In Robotics, Hill Climbing can often help a robot navigate its physical environment. In this problem, consider the environment presented on the right, where S is the s tart state and G is the goal state. Solve the following problems. (Feel free to use computational tools for assistance, but no need to submit your code.) Note that this environment consists of only convex polygons. a. Let us suppose that this environment is drawn to scale and that all the states in this environment are represented by Euclidean (x,y)-coordinates. Then, from the robot's perspective, describe (1) how many states there are, and (2) what they are. b. Run a Hill Climbing agent on this environment. You can either use the Hill Climbing Java code that we have provided during discussion sections, or write your own Python code, etc. Does your agent get stuck in a local optimum? In general, is it possible for any Hill Climbing agent to get stuck in a local optimum in such an environment? How about a convex environment (i.e. where the objective surface is convex)? c. Now, modify your environment so that some of the polygons become nonconvex. Then, run your Hill Climbing agent again. Does your agent get stuck in a local optimum this time? d. Now, instead of the default "step size" of 1 , run your Hill Climbing agent again but this time with a different step size of k - and we may customarily call this step size k a hyperparameter. (We will talk more about hyperparameters for the rest of the semester.) Try a few different k values at your own disposal; just make sure that k is a positive integer greater than 1. Can you find a best k-value for which your Hill Climbing agent is guaranteed to escape local optimum? In general for Hill Climbing, is it possible to always find such a k for every environment, convex or nonconvex