def lowerCamelCase  (       SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE     ):
    '''simple docstring'''







    __UpperCamelCase					:Tuple        =		0
    __UpperCamelCase					:Tuple        =		len(SCREAMING_SNAKE_CASE     ) - 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

        __UpperCamelCase					:Union[str, Any]        =		left + ((item - sorted_collection[left]) * (right - left)) // (
            sorted_collection[right] - sorted_collection[left]
        )

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

        __UpperCamelCase					:Optional[int]        =		sorted_collection[point]
        if current_item == item:
            return point
        else:
            if point < left:
                __UpperCamelCase					:List[Any]        =		left
                __UpperCamelCase					:str        =		point
            elif point > right:
                __UpperCamelCase					:Union[str, Any]        =		right
                __UpperCamelCase					:Optional[Any]        =		point
            else:
                if item < current_item:
                    __UpperCamelCase					:Any        =		point - 1
                else:
                    __UpperCamelCase					:Optional[Any]        =		point + 1
    return None



def lowerCamelCase  (       SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE     ):
    '''simple docstring'''







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

    __UpperCamelCase					:Union[str, Any]        =		left + ((item - sorted_collection[left]) * (right - left)) // (
        sorted_collection[right] - sorted_collection[left]
    )

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

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



def lowerCamelCase  (       SCREAMING_SNAKE_CASE     ):
    '''simple docstring'''







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


if __name__ == "__main__":
    import sys
    __lowercase										= 0
    if debug == 1:
        __lowercase										= [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''')
        __lowercase										= 67

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






def lowerCamelCase  (       SCREAMING_SNAKE_CASE     ):
    '''simple docstring'''







    if not grid or not grid[0]:
        raise TypeError('''The grid does not contain the appropriate information'''     )

    for cell_n in range(1  ,      len(grid[0]     )     ):
        grid[0][cell_n] += grid[0][cell_n - 1]
    __UpperCamelCase					:Union[str, Any]        =		grid[0]

    for row_n in range(1  ,      len(SCREAMING_SNAKE_CASE     )     ):
        __UpperCamelCase					:Optional[int]        =		grid[row_n]
        __UpperCamelCase					:Dict        =		fill_row(SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE     )
        __UpperCamelCase					:Any        =		grid[row_n]

    return grid[-1][-1]



def lowerCamelCase  (       SCREAMING_SNAKE_CASE  ,      SCREAMING_SNAKE_CASE     ):
    '''simple docstring'''







    current_row[0] += row_above[0]
    for cell_n in range(1  ,      len(SCREAMING_SNAKE_CASE     )     ):
        current_row[cell_n] += min(current_row[cell_n - 1]  ,      row_above[cell_n]     )

    return current_row


if __name__ == "__main__":
    import doctest

    doctest.testmod()





