Huffman coding is a popular algorithm used for lossless data compression. It is based on the concept of Huffman trees, which are binary trees used to encode characters or symbols into variable-length bit sequences. The algorithm assigns shorter codes to frequently occurring characters and longer codes to less frequent characters, ensuring an efficient encoding scheme.

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

1. Calculate the frequency of occurrence for each character in the input data.

2. Create a leaf node for each character, storing the character itself and its frequency.

3. Create a priority queue (min-heap) and insert all the leaf nodes into it based on their frequencies.

4. Repeat the following steps until there is only one node left in the priority queue:

a. Extract the two nodes with the lowest frequencies from the priority queue. These nodes will become the left and right children of a new internal node.

b. Create a new internal node with a frequency equal to the sum of the frequencies of the extracted nodes. Set the extracted nodes as the left and right children of the new node.

c. Insert the new node back into the priority queue.

5. The last remaining node in the priority queue is the root of the Huffman tree.

6. Traverse the Huffman tree from the root, assigning '0' to the left child edges and '1' to the right child edges.

7. Assign the corresponding bit sequences to each character based on their positions in the tree, where the path from the root to a character is the sequence of '0' and '1' obtained during the tree traversal.

After constructing the Huffman tree and assigning the bit sequences to each character, the original data can be encoded by replacing each character with its corresponding bit sequence. This results in a compressed representation of the data. To decode the data, the Huffman tree is used to traverse the bit sequence and reconstruct the original characters.

Huffman coding achieves data compression by assigning shorter codes to frequently occurring characters, which reduces the overall number of bits required to represent the data. Conversely, less frequent characters are assigned longer codes, but the impact on the overall compression is minimal.

The time complexity of the Huffman coding algorithm is O(n log n), where n is the number of unique characters in the input data. This is due to the construction of the Huffman tree, which involves repeatedly extracting and inserting nodes into the priority queue. However, once the Huffman tree is constructed, encoding and decoding are performed in linear time based on the length of the input data.

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