Question

Huffman Coding

Huffman coding is a lossless data compression algorithm. The idea is to assign variable- length codes to input characters; lengths of the assigned codes are based on the frequencies of corresponding characters. The most frequent character gets the smallest code and the least frequent character gets the largest code.

The variable-length codes assigned to input characters are Prefix Codes, means the codes (bit sequences) are assigned in such a way that the code assigned to one character is not prefix of code assigned to any other character. This is how Huffman Coding makes sure that there is no ambiguity when decoding the generated bit stream.

In this project, you will be using a priority queue and a binary tree of your design to implement a file compression/uncompression algorithm called "Huffman Coding".
Your program will read a text file and compress it using your implementation of the Huffman coding algorithm found in the explanation. The compressed text will be written to a file. That compressed file will be then be read back by your program and uncompressed. The uncompressed text will then be written to a third file. The uncompressed text file should of course match the original text file.

Summary of Processing

• Read the specified file and count the frequency of all characters in the file.

• Create the Huffman coding tree based on the frequencies.

• Create the table of encodings for each character from the Huffman coding tree.

• Encode the file and output the encoded/compressed file.

• Read the encoded/compressed file you just created, decode it and output the

  decoded file.

Answer 1

Prefix Codes, means the codes (bit sequences) are assigned in such a way that the code assigned to one character is not the prefix of code assigned to any other character.This is how Huffman Coding makes sure that there is no ambiguity when decoding the generated bitstream.Let us understand prefix codes with a counter example.Let there be four characters a, b, c and d, and their corresponding variable length codes be 00, 01, 0 and 1.This coding leads to ambiguity because code assigned to c is the prefix of codes assigned to a and b.If the compressed bit stream is 0001, the de-compressed output may be “cccd” or “ccb” or “acd” or “ab”.There are mainly two major parts in Huffman Coding1) Build a Huffman Tree from input characters...................

Steps to build Huffman Tree
Input is an array of unique characters along with their frequency of occurrences and output is Huffman Tree.

1. Create a leaf node for each unique character and build a min heap of all leaf nodes (Min Heap is used as a priority queue. The value of frequency field is used to compare two nodes in min heap. Initially, the least frequent character is at root)

2. Extract two nodes with the minimum frequency from the min heap.

3. Create a new internal node with a frequency equal to the sum of the two nodes frequencies. Make the first extracted node as its left child and the other extracted node as its right child. Add this node to the min heap.

4. Repeat steps#2 and #3 until the heap contains only one node. The remaining node is the root node and the tree is complete.

Let us understand the algorithm with an example:

character   Frequency
    a            5
    b           9
    c           12
    d           13
    e           16
    f           45

Step 1. Build a min heap that contains 6 nodes where each node represents root of a tree with single node.

Step 2 Extract two minimum frequency nodes from min heap. Add a new internal node with frequency 5 + 9 = 14.

Now min heap contains 5 nodes where 4 nodes are roots of trees with single element each, and one heap node is root of tree with 3 elements

character           Frequency
       c               12
       d               13
 Internal Node         14
       e               16
       f                45

Step 3: Extract two minimum frequency nodes from heap. Add a new internal node with frequency 12 + 13 = 25

Step 4: Extract two minimum frequency nodes. Add a new internal node with frequency 14 + 16 = 30

Steps to print codes from Huffman Tree:
Traverse the tree formed starting from the root. Maintain an auxiliary array. While moving to the left child, write 0 to the array. While moving to the right child, write 1 to the array. Print the array when a leaf node is encountered.

The codes are as follows:

character   code-word
    f          0
    c          100
    d          101
    a          1100
    b          1101
    e          111