





def 							_lowerCamelCase(  UpperCamelCase__    : int    ,       UpperCamelCase__    : list		)		->  Union[str, Any]:
    _enforce_args(UpperCamelCase__    ,       UpperCamelCase__		)
    if n == 0:
        return 0
    A       :       Dict							=						float('''-inf'''		)
    for i in range(1    ,       n + 1		):
        A       :       int							=						max(
            UpperCamelCase__    ,       prices[i - 1] + naive_cut_rod_recursive(n - i    ,       UpperCamelCase__		)		)

    return max_revue
def 							_lowerCamelCase(  UpperCamelCase__    : int    ,       UpperCamelCase__    : list		)		->  Any:
    _enforce_args(UpperCamelCase__    ,       UpperCamelCase__		)
    A       :       Union[str, Any]							=						[float('''-inf'''		) for _ in range(n + 1		)]
    return _top_down_cut_rod_recursive(UpperCamelCase__    ,       UpperCamelCase__    ,       UpperCamelCase__		)
def 							_lowerCamelCase(  UpperCamelCase__    : int    ,       UpperCamelCase__    : list    ,       UpperCamelCase__    : list		)		->  Any:
    if max_rev[n] >= 0:
        return max_rev[n]
    elif n == 0:
        return 0
    else:
        A       :       int							=						float('''-inf'''		)
        for i in range(1    ,       n + 1		):
            A       :       Tuple							=						max(
                UpperCamelCase__    ,       prices[i - 1] + _top_down_cut_rod_recursive(n - i    ,       UpperCamelCase__    ,       UpperCamelCase__		)    ,       )

        A       :       str							=						max_revenue

    return max_rev[n]
def 							_lowerCamelCase(  UpperCamelCase__    : int    ,       UpperCamelCase__    : list		)		->  str:
    _enforce_args(UpperCamelCase__    ,       UpperCamelCase__		)

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

    for i in range(1    ,       n + 1		):
        A       :       Any							=						max_rev[i]
        for j in range(1    ,       i + 1		):
            A       :       int							=						max(UpperCamelCase__    ,       prices[j - 1] + max_rev[i - j]		)

        A       :       Any							=						max_revenue_i

    return max_rev[n]
def 							_lowerCamelCase(  UpperCamelCase__    : int    ,       UpperCamelCase__    : list		)		->  Union[str, Any]:
    if n < 0:
        A       :       str							=						F'''n must be greater than or equal to 0. Got n = {n}'''
        raise ValueError(UpperCamelCase__		)

    if n > len(UpperCamelCase__		):
        A       :       List[str]							=						(
            '''Each integral piece of rod must have a corresponding price. '''
            F'''Got n = {n} but length of prices = {len(UpperCamelCase__		)}'''
        )
        raise ValueError(UpperCamelCase__		)
def 							_lowerCamelCase(  )		->  Optional[Any]:
    A       :       int							=						[6, 10, 12, 15, 20, 23]
    A       :       Optional[Any]							=						len(UpperCamelCase__		)

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

    A       :       Any							=						top_down_cut_rod(UpperCamelCase__    ,       UpperCamelCase__		)
    A       :       str							=						bottom_up_cut_rod(UpperCamelCase__    ,       UpperCamelCase__		)
    A       :       Any							=						naive_cut_rod_recursive(UpperCamelCase__    ,       UpperCamelCase__		)

    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'''






def 							_lowerCamelCase(  UpperCamelCase__    : Optional[int]    ,       UpperCamelCase__    : str		)		->  Optional[int]:
    A       :       Optional[int]							=						0
    A       :       str							=						len(UpperCamelCase__		) - 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

        A       :       Any							=						left + ((item - sorted_collection[left]) * (right - left)) // (
            sorted_collection[right] - sorted_collection[left]
        )

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

        A       :       Union[str, Any]							=						sorted_collection[point]
        if current_item == item:
            return point
        else:
            if point < left:
                A       :       Tuple							=						left
                A       :       Tuple							=						point
            elif point > right:
                A       :       Optional[Any]							=						right
                A       :       str							=						point
            else:
                if item < current_item:
                    A       :       Tuple							=						point - 1
                else:
                    A       :       Optional[Any]							=						point + 1
    return None
def 							_lowerCamelCase(  UpperCamelCase__    : Dict    ,       UpperCamelCase__    : str    ,       UpperCamelCase__    : Dict    ,       UpperCamelCase__    : List[str]		)		->  List[Any]:

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

    A       :       Dict							=						left + ((item - sorted_collection[left]) * (right - left)) // (
        sorted_collection[right] - sorted_collection[left]
    )

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

    if sorted_collection[point] == item:
        return point
    elif point < left:
        return interpolation_search_by_recursion(UpperCamelCase__    ,       UpperCamelCase__    ,       UpperCamelCase__    ,       UpperCamelCase__		)
    elif point > right:
        return interpolation_search_by_recursion(UpperCamelCase__    ,       UpperCamelCase__    ,       UpperCamelCase__    ,       UpperCamelCase__		)
    else:
        if sorted_collection[point] > item:
            return interpolation_search_by_recursion(
                UpperCamelCase__    ,       UpperCamelCase__    ,       UpperCamelCase__    ,       point - 1		)
        else:
            return interpolation_search_by_recursion(
                UpperCamelCase__    ,       UpperCamelCase__    ,       point + 1    ,       UpperCamelCase__		)
def 							_lowerCamelCase(  UpperCamelCase__    : Optional[int]		)		->  List[Any]:
    if collection != sorted(UpperCamelCase__		):
        raise ValueError('''Collection must be ascending sorted'''		)
    return True


if __name__ == "__main__":
     import sys
     snake_case_     =	0
     if debug == 1:
          snake_case_     =	[10, 30, 40, 45, 50, 66, 77, 93]
          try:
               __assert_sorted(collection)
          except ValueError:
               sys.exit("""Sequence must be ascending sorted to apply interpolation search""")
          snake_case_     =	67

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