				end=' ' )




def     lowercase__						(					) ->      str:






				"""simple docstring"""




				UpperCAmelCase									=					[30, 35, 15, 5, 10, 20, 25]
				UpperCAmelCase									=					len(lowercase__ )
				# Size of matrix created from above array will be
				# 30*35 35*15 15*5 5*10 10*20 20*25
				UpperCAmelCase			,							UpperCAmelCase									=					matrix_chain_order(lowercase__ )

				print('No. of Operation required: ' + str(matrix[1][n - 1] ) )
				print_optiomal_solution(lowercase__ ,				1 ,				n - 1 )


if __name__ == "__main__":
			main()





"""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()



