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hackercup / 2022 /quals /second_meaning_sol.md
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2022 Problems
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An unambiguous encoding is synonymous with a uniquely decodable code.

One approach is to use the fact that prefix codes, i.e. codes where no whole codeword is a prefix of any other codeword, are uniquely decodable. For instance, if (C_1) starts with a dash, then output the prefix code [.-, ..-, ...-, etc.], else output the prefix code [-., --., ---., etc.].

Doing so, (C_1) cannot possibly be a prefix of the other codewords (and vice versa) due to its differing first index. This yields a solution where (|C_i| \le N), though there are other approaches that take advantage of the generous length limit.

See David Harmeyer's solution video here.