$1.$ Consider a file that uses the following list of symbols with the corresponding frequencies:

Find an optimal prefix code based on Huffman's algorithm $($using the symbols $0$ and $1$ only$).$ Work out the code by drawing the tree and then describing the mapping from symbols to bit strings.

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$2.$ In general, are Huffman codes unique? That is$,$ for a given set of letters and corresponding frequencies is there a unique Huffman encoding? Note that different letters may have the same frequency in the general case. If yes, justify. Otherwise provide a counterexample.