Implementation Restrictions

You must use the permutation "used" array technique in your solution

There are three tiers of credit for this program. If you can get the code to run fast enough for $n=5,$ then that's

worth $80\%$ of the points. If you can get it to run fast enough for $n=6,$ that's worth $95\%$ of the points, and for

full credit, it has to run fast for $n=8.$

For most part of the code like for $n=5,$ you are not allowed to use ChatGPT. You must use the permutation

code discussed in the class and modify it to solve this problem. However, for optimizing the code for $n=6$ or

more, you must explore how ChatGPT can help you to optimize your code and you must submit a report with

your finding that should contain:

a$.$ Your code that runs fast enough for $n=5$

b$.$ Screenshot of the prompts and response from ChatGPT that helped you to improve your code to run

faster with $n=6$ or more.

c$.$ A short paragraph with few lines explaining how ChatGPT was able to helped you to optimize your

code.

It's completely okay if you don't find a solution that runs fast enough for $n=8.$ You will not lose much credit.

My expectation is that students will be able to solve the problem for $n=5.$ I am curious to see how many can

solve it for $n=6$ and $n=8.$

Your permutation must be a recursive code and should be based on the used array technique even after

optimization.

You are allowed to use only two global variables. No other global variables are allowed:

a$.$ One for array of garages

b$.$ One for the final set of permutation int array that stores the index of the garages that gave you the

minimum distance Read the problem completely and try to draw the example points provided in the sample input and s

how the result is calculated from those points, which points are finally connected to minimize the

distance.

Think, how can you use permutation and the "used" array approach to keep track which garage is us

in this process $($We have discussed how to perform permutations for any set objects in the permutati

lecture!. Think about, permutation of a string "CAT" could be achieved by creating permutation of t

numbers from $0$ to $2($as the length of the string is $3).$ If you get a permutation $1,2,0,$ it means the

permutation is "ATC", as $1$ is the index of $A,2$ is the index of T and C $0$ is the index of C $)$

Start your coding by loading the test cases and data and make sure you code is able to read them

properly before processing.