Our Range class, from Section 2.3.5, relies on the formula max(0, (stop start + step 1) // step) to compute the number of elements in the range. It is not immediately evident why this formula provides the correct calculation, even if assuming a positive step size. Justify this formula, in your own words

IN SECTION 2.3.3

class Range:

2 A class that mimic s the built-in range class.

3

4 def init (self, start, stop=None, step=1):

5 Initialize a Range instance.

6

7 Semantics is similar to built-in range class.

8

9 if step == 0:

10 raise ValueError( step cannot be 0 )

11

12 if stop is None: # special case of range(n)

13 start, stop = 0, start # should be treated as if range(0,n)

14

15 # calculate the effective length once

16 self. length = max(0, (stop start + step 1) // step)

17

18 # need knowledge of start and step (but not stop) to support getitem

19 self. start = start

20 self. step = step

21

22 def len (self):

23 Return number of entries in the range.

24 return self. length

25

26 def getitem (self, k):

27 Return entry at index k (using standard interpretation if negative).

28 if k < 0:

29 k += len(self) # attempt to convert negative index

30

31 if not 0 <= k < self. length:

32 raise IndexError( index out of range )

33

34 return self. start + k self. step