Potential incorrect calculation of Auxiliary mtable

[utkarshmttl]

For k=12, p=0.5, alpha=0.1:

The (unadjusted) mtable: [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4]

For this case, the blocks should be: [0, 0, 0, 1 | 1, 1, 2 | 2, 3 | 3, 3, 4]

which implies that block sizes should be [4, 3, 2, 3]

which is also as described in the paper's Table 3 on page 5.

However, the behaviour is different using the code:

This seems to be because inside the function compute_aux_mtable(mtable) in fairsearchcore/mtable_generator.py, the loop for position in range(1, len(mtable)): at line 69 goes from range(1,len(mtable) when probably it should go from range(1,len(mtable)+1.

Another case- For k=10, p=0.5, alpha=0.1:

The (unadjusted) mtable: [0, 0, 0, 1, 1, 1, 2, 2, 3, 3]

For this case, the blocks should be: [0, 0, 0, 1 | 1, 1, 2 | 2, 3 | 3]

In this case, should there be

1. three blocks with sizes [4, 3, 2]
   (in this case the problem is maxProtected would be 4+3+2 = 9, missing 1 candidate as total candidates should be 10.)
   or
2. three blocks with sizes [4, 3, 3]
   or
3. four blocks with sizes [4, 3, 2, 1].
   (in this case the problem is that since m(k=10) = 3, total blocks are expected to be 3 and not 4?)

In code behaviour as per point 1 is seen:

The change mentioned above (changing the range of loop to include last element) solves the first case (k=12) but not the second case (k=10), for which appropriate changes might need to be made considering what is the expected behaviour - one of points 1, 2 or 3.