3. For the maze shown below, use graph theory to determine whether it is possible to get out from the Entrance to the Exit. Walk through each doorway exactly once and exit the maze with the shortest path/ walking distance. Give justification to your answer why you chose this theory? Compare your answer with another theory/approach? [10] Exit H G F E D B A Entrance

There are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?

Don't need to solve question 1. Use the graph in question 1 to solve question 3 part (a).  Thanks!

Consider navigating the maze shown below. N (М G 1. S 2. A 3. B 4. F 8. 5. H 6. D L 7. P (2 G 2 2 4 C E P 2 2 2 A S B FL The maze is represented as a graph with edge costs as shown on the edges. The edge cost is 1 for all edges where the cost is not shown. Let S be the initial state and G be the goal state. List the first 8 vertices expanded by Uniform Cost Search (enter the single letter label of a node). K 2 2 J 2 D H

Consider navigating the maze shown below. 3. 4. (z) 1. S 2. A 5. N L M G B F H 6. D 7. P 2 8. G 2 4 C E P 2 2 2 A S The maze is represented as a graph with edge costs as shown on the edges. The edge cost is 1 for all edges where the cost is not shown. Let S be the initial state and G be the goal state. List the first 8 vertices expanded by Uniform Cost Search (enter the single letter label of a node). B FL K 2 2 J 2 D H

Problem 2. 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? 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 recorded 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: A B C D E F…