


'''simple docstring'''

def _SCREAMING_SNAKE_CASE      (A  , A  , A       )       ->       Optional[Any]:






       """simple docstring"""







       def count_of_possible_combinations(A       ) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              return sum(count_of_possible_combinations(target - item       ) for item in array       )

       return count_of_possible_combinations(_A       )

def _SCREAMING_SNAKE_CASE      (A  , A  , A       )       ->       str:






       """simple docstring"""







       def count_of_possible_combinations_with_dp_array(
           A  , A       ) -> int:
              if target < 0:
                     return 0
              if target == 0:
                     return 1
              if dp_array[target] != -1:
                     return dp_array[target]
              lowercase__      			= sum(
                  count_of_possible_combinations_with_dp_array(target - item  , _A       )
                  for item in array       )
              lowercase__      			= answer
              return answer

       lowercase__      			= [-1] * (target + 1)
       return count_of_possible_combinations_with_dp_array(_A  , _A       )

def _SCREAMING_SNAKE_CASE      (A  , A  , A       )       ->       Dict:






       """simple docstring"""







       lowercase__      			= [0] * (target + 1)
       lowercase__      			= 1

       for i in range(1  , target + 1       ):
              for j in range(_A       ):
                     if i - array[j] >= 0:
                            dp_array[i] += dp_array[i - array[j]]

       return dp_array[target]


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 lowerCamelCase							:   Tuple  						=	3
 lowerCamelCase							:   str  						=	5
 lowerCamelCase							:   Dict  						=	[1, 2, 5]
 print(combination_sum_iv(n, array, target))








def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)
      if n == 0:
            return 0
      lowerCamelCase__		:				Union[str, Any]    =  float("-inf"						)
      for i in range(1    ,					n + 1						):
            lowerCamelCase__		:				int    =  max(
                _A    ,					prices[i - 1] + naive_cut_rod_recursive(n - i    ,					_A						)						)

      return max_revue

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)
      lowerCamelCase__		:				int    =  [float("-inf"						) for _ in range(n + 1						)]
      return _top_down_cut_rod_recursive(_A    ,					_A    ,					_A						)

def       lowercase_		(		_A			:    int    ,					_A			:    list    ,					_A			:    list						):

      """simple docstring"""




      if max_rev[n] >= 0:
            return max_rev[n]
      elif n == 0:
            return 0
      else:
            lowerCamelCase__		:				Dict    =  float("-inf"						)
            for i in range(1    ,					n + 1						):
                  lowerCamelCase__		:				int    =  max(
                      _A    ,					prices[i - 1] + _top_down_cut_rod_recursive(n - i    ,					_A    ,					_A						)    ,					)

            lowerCamelCase__		:				List[Any]    =  max_revenue

      return max_rev[n]

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)

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

      for i in range(1    ,					n + 1						):
            lowerCamelCase__		:				Union[str, Any]    =  max_rev[i]
            for j in range(1    ,					i + 1						):
                  lowerCamelCase__		:				Any    =  max(_A    ,					prices[j - 1] + max_rev[i - j]						)

            lowerCamelCase__		:				Any    =  max_revenue_i

      return max_rev[n]

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      if n < 0:
            lowerCamelCase__		:				Optional[int]    =  F"n must be greater than or equal to 0. Got n = {n}"
            raise ValueError(_A						)

      if n > len(_A						):
            lowerCamelCase__		:				Optional[int]    =  (
                "Each integral piece of rod must have a corresponding price. "
                F"Got n = {n} but length of prices = {len(_A						)}"
            )
            raise ValueError(_A						)

def       lowercase_		(		):

      """simple docstring"""




      lowerCamelCase__		:				Optional[Any]    =  [6, 10, 12, 15, 20, 23]
      lowerCamelCase__		:				Dict    =  len(_A						)

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

      lowerCamelCase__		:				List[Any]    =  top_down_cut_rod(_A    ,					_A						)
      lowerCamelCase__		:				List[Any]    =  bottom_up_cut_rod(_A    ,					_A						)
      lowerCamelCase__		:				List[Any]    =  naive_cut_rod_recursive(_A    ,					_A						)

      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()


