Q$1,$ Design an optimized algorithm for this problem using a Dynamic Programming or$/$and Greedy approach. You can use the example instance of this problem given in the problem statement, but you will need to prove that your algorithm works for any instance of this problem $($not only for the given example$).$ The design of your algorithm must include diagrams of your city showing every step in your algorithm, and short written step$-$by$-$step instructions explaining $($at the high level$)$ how your algorithm works. Show ALL your work to get credit. Algorithm designs using approaches other than Dynamic Programming or$/$and Greedy won$$t get credit for this homework assignment. Q$2,$ Create the pseudocode to solve all the instances of this problem based on your al$-$ gorithm from problem $1.$ Your pseudocode must use a Dynamic Programming or$/$and Greedy approach. Students writting code instead of pseudocode, or pseudocode that uses a different approach than the ones mentioned, won$$t get credit for this problem. Q$3,$ Find the T$($n$)$ function for your pseudocode provided in problem $2,$ solve the function using a step counting approach, and define the space and time complexity of your algorithm based on your computations from the T$($n$)$ function. Note that you need to use a Step Counting approach to compute complexity and time complexity for this problem. Show all your work, including summations to get credit. Q$4,$ Create a program, using your favorite programming lan$-$ guage, that implements your algorithm. To get credit for this problem students must provide some unit tests to test that your program performs as per your algorithm specifications. Cre$-$ ate this program in an online editor and share here the link to your program. Broken links or code that doesn$$t work as per your algorithm specifications won$$t get credit.