Huffman Coding - Algorithm, Tree, Example, Methods, Encoding

By Anjnee Bhatnagar|Updated : August 3rd, 2022

Huffman Coding is a greedy technique to obtain an optimal solution to a problem. The Huffman coding is generally used for lossless data compression mechanisms. Sometimes, it is also called data compression encoding. It makes sure that there is no ambiguity while decoding the output bitstream.

Greedy algorithms use a heuristic approach to make an optimal choice at each stage while problem-solving to find a globally optimized solution. Before learning the Huffman coding algorithm, we will first see the greedy design technique, followed by the Huffman coding algorithm meaning and an example for better understanding.

What is Huffman Coding?

The Huffman coding is widely used in data compression techniques. It is used for both encoding and decoding. It uses a greedy approach to solve problems. The greedy approach allows us to solve a problem and find an optimal solution using the optimal substructure. An optimal substructure to a problem is achieved if an optimal solution can be created from the optimal solutions of its subproblems.

The Huffman coding uses a prefix rule that avoids ambiguity while decoding. The two steps involved in Huffman coding are:

  • Construct a Huffman tree from the input string or text or characters.
  • Assigning a Huffman code to each character by traversing the tree.

Huffman Coding Algorithm

The Huffman coding algorithm, as already discussed, follows the greedy design approach to arrive at an optimal solution. It uses a Huffman tree to encode and decode the data. A Huffman tree is created using the following steps:

  1. Create a leaf node for each character of the text.
  2. Arrange all the nodes in the increasing order of their frequency.
  3. Considering the first two nodes have the minimum frequency.
    -Create an internal node.
    -The frequency of this internal node is the sum of the frequency of the previous two nodes.
    -Make the first and second nodes the left and right children respectively of the newly created node.
  4. Repeat steps 2 and 3 until all the nodes form a tree. The tree thus obtained is a Huffman tree.

After the Huffman tree is created, each character is assigned a unique code. For decoding, the same Huffman tree is traversed.

Applications of Huffman Coding

We have thoroughly discussed the Huffman coding approach (Greedy Design Technique) and its algorithm. Now let us see the applications of the Huffman coding mechanism, which are as follows:

  • It is applied where a series of frequently occurring characters are used.
  • Used for transmitting the data in the form of text or fax etc.
  • Used by conventional compression formats like GZIP, PKZIP, etc.
  • Multimedia formats like JPEG, PNG, and MP3 use Huffman encoding.

Huffman Coding Example

We will see an example to understand how we should approach solving a problem using the Huffman code.

Question: Consider the following message: ppqqrrsspqrsprrsss?

Find the number of bits required for Huffman coding?

Answer: 36.


Frequencies: p-4 , q-3 , r-5 , s-6

Huffman Coding Example

p – 01, q – 00, r – 10, s – 11

The total bits required for Huffman coding is

∑ (frequency) x (bits) = 4(2) + 3(2) + 5(2) + 6(2) = 36

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Huffman Coding FAQs

  • The Huffman coding mechanism is a data compression technique that is used both for encoding data and decoding data. It makes use of a Huffman tree for encoding data and assigns a unique variable length code to each character. To decode the same Huffman tree is used.

  • The two major steps that are to be followed in the Huffman coding algorithm are as follows:

    • To build a Huffman tree from the input characters.
    • To traverse the Huffman tree to assign codes to the characters.
  • The drawback of using the Huffman coding algorithm is it achieves a lower compression ratio as compared to the lossy encoding techniques. Due to the same reason, it is not suitable for encoding digital images. And it is only suitable for encoding text-based files.

  • The advantage of Huffman coding is, that it uses less storage space for a frequently occurring character while at the same time using more storage space for the characters that occur rarely. This allows us to store the more frequently occurring characters at a low cost.

  • There are numerous applications of Huffman coding algorithm. It is often used in compression formats like BZIP2, GZIP, etc. Other multimedia formats like JPEG, PNG, and MP3 also make use of Huffman coding for precision.

  • The time complexity of the Huffman coding algorithm is O(nlogn), where n is the number of input characters. First, extract the minimum frequency element using extractMin() which takes O(n) time, and then call minHeapify() which takes O(log n) time. Therefore, the time complexity= O(nlogn).

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