






"""simple docstring"""







def _a			(		_snake_case				,	_snake_case							):







      """simple docstring"""






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

      return max_revue

def _a			(		_snake_case				,	_snake_case							):







      """simple docstring"""






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

def _a			(		_snake_case				,	_snake_case				,	_snake_case							):







      """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(
                      _snake_case				,	prices[i - 1] + _top_down_cut_rod_recursive(n - i				,	_snake_case				,	_snake_case							)				,	)

            UpperCAmelCase          =	max_revenue

      return max_rev[n]

def _a			(		_snake_case				,	_snake_case							):







      """simple docstring"""






      _enforce_args(_snake_case				,	_snake_case							)

      # 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(_snake_case				,	prices[j - 1] + max_rev[i - j]							)

            UpperCAmelCase          =	max_revenue_i

      return max_rev[n]

def _a			(		_snake_case				,	_snake_case							):







      """simple docstring"""






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

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

def _a			(		):







      """simple docstring"""






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

      # 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(_snake_case				,	_snake_case							)
      UpperCAmelCase          =	bottom_up_cut_rod(_snake_case				,	_snake_case							)
      UpperCAmelCase          =	naive_cut_rod_recursive(_snake_case				,	_snake_case							)

      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()











"""simple docstring"""







import numpy as np

def _a			(		_snake_case							):







      """simple docstring"""






      return 1 / (1 + np.exp(-vector							))


if __name__ == "__main__":
  import doctest

  doctest.testmod()



