# What is the running time of the Huffman encoding algorithm?

## What is the running time of the Huffman encoding algorithm?

The running time of the Huffman encoding algorithm depends on the number of symbols in the input and the frequency distribution of those symbols. In general, the algorithm has a time complexity of O(n log n), where n is the number of symbols.

The basic steps of the Huffman encoding algorithm involve constructing a binary tree, known as the Huffman tree, based on the frequency of occurrence of each symbol. This construction process typically involves repeatedly merging two nodes with the lowest frequencies until a single tree is formed.

The time complexity of constructing the Huffman tree is O(n log n) in the worst case, where n is the number of symbols. This is because each merge operation takes O(log n) time, and there are n-1 merge operations required to build the tree.

After constructing the Huffman tree, the encoding process involves traversing the tree to assign binary codes to each symbol. The time complexity of this step is O(n), as each symbol needs to be visited once to determine its code.

Therefore, the overall running time of the Huffman encoding algorithm is O(n log n), where n is the number of symbols. However, it is worth noting that the actual running time can vary depending on the implementation and the specific characteristics of the input symbol frequencies.

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