To save even more data, replace every symbol with A. Then just store the amount of As.
Would it be better to use A's and B's? We could half the necessary length of a symbol by assigning a certain combination of A's and B's to a symbol. And if characters take up too much space we could use 1's and 0's instead!
Then we could make a language where the letters are equivalent to the number of As
To save sending the tree every time, we could just have a fixed layout of letters and symbols. This would have the advantage that we could put them in order, which would be easier to work with.
Before I opened this article I thought "I bet they just learned what Huffman Encoding is" and I stand my hypothesis. It's an extremely fun compression algorithm as it's very trivial to comprehend and reason about... it's straightforward enough you can write it yourself!
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