

'''simple docstring'''



def    a__       (  a__      ,    a__						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      0
     __SCREAMING_SNAKE_CASE     =      len(a__						) - 1

     while left <= right:
          # avoid divided by 0 during interpolation
          if sorted_collection[left] == sorted_collection[right]:
               if sorted_collection[left] == item:
                    return left
               else:
                    return None

          __SCREAMING_SNAKE_CASE     =      left + ((item - sorted_collection[left]) * (right - left)) // (
              sorted_collection[right] - sorted_collection[left]
          )

          # out of range check
          if point < 0 or point >= len(a__						):
               return None

          __SCREAMING_SNAKE_CASE     =      sorted_collection[point]
          if current_item == item:
               return point
          else:
               if point < left:
                    __SCREAMING_SNAKE_CASE     =      left
                    __SCREAMING_SNAKE_CASE     =      point
               elif point > right:
                    __SCREAMING_SNAKE_CASE     =      right
                    __SCREAMING_SNAKE_CASE     =      point
               else:
                    if item < current_item:
                         __SCREAMING_SNAKE_CASE     =      point - 1
                    else:
                         __SCREAMING_SNAKE_CASE     =      point + 1
     return None







def    a__       (  a__      ,    a__      ,    a__      ,    a__						):




     """simple docstring"""


     if sorted_collection[left] == sorted_collection[right]:
          if sorted_collection[left] == item:
               return left
          else:
               return None

     __SCREAMING_SNAKE_CASE     =      left + ((item - sorted_collection[left]) * (right - left)) // (
         sorted_collection[right] - sorted_collection[left]
     )

     # out of range check
     if point < 0 or point >= len(a__						):
          return None

     if sorted_collection[point] == item:
          return point
     elif point < left:
          return interpolation_search_by_recursion(a__      ,    a__      ,    a__      ,    a__						)
     elif point > right:
          return interpolation_search_by_recursion(a__      ,    a__      ,    a__      ,    a__						)
     else:
          if sorted_collection[point] > item:
               return interpolation_search_by_recursion(
                   a__      ,    a__      ,    a__      ,    point - 1						)
          else:
               return interpolation_search_by_recursion(
                   a__      ,    a__      ,    point + 1      ,    a__						)







def    a__       (  a__						):




     """simple docstring"""


     if collection != sorted(a__						):
          raise ValueError("""Collection must be ascending sorted"""						)
     return True


if __name__ == "__main__":
  import sys
  UpperCAmelCase :       Any			   =     0
  if debug == 1:
    UpperCAmelCase :       int			   =     [1_0, 3_0, 4_0, 4_5, 5_0, 6_6, 7_7, 9_3]
    try:
      __assert_sorted(collection)
    except ValueError:
      sys.exit('Sequence must be ascending sorted to apply interpolation search')
    UpperCAmelCase :       Any			   =     6_7

  UpperCAmelCase :       List[str]			   =     interpolation_search(collection, target)
  if result is not None:
    print(f"""{target} found at positions: {result}""")
  else:
    print('Not found')









'''simple docstring'''



def    a__       (  a__      ,    a__						):




     """simple docstring"""


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

     return max_revue







def    a__       (  a__      ,    a__						):




     """simple docstring"""


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







def    a__       (  a__      ,    a__      ,    a__						):




     """simple docstring"""


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

          __SCREAMING_SNAKE_CASE     =      max_revenue

     return max_rev[n]







def    a__       (  a__      ,    a__						):




     """simple docstring"""


     _enforce_args(a__      ,    a__						)

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

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

          __SCREAMING_SNAKE_CASE     =      max_revenue_i

     return max_rev[n]







def    a__       (  a__      ,    a__						):




     """simple docstring"""


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

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







def    a__       (  ):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      [6, 10, 12, 15, 20, 23]
     __SCREAMING_SNAKE_CASE     =      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.
     __SCREAMING_SNAKE_CASE     =      36

     __SCREAMING_SNAKE_CASE     =      top_down_cut_rod(a__      ,    a__						)
     __SCREAMING_SNAKE_CASE     =      bottom_up_cut_rod(a__      ,    a__						)
     __SCREAMING_SNAKE_CASE     =      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()






