Part d is the most important part.

The lecture slide of the Water Jug problem

The question is not as big as it seems, it just explains a lot. No codes are required lem 2: [20] Stimulus Plan The government wants to implement a stimulus program and has allocated N million dollars for this. They placed the money into an account called Stimulus. Due to budgetary and legal constraints, it must spend this money in a rather specific way: The money must be spent in chunks of 1 million dollars. . . In the first and last year, it must spend exactly 1 million dollars. In any given year, the amount of money spent must be within 1 million dollars of the amount spent in the previous year. The spending for any given year may be non-positive (i.e., it can be 0, or even negative, for example, by levying a tax to increase the amount of money). The amount of money in the account (starting at N million dollars) can be non-positive in a given year (i.e., run a deficit) . . The goal is to minimize the number of years to make the balance in the account equal 0. (a) [4] Let's define each state as a tuple of three numbers, (1) the amount n in the account at the beginning of the current year, (2) the amount s that will be spent in the current year, and (3) the amount s' spent in the previous year: (n, s, s'). Define the initial state, the goal state, the step cost function, and the successor function. An example formulation is shown for the Water Jugs problem in the lecture slides. (b) [5] Is "the total amount of money in the account at the beginning of the current year" an admissible heuristic? Is it consistent? If not, provide a counterexample. (c) [5] Assume the amount of money spent in the current year is s million dollars. Is the heuristic function h = |s|-| admissible? Is it consistent? If not, provide a counterexample. (d) [6] Assume the amount of money remaining at the beginning of the current year is n million dollars. One possible admissible heuristic function can be defined as the smallest value of k such that Tk 2 nl. Tk is the k-th triangular number, which can be calculated as -1 l. For example, when n = 5, our heuristic value is 3, since T2