Name: Simran Singh partnered with Trishul Nagenalli
NetID: ss810 and tn74
Hours Spent: 6.0
Consulted With: Ramil
Resources Used: NONE
Impressions: I thought the assignment was really cool.
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Problem 1: Describe testing
We tested our files using the tester tab provided in the GUI to ensure that all provided files could be properly compressed
and decompressed. We checked the frequency count of different characters in the data and the compression rate to ensure that
a more highly concentrated frequency count for the file's characters did lead to better compression rates. We also used this
information when testing if tiff images or text files compressed better.

Following testing with given files, we ran our own tests with edge cases and ascertained compression rates
to see if they made sense. We compressed/decompressed a file that consisted entirely of a single repeated character. Because
there is only one character repeated several times, we expect compression to be very high since the Huffman tree is essentially
encoding that character with one bit. The compression rate for such a file should approach 88.5% (8:1 compression) as the length
of the file approaches infinity, we were getting compression rates just above above 80%

We next tested with files that had 0 and 1 character(s) respectively. We discovered that a file with one character worked fine
in our program though it did have a terrible compression rate. Rather than have the single character be represented by one
byte, it had to be represented by 7 so the Huffman tree could be stored before it. This is expected as Huffman compression
is rather unnecessary for a file that is only one character long. The empty file initially crashed our  program, which we
resolved by treating an empty file as an outlier case that would throw a HuffException.


Problem 2: Benchmark and analyze your code

For Calgary:
AlphFreq: 82
AlphFreq: 83
AlphFreq: 97
AlphFreq: 257
AlphFreq: 99
AlphFreq: 257
AlphFreq: 257
AlphFreq: 96
AlphFreq: 92
AlphFreq: 85
AlphFreq: 94
AlphFreq: 160
AlphFreq: 93
AlphFreq: 88
AlphFreq: 90
AlphFreq: 100
File Length: 111261
Compresion Rate: 0.34496364404418445
File Length: 768771
Compresion Rate: 0.41891317588451327
File Length: 610856
Compresion Rate: 0.40987183477229683
File Length: 102400
Compresion Rate: 0.4020340327674595
File Length: 377109
Compresion Rate: 0.39135717319910657
File Length: 21504
Compresion Rate: 0.38968904579093033
File Length: 246814
Compresion Rate: 0.3701141056364924
File Length: 53161
Compresion Rate: 0.37011862770935255
File Length: 82199
Compresion Rate: 0.37181512799721994
File Length: 46526
Compresion Rate: 0.3725706962857571
File Length: 38105
Compresion Rate: 0.3724690955323654
File Length: 513216
Compresion Rate: 0.44490770619148146
File Length: 39611
Compresion Rate: 0.44355947618704494
File Length: 71646
Compresion Rate: 0.4425078790430267
File Length: 49379
Compresion Rate: 0.44160906198704064
File Length: 93695
Compresion Rate: 0.43756642767941634



For Waterloo:
AlphFreq: 231
AlphFreq: 156
AlphFreq: 231
AlphFreq: 257
AlphFreq: 254
AlphFreq: 21
AlphFreq: 257
AlphFreq: 19
AlphFreq: 250
AlphFreq: 117
AlphFreq: 186
AlphFreq: 227
AlphFreq: 25
AlphFreq: 227
AlphFreq: 227
AlphFreq: 254
AlphFreq: 118
AlphFreq: 256
AlphFreq: 252
AlphFreq: 238
AlphFreq: 249
AlphFreq: 21
AlphFreq: 18
AlphFreq: 254
AlphFreq: 51
AlphFreq: 188
File Length: 262274
Compresion Rate: 0.06235844956038339
File Length: 65666
Compresion Rate: 0.07893517106787828
File Length: 262274
Compresion Rate: 0.0905214041008855
File Length: 65666
Compresion Rate: 0.08469689577361716
File Length: 65666
Compresion Rate: 0.08725708409443056
File Length: 65666
Compresion Rate: 0.14319395537669655
File Length: 2149096
Compresion Rate: 0.07761447368600294
File Length: 65666
Compresion Rate: 0.09495118878444653
File Length: 333442
Compresion Rate: 0.10647037730825781
File Length: 309388
Compresion Rate: 0.12919953994782707
File Length: 3706306
Compresion Rate: 0.2706247083773743
File Length: 65666
Compresion Rate: 0.26873833050910534
File Length: 65666
Compresion Rate: 0.2738776992858748
File Length: 163458
Compresion Rate: 0.2736700715416105
File Length: 262274
Compresion Rate: 0.2671126103193986
File Length: 1179784
Compresion Rate: 0.240192791383939
File Length: 307330
Compresion Rate: 0.23946940210880174
File Length: 786568
Compresion Rate: 0.22394345392431403
File Length: 1179784
Compresion Rate: 0.20904772550441664
File Length: 1498414
Compresion Rate: 0.21357569727156667
File Length: 65666
Compresion Rate: 0.21275712300746108
File Length: 65666
Compresion Rate: 0.21587134736817148
File Length: 65666
Compresion Rate: 0.21911408486387285
File Length: 1179784
Compresion Rate: 0.20408930748376952
File Length: 262274
Compresion Rate: 0.21189652330384412
File Length: 262274
Compresion Rate: 0.20967661297883722

For a fixed alphabet size and varying file length, the compression rate was largely unchanged. This data suggests
that file length does not heavily influence the compression rate. This held true for waterloo and calgary.
The alphabet size, however, did result in changes to the compression rate in both tests. The greater the alphabet size,
the slower the compression. This makes sense as file length does not influence the tree size and hence the compression,
but a wide range of characters increases the tree size, thus decreasing compression rate.
Conversely, for time (not shown, but was evaluated in huffviewer), the larger the file length,
the greater the time, and time was indifferent with respect to alphabet size. For time, file length matters as it takes
more time to traverse the bit stream, but the time to traverse to 0s and 1s is the same regardless of the actual value
of the bits.

Problem 3: Text vs. Binary

The Binary files compressed about 21%, while the text compressed about 44%. The Binary files have a wider variety of
character use than text files. This results in more branches in the tree and therefore less compression. As the data
clearly shows, the more variety in characters, the worse the compression.

Problem 4: Compressing compressed files

Generally, no extra compression is achived by compressing a compressed file again, for our case, it was consistently worse
by about .65% every time we tried to comrpess again for the Melville text specifically.
For Huffman coding, compressing an already compressed file is inefficient as the second compression will try to
compress the header that was written for the first compression. This results in larger files than the original compression.
This trend continues as you constantly attempt to compress files that are already compressed by a Huffman method.