CMPUT 274 — Tangible Computing Fall 2018
Assignment 1 — Huffman Coding
This assignment will require you to know something about:
1. The basics of binary representation and number systems.
2. How characters are represented on a computer in binary.
3. Simple binary trees and how to traverse a tree from root to leaf.
4. The Huffman compression algorithm.
5. Classes in Python.
6. The BitReader and BitWriter classes implemented in bitio.py
7. The Pickle module in Python.
For this assignment, you will be writing programs that compress and decompress files using Huffman
codes. The compressor will be a command-line utility that encodes any file into a compressed version
with a .huf extension. The decompressor will be a web server that will let you directly browse compressed files, decoding them on-the-fly as they are being sent to your web browser.
Important: You are only responsible for implementing code in util.py. The steps below are a broad
overview of what will be done for the project; however, all of the code in huffman.py will be written
in class, and the code in all other files will be given for you to use.
Encoding a message using Huffman codes requires the following steps:
1. Read through the message and construct a frequency table counting how many times each symbol
(i.e. byte in our case) occurs in the input (huffman.make_freq_table does this).
2. Construct a Huffman tree (called tree) using the frequency table (huffman.make_tree does
3. Write tree to the output file, so that the recipient of the message knows how to decode it (you
will write the code to do this in util.write_tree).
4. Read each byte from the uncompressed input file, encode it using tree, and write the code sequence of bits to the compressed output file. The function huffman.make_encoding_table
takes tree and produces a dictionary mapping bytes to bit sequences; constructing this dictionary
once before you start coding the message will make your task much easier,
Decoding a message produced in this way requires the following steps:
5. Read the description of tree from the compressed file, thus reconstructing the original Huffman
tree that was used to encode the message (you will write the code to do this in util.read_tree
using the pickle module in Python to deserialize the tree.).
6. Repeatedly read coded bits from the file, decode them using tree (the util.decode_byte
function does this), and write the decoded byte to the uncompressed output.
You will implement the following functionality:
• The util.write_tree function to write Huffman trees into files using the pickle module
in Python to serialize the tree.
• The util.compress function to accomplish steps 3 and 4 above (using util.write_tree
for step 3).
• The util.decode_byte function that will return a single byte representing the next character
of the original text that is encoded in the BitReader corresponding to the compressed text.
• The util.read_tree function to read Huffman trees from files (step 5 above)
• The util.decompress function to accomplish steps 5 and 6 above (using util.read_tree
for step 5).
More details on each task are provided below. You will use the huffman.py module developed in
class to create Huffman trees and use them for encoding and decoding; this code is included with the
assignment. To perform bitwise input and output, the bitio.py module introduced in class is also
You will have to implement the functions described above in the util.py module. You should submit
only this module. The assignment is due Monday, October 15 at 11:55 pm. You can submit multiple
times; only the last submission will be graded. You should submit early to avoid being cut off because
the server is overloaded.
Representing Huffman Trees in Python
We represent trees as instances of the following classes in the huffman.py module:
• TreeLeaf: Leaves representing symbols (i.e. bytes, or numbers in the 0-255 range) as well as
the special “end-of-message” symbol, which occurs only once in each message, marking its end.
• TreeBranch: A branch, which in turn consists of two subtrees.
For example, consider the following Huffman tree, which has leaves for the symbols A, B, and the special
end-of-message symbol ⊗.
In Python, we would represent the above tree as
The symbol associated with each leaf is stored as a byte, which is an integer in the range 0–255. This is
why the symbol A is represented by its ASCII value 65, given by ord(’A’).
Representing Huffman Trees as Bit Sequences
As we saw above, we want to be able to read and write Huffman trees into files. Note that this is very
different from encoding a message using a Huffman tree; here we are concerned with representing the
tree itself. In this assignment, you will use the pickle module in Python to convert the tree from a
Python form to a serialized form that can be stored in a file.
Effectively, this means that you will convert the Tree class as it is stored in Python into a form that can
be compressed and stored into a file. Your read_tree and write_tree functions will use pickle
to convert between the Python representation of Huffman trees and the serialized representation. More
precisely, the read_tree function should take an instance of BitReader and use pickle to reconstruct a full tree according to the above format, and then return the tree. The write_tree function
should write a tree to the provided instance of BitWriter also using pickle.
Task I: Decompression
For this part of the assignment you will write code that reads a description of a Huffman tree from an
input stream, constructs the tree, and uses it to decode the rest of the input stream. The code we provide
will set up a simple web server that uses your decompression routines to serve compressed files to a web
The util.read_tree Function
You will first implement the read_tree function in the util.py module. It will have the following
’’’Read a description of a Huffman tree from the given compressed
tree stream, and use the pickle module to construct the tree object.
Then, return the root node of the tree itself.
tree_stream: The compressed stream to read the tree from.
A Huffman tree root constructed according to the given description.
The util.decode_byte Function
You will next implement the decode_tree function in the util.py module. It will have the following specification.
def decode_byte(tree, bitreader):
Reads bits from the bit reader and traverses the tree from
the root to a leaf. Once a leaf is reached, bits are no longer read
and the value of that leaf is returned.
bitreader: An instance of bitio.BitReader to read the tree from.
tree: A Huffman tree.
Next byte of the compressed bit stream.
The util.decompress Function
You will use the above read_tree and decode_byte functions to implement the following decompress
function in the util module.
def decompress(compressed, uncompressed):
’’’First, read a Huffman tree from the ’tree_stream’ using your
read_tree function. Then use that tree to decode the rest of the
stream and write the resulting symbols to the ’uncompressed’
compressed: A file stream from which compressed input is read.
uncompressed: A writable file stream to which the uncompressed
output is written.
You will have to construct a bitio.BitReader object wrapping the compressed stream to be able
to read the input one bit at a time. As soon as you decode the end-of-message symbol, you should stop
Task II: Compression
The code we provide will open an input file, construct a frequency table for the bytes it contains, and
generate a Huffman tree for that frequency table. You will write code that writes this tree to the output
file using the format described below, followed by the actual coded input.
The util.write_tree Function
You will first implement the write_tree function in the util.py module. It will have the following
def write_tree(tree, tree_stream):
’’’Write the specified Huffman tree to the given tree_stream
tree: A Huffman tree.
tree_stream: The binary file to write the tree to.
As noted in the specification, do not flush the bit writer when you’ve written the tree; the coded data will
be written out directly following the tree with no extraneous zero bits in between.
The util.compress Function
You will use the above write_tree function to implement the following compress function in the
def compress(tree, uncompressed, compressed):
’’’First write the given tree to the stream ’tree_stream’ using the
write_tree function. Then use the same tree to encode the data
from the input stream ’uncompressed’ and write it to ’compressed’.
If there are any partially-written bytes remaining at the end,
write 0 bits to form a complete byte.
Flush the bitwriter after writing the entire compressed file.
tree: A Huffman tree.
uncompressed: A file stream from which you can read the input.
compressed: A file stream that will receive the tree description
and the coded input data.
tree_stream: A file stream where the tree data should be dumped.
You will have to construct a bitio.BitWriterinstance wrapping the output stream compressed.
You will also find the huffman.make_encoding_table function useful.
Testing Your Code
Running the Web Server
Once you have implemented the decompress function, you will be able to run the webserver.py
script to serve compressed files. To try this out, change to the wwwroot/ directory included with the
assignment and run
Then open the url http://localhost:8000 in your web browser. If all goes well, you should
see a web page including an image. Compressed versions of the web page and the image are stored as
index.html.huf and huffman.bmp.huf in the wwwroot/ directory. The web server is using
your decompress function to decompress these files and serve them to your web browser.
Running the Compressor
Once you have implemented the util.compress function, you will be able to run the compress.py
script to compress files. For example, to add a new file somefile.pdf to be served by the web server,
copy it to the wwwroot/ directory, change to that directory, and run
python3 ../compress.py somefile.pdf
This will generate somefile.pdf.huf and you will be able to access the decompressed version at
the URL http://localhost:8000/somefile.pdf. You should download the decompressed
file and compare it to the original using the cmp command, to make sure there are no differences.
Please submit the following files as assignment1.tar.gz or assignment1.zip:
1. the modified util.py file containing your solution
2. your README, following the Code Submission Guidelines
Your archive when extracted should contain only these two files, which should not reside within a directory!
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