How does the Huffman coding algorithm work?

The Huffman coding algorithm is a greedy algorithm used for data compression. It works by assigning variable-length codes to different characters in a given input text, with the goal of minimizing the total number of bits required to represent the text.

Here is a step-by-step explanation of how the Huffman coding algorithm works:

1. Calculate the frequency of occurrence for each character in the input text.
2. Create a priority queue or a min-heap based on the character frequencies. Each node in the priority queue will represent a character along with its frequency.
3. Repeat the following steps until there is only one node left in the priority queue:
a. Remove the two nodes with the lowest frequencies from the priority queue.
b. Create a new node with a frequency equal to the sum of the frequencies of the two removed nodes. Make this new node the parent of the two removed nodes.
c. Insert the new node back into the priority queue.
4. The remaining node in the priority queue is the root of the Huffman tree.
5. Traverse the Huffman tree from the root, assigning a '0' bit to each left branch and a '1' bit to each right branch.
6. Assign the resulting binary codes to each character based on their position in the Huffman tree. The binary code for each character is the sequence of '0' and '1' bits obtained by traversing the tree from the root to that character.
7. Encode the input text using the generated Huffman codes, replacing each character with its corresponding binary code.
8. The encoded text is the compressed representation of the original input text.

The Huffman coding algorithm ensures that characters with higher frequencies are assigned shorter codes, while characters with lower frequencies are assigned longer codes. This property allows for efficient compression, as frequently occurring characters are represented by fewer bits, reducing the overall size of the encoded text.