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Friday 26 August 2022

[Solution] Second Second Meaning Meta Hacker Cup Qualification Round Solution



Morse code is a classic way to send messages, where each letter in an alphabet is substituted with a codeword: a unique sequence of dots and dashes. However, ignoring spaces, it's possible for a coded message to have multiple meanings. For example, ".....--.-.-.-..-.-.-...-.--." can be interpreted as either "HACKER CUP" or "SEE META RENT A VAN":
Beyond Morse code, a general set of codewords is an unambiguous encoding if any possible sequence of dots and dashes corresponds to either zero or exactly one sequence of codewords.
Given one codeword C_1 from a set of N distinct codewords, your task is to generate another N - 1 codewords C_2, ..., C_N to yield an unambiguous encoding. It can be shown that an answer always exists. If there are multiple answers, you may print any one of them.

Constraints

1 \le T \le 95 2 \le N \le 100 The length of C_1 is between 1 and 100, inclusive. The length of each C_2, ..., C_N must be between 1 and \mathbf{10}, inclusive.

Input Format

Input begins with an integer T, the number of test cases. For each case, there is first a line containing a single integer N. Then, there is a line containing the codeword C_1.

Output Format

For the ith case, output a line containing only "Case #i:", followed by N - 1 lines, the


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codewords C_2, ..., C_N, one per line.

Sample Explanation

In the first case, it can be shown that the codewords {".-.", "...", "---"} are an unambiguous encoding. Any sequence of dots and dashes can be interpreted if and only if it has a length that's a multiple of 3, and can be broken up into instances of the three length-3 codewords.
In the second case, it can be shown that the codewords {"-", "...", ".-", "..-"} are an unambiguous encoding. For instance, ".." has no possible interpretation, and ".-...--" can only be interpreted as ".- ... - -".
In the third case, it can be shown that the codewords {"..", "-", ".-"} are an unambiguous encoding. For any sequence of dots and dashes:
  • every odd group of dots followed by a dash can only be interpreted as repeated ".."s followed by a final ".-"
  • every even group of dots followed by a dash can only be interpreted as repeated ".."s followed by a final "-"
  • every group of dots not followed by a dash (i.e. at the end of the sequence), is interpretable if and only if there is an even number of dots
  • this leaves only groups of dashes, interpreted only as repeated "-"s

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