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Hazardous Huffman Trees

Due: Mar 03, 23:59 PM

Assignment Description

In this lab, you will be exploring a different tree application (Huffman Trees), which allow for efficient lossless compression of files. There are a lot of files in this lab, but you will only be modifying huffman_tree.cpp.

Lab Insight

Huffman encoding is a fundamental compression algorithms for data. Compressing data is a very powerful tool that can represent a given set of information in less space, thus allowing the data to be transferred more efficiently. Different types of compression can be seen within images formats like JPG(lossy) or PNG(lossless). It can also be seen in ZIP files for compressing multiple files. The concept of encoding data can be seen in future courses CS 438, Communication Networks, dealing with transferring large amounts of data, and CS 461, Computer Security, which deals with encoding data for a layer of privacy.

Getting Set Up

From your CS 225 git directory, run the following on EWS:

git fetch release
git merge release/lab_huffman -m "Merging initial lab_huffman files"

If you’re on your own machine, you may need to run:

git fetch release
git merge --allow-unrelated-histories release/lab_huffman -m "Merging initial lab_huffman files"

Upon a successful merge, your lab_huffman files are now in your lab_huffman directory.

The code for this activity resides in the lab_huffman/ directory. Get there by typing this in your working directory:

cd lab_huffman/

Video Intro

There is a video introduction for this lab! If you are interested in seeing a step-by-step execution of the Huffman Tree algorithms, please watch it:

The Huffman Encoding

In 1951, while taking an Information Theory class as a student at MIT, David A. Huffman and his classmates were given a choice by the professor Robert M. Fano: they can either take the final exam, or if they want to opt out of it they need to find the most efficient binary code. Huffman took the road less traveled and the rest they say is history.

Put simply, Huffman encoding takes in a text input and generates a binary code (a string of 0’s and 1’s) that represents that text. Let’s look at an example: Input message: “feed me more food”

Building the Huffman tree

Input: “feed me more food”

Step 1: Calculate frequency of every character in the text, and order by increasing frequency. Store in a queue.

r : 1 | d : 2 | f : 2 | m : 2 | o : 3 | 'SPACE' : 3 | e : 4

Step 2: Build the tree from the bottom up. Start by taking the two least frequent characters and merging them (create a parent node for them). Store the merged characters in a new queue:

SINGLE: f : 2 | m : 2 | o : 3 | 'SPACE' : 3 | e : 4

MERGED: rd : 3

Step 3: Repeat Step 2 this time also considering the elements in the new queue. ‘f’ and ‘m’ this time are the two elements with the least frequency, so we merge them:

SINGLE: o : 3 | 'SPACE' : 3 | e : 4

MERGED: rd : 3 | fm : 4

Step 4: Repeat Step 3 until there are no more elements in the SINGLE queue, and only one element in the MERGED queue:

SINGLE: e : 4

MERGED: rd : 3 | fm : 4 | o+SPACE : 6

MERGED: fm : 4 | o+SPACE : 6 | rde: 7

MERGED: rde: 7 | fmo+SPACE: 10

MERGED: rdefmo+SPACE: 17

From Text to Binary

Now that we built our Huffman tree, its time to see how to encode our original message “feed me more food” into binary code.

Step 1: Label the branches of the Huffman tree with a ‘0’ or ‘1’. BE CONSISTENT: in this example we chose to label all left branches with ‘0’ and all right branches with ‘1’. In the case of our visualizations, some of the nodes may be swapped for convenience of placement. However, any path with label ‘1’ is intended to be on the right side, and any path with label ‘0’ is intended to be on the left side.

Step 2: Taking one character at a time from our message, traverse the Huffman tree to find the leaf node for that character. The binary code for the character is the string of 0’s and 1’s in the path from the root to the leaf node for that character. For example: ‘f’ has the binary code: 100

So our message “feed me more food” becomes 10001010011111111010111111110111000001111111100110110001

From Binary Code to Text

We can also decode strings of 0’s and 1’s into text using our Huffman tree. What word does the code 00001001 translate to?

What About the Rest of the Alphabet?

Notice that in our example above, the Huffman tree that we built does not have all the alphabet’s letters; so while we can encode our message and some other words like “door” or “deer”, it won’t help us if we need to send a message containing a letter that’s not in the tree. For our Huffman encoding to be applicable in the real world we need to build a huffman tree that contains all the letters of the alphabet; which means instead of using “feed me more food” to build our tree, we should use a text document that contains all letters of the alphabet to build our Huffman tree. As a fun example, here is the Huffman tree that results when we use the text of the Declaration of Independence to build it.

Here is the Doxygen generated list of files and their uses.

Implement buildTree() and removeSmallest()

Your first task will be to implement the buildTree() function on a HuffmanTree. This function builds a HuffmanTree based on a collection of sorted Frequency objects. Please see the Doxygen for buildTree() for details on the algorithm. You also will probably want to consult the list of constructors for TreeNodes.

You should implement removeSmallest() first as it will help you in writing buildTree()!

Implement decode()

Your next task will be using an existing HuffmanTree to decode a given binary file. You should start at the root and traverse the tree using the description given in the Doxygen. Here is the Doxygen for decode().

You will probably find the Doxygen for BinaryFileReader useful here.

We’re using a standard stringstream here to build up our output. To append characters to it, use the following syntax:

ss << myChar;

Implement writeTree() and readTree()

Finally, you will write a function used for writing HuffmanTrees to files in an efficient way, and a function to read this efficiently stored file-based representation of a HuffmanTree.

Here is the Doxygen for writeTree() and the Doxygen for readTree().

You will probably find the Doxygen for BinaryFileWriter useful here.

Testing Your Code!

We’ve provided you with a collection of data files to help you explore Huffman encoding. Run the following command to download and extract the files. They will be in a newly-created data directory.

wget && tar -xf lab_huffman_data.tar && rm lab_huffman_data.tar

When you run make, two programs should be generated: encoder and decoder, with the following usages:

$ ./encoder
	./encoder input output treefile
		input: file to be encoded
		output: encoded output
		treefile: compressed huffman tree for decoding

$ ./decoder
	./decoder input treefile output
		input: file to be decoded
		treefile: compressed huffman tree to use for decoding
		output: decompressed file

Use your encoder to encode a file in the data directory, and then use your compressed file an the huffman tree it built to decode it again using the decoder. If diff-ing the files produces no output, your HuffmanTree should be working!

When testing, try using small files at first such as data/small.txt. Open it up and look inside. Imagine what the tree should look like, and see what’s happening when you run your code.

Now try running your code:

$ ./encoder data/small.txt output.dat treefile.tree
Printing generated HuffmanTree...
                                  ______________ 28 _____________
                   ______________/                               \______________
          ______ 11 _____                                                 ______ 17 _____
   ______/               \______                                   ______/               \______
s:5                           __ 6 __                         __ 8 __                         __ 9 __
                           __/       \__                   __/       \__                   __/       \__
                        y:3              3              l:4             i:4              4               :5
                                       /   \                                           /   \
                                    h:1     t:2                                      2       2
                                                                                    / \     / \
                                                                                 \n:1 r:1 o:1 a:1
Saving HuffmanTree to file...

You can also test under catch as usual by running:

make test && ./test

Submitting Your Work

The following files are used to grade this assignment:

  • huffman_tree.cpp
  • huffman_tree.h
  • partners.txt

All other files including any testing files you have added will not be used for grading.

Good luck!