# [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 $i$th case, output a line containing only "Case #i:", followed by $N - 1$ lines, the

👇👇👇👇👇

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

## No comments:

## Post a Comment