A Huffman tree, also known as a Huffman coding tree, is a fundamental concept in data structure and information theory. It is used for efficient data compression and decompression, making it an essential tool in many applications, including file compression, image compression, and network protocols.
Understanding Huffman Coding
Huffman coding is a lossless data compression algorithm that assigns variable-length codes to different characters based on their frequencies in the input. The more frequently a character occurs in the input, the shorter its corresponding code will be.
The Huffman tree is constructed based on the frequency of each character in the input. The tree is built bottom-up, starting with individual characters as leaves and combining them into higher-level nodes until a single root node is formed.
Building a Huffman Tree
To build a Huffman tree:
- Step 1: Calculate the frequency of each character in the input.
- Step 2: Create leaf nodes for each character and assign their frequencies.
- Step 3: Arrange all leaf nodes in ascending order of frequencies.
- Step 4: Take the two nodes with the lowest frequencies and combine them into a new internal node. Assign their sum as the frequency of this internal node.
- Step 5: Repeat Step 4 until there is only one node left. This remaining node becomes the root of the Huffman tree.
An Example
To illustrate how a Huffman tree is built, let’s consider an example where we have four characters (A, B, C, D) with corresponding frequencies (10, 15, 30, 45).
Step 1: Calculate the frequency of each character.
- A: 10
- B: 15
- C: 30
- D: 45
Step 2: Create leaf nodes for each character.
- A (10)
- B (15)
- C (30)
- D (45)
Step 3: Arrange leaf nodes in ascending order of frequencies.
- A (10)
- B (15)
- C (30)