"Dirk Wangsadirdja" <d...@pensiun.com> wrote
I tested it and it works. But I dont understand why it works. Can
someone please explain it further? Thanks.
~n means the bitwise complement (or inverse) of n.
This simply means reversing every bit of n so that 1-> 0 and 0->1
This trick relies on the fact that negative numbers are stored
on computers using a thing called twos-complement (or
ones-complement sometimes) . This ensures tjhe leftmost bit
is always 1 which the PC uses to indicate a negative number.
Thus to represent -1 we take the bitwise inverse of 1 and add 1
1 = 0001 -> 1110 + 1 -> 1111
To get back we subtract 1 and then take the bitwise complement
1111-1 -> 1110 -> 0001
But with this trick we omit the initial add by 1 stage so
range(n) yields 0...n
But the inverse of 0000 is 1111 which is interpreted as -1 by Python
as above, so 0 maps to -1 in decimal!
and thus 1 (0001) becomes 1110 to which python does:
1110 subtracting 1 becomes 1101, and inverting gives 0010 = -2!
and so on.
So using ~ maps 0,1,2... to -1,-2,-3...
Very, very sneaky and the first time I've sen it done!
(because its so opaque I wouldn't actually recommend it,
most programmers would struggle to figure out what was going on
and probably think ~ was a typo for - I suspect)
See wikipedia for more on twos-complement, and the related trick ,
which is also used sometimes, of ones-complement.
--
Alan Gauld
Author of the Learn to Program web site
http://www.alan-g.me.uk/
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