How to Efficiently Store Huffman Trees for Incremental Encoding?

Efficient Storage of Huffman Trees

When implementing Huffman encoding/decoding, it is crucial to find an efficient way to store the Huffman tree to minimize the size of the output file.

Two Scenarios

There are two scenarios to consider:

• Single Tree Storage: When the entire file is processed at once, only one tree needs to be stored.
• Incremental Tree Storage: When processing large data in chunks, a new tree needs to be stored for each chunk. In this case, saving space is important.

Proposed Solution

For incremental tree storage, a bit-based approach is recommended:

1. Leaf Nodes: Output 1 bit N-bit character/byte.
2. Non-Leaf Nodes: Output 0 bit, then encode both child nodes recursively.

Decoding

Decoding is done as follows:

1. Read 1 bit. If 1, read N bits and return a new node with no children.
2. If 0, decode left and right child nodes and return a new node with no value.

Advantages

• The tree size can be calculated in advance.
• It removes the need to store frequencies, which are not essential for decoding.
• It allows for efficient encoding and decoding.

Evaluation

For a concrete example of "AAABBBCCCDE," the resulting output using this approach would be:

001A1B001B1C1D01E = 59 bits (Tree)
000110010111 = 18 bits (Data)
Total: 77 bits = 10 bytes

While efficient, it's important to note that for very small data, the overhead of storing the tree may outweigh any savings.

The above is the detailed content of How to Efficiently Store Huffman Trees for Incremental Encoding?. For more information, please follow other related articles on the PHP Chinese website!