There are four problems on the final.Note: Recall that there is no collaboration on the final.Problem 8.1. A hospital is trying to schedule their doctors for night shifts over the next nnights. There are d doctors. Each doctor i can only work certain nights Pi due to personalconstraints. For night k, the hospital needs exactly sk doctors to do the night shift. To befair, the hospital doesn’t want any doctor to do more than m night shifts.Give a polynomial-time algorithm to determine whether the hospital can schedule theirdoctors so that all the constraints are met. If the hospital can, your algorithm should alsooutput for each doctor the list of its night shifts.Problem 8.2. Let M2C be the following problem. Given a 2CNF formula φ and an integerk, decide if φ has a satisfying assignment with at least k variables set to true. In other words:M2C = {(φ, k) : φ is a 2CNF which has a satisying assignment with ≥ k variables true}.For example, consider φ = (x ∨ y) ∧ (y ∨ z). We have that (φ, 2) ∈ M2C becauseyou can set x and y to true and z to false, but (φ, 3) 6∈ M2C.Give a polynomial-time reduction from CLIQUE to M2C. Prove that the reduction iscorrect.(Hint: It may be useful to notice that a set of nodes C is a clique if and only if for every{i, j} which is not an edge, at least one o代写polynomial-time作业、代做2CNF formula作业、代写c/c++，Python编程语言作业、Jaf i and j is not in C.)Problem 8.3. For your co-op you are developing the next state-of-the-art flight searchengine. You have the list of all n daily flights in the world. For each flight you have startingcity, destination city, departure time, arrival time, and price. (The arrival time is alwaysafter the departure time.) A customer currently at city cs wants to get to city cd. It is nowtime ct.1. Describe an algorithm to compute the earliest possible time the customer can arriveat destination, using any number of flights and at any cost.2. Same as 1., but now the customer won’t pay more than cp in total for the trip.3. Same as 2., but in addition the customer won’t do more than cf flights. (Note youhave both a constraint on the price and on the number of flights.)Your running time should be polynomial in n.Problem 8.4. Starting with an empty AA tree, you do the following operations in order:insert(3), insert(5), insert(1), insert(2), insert(7), insert(8), insert(6), insert(4), delete(2),delete(6). Draw the tree after each insertion and deletion, including the levels of the nodes.(Note that insertion and deletion call other functions. You are only required to draw the treeat the end of insertion and deletion; but feel free to draw intermediate trees for convenience.)60转自：http://www.7daixie.com/2019042536756596.html
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