Consider a set of movies M1, M2, ... , Mk. There is a set of customers, each one of which indicates the two movies they would like to see this weekend. Movies are shown on Saturday evening and Sunday evening. Multiple movies may be screened at the same time. You must decide which movies should be televised on Saturday and which on Sunday, so that every customer gets to see the two movies they desire. Is there a schedule where each movie is shown at most once? Design an efficient algorithm to find such a schedule if one exists.
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- Three prisoners have been sentenced to long terms in prison, but due to over crowed conditions, one prisoner must be released. The warden devises a scheme to determine which prisoner is to be released. He tells the prisoners that he will blindfold them and then paint a red dot or blue dot on each forehead. After he paints the dots, he will remove the blindfolds, and a prisoner should raise his hand if he sees at least one red dot on the other two prisoners. The first prisoner to identify the color of the dot on his own forehead will be release. Of course, the prisoners agree to this. (What do they have to lose?) The warden blindfolds the prisoners, as promised, and then paints a red dot on the foreheads of all three prisoners. He removes the blindfolds and, since each prisoner sees a red dot (in fact two red dots), each prisoner raises his hand. Some time passes when one of the prisoners exclaims, "I know what color my dot is! It's red!" This prisoner is then released. Your problem…In the new post-apocalyptic world, the world queen is desperately concernedabout the birth rate. Therefore, she decrees that all families should ensure that they have one girl orelse they face massive fines. If all families abide by this policy-that is, they have continue to havechildren until they have one girl, at which point they immediately stop-what will the gender ratioof the new generation be? (Assume that the odds of someone having a boy or a girl on any givenpregnancy is equal.) Solve this out logically and then write a computer simulation of it.a. Given n items, where each item has a weight and a value, and a knapsack that can carry at most W You are expected to fill in the knapsack with a subset of items in order to maximize the total value without exceeding the weight limit. For instance, if n = 6 and items = {(A, 10, 40), (B, 50, 30), (C, 40, 80), (D, 20, 60), (E, 40, 10), (F, 10, 60)} where each entry is represented as (itemIdi, weighti, valuei). Use greedy algorithm to solve the fractional knapsack problem. b. Given an array of n numbers, write a java or python program to find the k largest numbers using a comparison-based algorithm. We are not interested in the relative order of the k numbers and assuming that (i) k is a small constant (e.g., k = 5) independent of n, and (ii) k is a constant fraction of n (e.g., k = n/4). Provide the Big-Oh characterization of your algorithm.
- This is an algorithmic graph problem. Consider a set of movies M1, M2, ... , Mk. There is a set of customers, each one of which indicates the two movies they would like to see this weekend. Movies are shown on Saturday evening and Sunday evening. Multiple movies may be screened at the same time. You must decide which movies should be televised on Saturday and which on Sunday, so that every customer gets to see the two movies they desire. Is there a schedule where each movie is shown at most once? Design an efficient algorithm to find such a schedule if one exists.You work for a company that has warehouses of items. The items are all packaged in boxes that are roughly the same size. Each warehouse has some shelves in it. The shelves all hold the same number of boxes. To keep things from getting confusing, a shelf will only contain one kind of item on it, and a warehouse will have at most one shelf storing a given kind of item. (If the shelf is full, that item would go to a different warehouse to make sure that items are evenly distributed, but your code won’t track multiple warehouses.) You will create a Warehouse class to simulate a warehouse according to the above description. If you would like to make use of another class of your design, declare it inside the Warehouse class (this is called an inner class). It is possible to create an efficient solution without having to do this. You can imagine each shelf sitting in a long line; what kind of data structure have we seen that can take advantage of this? If each shelf has multiple properties,…You work for a company that has warehouses of items. The items are all packaged in boxes that are roughly the same size. Each warehouse has some shelves in it. The shelves all hold the same number of boxes. To keep things from getting confusing, a shelf will only contain one kind of item on it, and a warehouse will have at most one shelf storing a given kind of item. (If the shelf is full, that item would go to a different warehouse to make sure that items are evenly distributed, but your code won’t track multiple warehouses.) You will create a Warehouse class to simulate a warehouse according to the above description. If you would like to make use of another class of your design, declare it inside the Warehouse class (this is called an inner class). It is possible to create an efficient solution without having to do this. You can imagine each shelf sitting in a long line; what kind of data structure have we seen that can take advantage of this? If each shelf has multiple properties,…
- Give an example of a situation in which the total denial of a service to a user (the user receiving no response from the computer) presents a big problem for that user. Another example is offered in which a 10% denial of service (that is, the user's calculation advances but at a 10% slower rate than usual) is a severe problem for that user. Illegal access to a computing system might result in a 10% denial of service to legitimate users of that computing system. If that's the case, how would you go about doing it?Consider the following snapshot of a system: Allocation: A B C DT0 0 0 1 2T1 1 0 0 0T2 1 3 5 4T3 0 6 3 2T4 0 0 1 4 Max: A B C DT0 3 0 1 2T1 1 7 5 0T2 2 3 5 6T3 0 6 5 3T4 0 6 5 6 Available: A B C D2 5 1 0 Answer using the banker’s algorithm. If you think the system is in an unsafe state, write "unsafe" in the answer box, otherwise, write the process sequence that satisfies the safe state. While answering the question write only the id of the Tasks separated with comma, (e.g., for sequence <T4,T2,T1,T0,T3> write only 4,2,1,0,3 ).After college, a group of students of a certain height planned to go to the movies. The cinema they go to is quite unique because the number of cinema rows is always 2 and the number of seats is as many as the number of students. Because this is a unique cinema, the way they sit is also unique. They will try to minimize their height difference with the one next to it so that the biggest height difference of each pair of students next to each other is as minimal as possible. Example: There are 6 students with height of 1, 6, 9, 7, 2, and 3. There are various sequences that can produce the biggest difference in height. Ordering 1:1 3 62 7 9Difference 1 and 3 is 2.Difference 3 and 6 is 3.Difference 2 and 7 is 5.Difference 7 and 9 is 2.So the biggest difference in height is 5. Ordering 2:1 3 26 7 9The biggest difference in height is 2.This difference is also an optimal answer. Format Input : There are T test cases. Each testcase contains integers N which indicates the number of students…
- A book salesperson living in New York needs to visit clients in Utah, Jersey, LA, and Milan within a month. The distances between these cities are given in the table in the picture. Solve the problem with the nearest neighbor heuristic.You and your friends decided to hold a “Secret Santa” gift exchange, where each person buys a gift for someone else. To see how this whole thing works, let’s consider the following example. Suppose there are 7 people A, B, C, D, E, F, and G. We denote x → y to mean “x gives a gift to y.” If the gift exchange starts with person A, then they give a gift to E. Then E gives a gift to B. And it is entirely possible that B gives a gift to A; in such a case we have completed a “cycle.” In case a cycle occurs, the gift exchange resumes with another person that hasn’t given their gift yet. If the gift exchange resumes with person D, then they give a gift to G. Then G gives a gift to F. Then F gives a gift to C. Then finally C gives a gift to D, which completes another cycle. Since all of the people have given their gifts, the giftexchange is done, otherwise the gift exchange resumes again with another person. All in all, there are two cycles that occurred during the gift exchange: A → E → B → A…Consider the challenge of determining whether a witness questioned by a law enforcement agency is telling the truth. An innovative questioning system pegs two individuals against each other. A reliable witness can determine whether the other individual is telling the truth. However, an unreliable witness's testimony is questionable. Given all the possible outcomes from the given scenarios, we obtain the table below. This pairwise approach could then be applied to a larger pool of witnesses. Answer the following: 1) If at least half of the K witnesses are reliable, the number of pairwise tests needed is Θ(n). Show the recurrence relation that models the problem. Provide a solution using your favorite programming language, that solves the recurrence, using initial values entered by the user.