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Adaptive Huffman is used for real time compression and decompression. My question is can we use it where we want to encode in real time,save all the encoded data and decode later any other time? Because I found that the Huffman tree keep changing for each new character.

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Yes. You replicate the building of the Huffman tree on the decoding side. So long as the process of updating the tree depends only on previous data, then it can be replicated exactly on the other end using the decoded data so far.