7. The two problems below can be solved using graph coloring. For each problem, represent the situation with a graph, say whether you should be coloring vertices or edges and why, and use the coloring to solve the problem. a. Your Quidditch league has 5 teams. You will play a tournament next week in which every team will play every other team once. Each team can play at most one match each day, but there is plenty of time in the day for multiple matches. What is the fewest number of days over which the tournament can take place? FE b. Ten members of Math Club are driving to a math conference in a neighboring state. However, some of these students have dated in the past, and things are still a little awkward. Each student lists which other students they refuse to share a car with; these conflicts are recored in the table below. What is the fewest number of cars the club needs to make the trip? Do not worry about running out of seats, Just avoid the conflicts. Student: B CDEFIG H Conflicts: BEJ ADG HI BF Al D B CI EH ACFI Hint For (a), you will want the teams to be vertices and games to be edges. Which does it make sense to color?

Alice, a friend of Mr. Bernard’s, wants to compose a song. She asks Mr. Bernard for help. Although Mr. Barnard knows nothing about music, he finds that the sequence of notes in a numbered musical notation can be expressed as an FSM with input the alphabet {1, 2, 3, 4, 5, 6, 7} (“do”, “re”, “mi”, “fa”, “so”, “la”, “ti”). Alice wants to compose a song that contains the pattern “15” an even number of times. Please draw an FSM that only accepts a sequence of notes that satisfies the above pattern.   Note that you should provide a detailed description of the FSMs in your design to show how it works. Specifically, you should describe the meaning of each state.

#2

I need help with this code because I am struggling and I don't know what to do : question: you will develop a solver for the n-queens problem: n queens are to be placed on an n x n chessboard so that no pair of queens can attack each other. Recall that in chess, a queen can attack any piece that lies in the same row, column, or diagonal as itself. A brief treatment of this problem for the case where n = 8 is given below (from the 3rd edition of AIMA). N-queens is a useful test problem for search, with two main kinds of formulation. An incremental formulation involves operators that augment the state description, starting with an empty state; for the 8-queens problem, this means that each action adds a queen to the state. A complete-state formulation starts with all 8 queens on the board and moves them around. (In either case, the path cost is of no interest because only the final state counts.) The first incremental formulation one might try is the following, but (!) there are a very…