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--------- ---------
a 5
b 2
r 2
c,d 2
And we have a partial tree:
d
/
root - c
Now we repeat the procedure. This time, however, we
have more than one choice. We could choose "b" and "r", or
"b" and "c,d" or "r" and "c,d". As far as the resulting file
is concerned, it makes no difference which one we choose.
The squeezed files length will be the same! Lets do it two
different ways just to see what happens.
character frequency character frequency
--------- --------- --------- ---------
a 5 a 5
b,r 4 c,d,r 4
c,d 2 b 2
Which gives:
b c r d
/ / / /
root - r root - d root - - c
And again:
character frequency character frequency
--------- --------- --------- ---------
c,d,b,r 6 c,d,b,r 6
a 5 a 5
Which gives:
d
/
/--c
/
/ b or: b r d
/ / / / /
root -- - r root - - - - c
ARC VERSION 2.20 PAGE - 34
And finally we combine these to get:
d
/
/--c
/
a / b or: a b r d
/ / / / / / /
root - - - - -r root - - - - - c
We end up with the following tables:
character frequency code1 code2
--------- --------- ----- -----
a 5 0 0
b 2 110 10
r 2 111 110
c 1 101 1111
d 1 100 1110
If you multiply the code length times the frequency for
each character and sum the results, you will get the files
squeezed length in bits. You will find that it is the same
in both cases. ARC will, however, always choose the option
which results in the shortest code lengths. ARC only allows
a maximum code length of 24 bits. Note also that there are a
total of only 13 bits on the left, but 14 on the right. This
also makes the length of the encoding table a bit shorter.
No pun intended.
Since we are building the codes two groups at a time,
the time that it takes to generate the codes is directly
proportional to the number of entries in the table. After
ARC finishes its analyze pass, you will notice a delay of a
second or two before ARC actually starts squeezing a file.