A student is taking a test on n different subjects. For each iith subject they have already answered answered[i] questions and have time to answer a total of q more questions overall. For each iit subject, the number of questions answered has to be at least needed[i] in order to pass. Determine the maximum number of subjects the student can pass if the q additional answered questions are optimally distributed among the subjects.
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A student is taking a test on n different subjects. For each iith subject they have already answered answered[i] questions and have time to answer a total of q more questions overall. For each iit subject, the number of questions answered has to be at least needed[i] in order to pass. Determine the maximum number of subjects the student can pass if the q additional answered questions are optimally distributed among the subjects.
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- Suppose we have a heuristic h that over-estimates h* by at most epsilon (i.e., for all n, 0<= h(n) <= h*(n)+epsilon). Show that A* search using h will get a goal whose cost is guaranteed to be at most epsilon more than that of the optimal goal.Let pn(x) be the probability of selling the house to the highest bidder when there are n people, and you adopt the Look-Then-Leap algorithm by rejecting the first x people. For all positive integers x and n with x < n, the probability is equal to p(n(x))= x/n (1/x + 1/(x+1) + 1/(x+2) + … + 1/(n-1)) If n = 100, use the formula above to determine the integer x that maximizes the probability n = 100 that p100(x). For this optimal value of x, calculate the probability p100(x). Briefly discuss the significance of this result, explaining why the Optimal Stopping algorithm produces a result whose probability is far more than 1/n = 1/100 = 1%.A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonable time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? A. Unreasonable algorithms may sometimes also be undecidable B. Heuristics can be used to solve some problems for which no reasonable algorithm exists C. Two algorithms that solve the same problem must also have the same efficiency D. Approximate solutions are often identical to optimal solutions
- Computer Science Consider the demand and supply system p = ad +bdqd +ud p = as +bsqs +us with the equilibrium condition qd = qs = q. The parameters bd and bs are −2 and 1.5, respectively. Find the parameters ad and as are such that q = 5 and p = 10. Throughout this question use N = 100, and set the random seed to 14022022. The variable ud has a standard deviation of 3. All randomly generated variables have a mean of zero and are normally distributed unless something else is specified. All Monte Carlo studies should be done with 10,000 repetitions. Part a. Illustrate the supply and demand curves in a graph, together with a sample of simulated price and quantity data. Provide an additional graph where you have included the OLS estimated line of demand equation above. Are your estimates close to the true values of ad and bd ? Solve the question in Python language on Jupyter notebook.If a Genetic Algorithm only finds local optimal solutions, what should be done to find a better one globally?A version of simple exponential smoothing can beused to predict the outcome of sporting events. To illustrate,consider pro football. We first assume that all games areplayed on a neutral field. Before each day of play, we assumethat each team has a rating. For example, if the Bears’ ratingis 10 and the Bengals’ rating is 6, we would predict theBears to beat the Bengals by 10 6 4 points. Supposethe Bears play the Bengals and win by 20 points. For thisobservation, we “underpredicted” the Bears’ performanceby 20 4 16 points. The best a for pro football is 0.10.After the game, we therefore increase the Bears’ rating by16(0.1) 1.6 and decrease the Bengals’ rating by 1.6 points.In a rematch, the Bears would be favored by (10 1.6) (6 1.6) 7.2 points. a How does this approach relate to the equation At=At1 a(et)?b Suppose the home-field advantage in pro football is 3 points; that is, home teams tend to outscore visiting teams by an average of 3 points a game. How could the home-field advantage…
- True or False: - Best-first search is optimal in the case where we have a perfect heuristic (i.e., h(?) = h∗(?), the true cost to the closest goal state). - Suppose there is a unique optimal solution. Then, A* search with a perfect heuristic will never expand nodes that are not in the path of the optimal solution.- A* search with a heuristic which is admissible but not consistent is complete.Assume that you are asked to write a pseudocode of a genetic algorithm to find an optimal road for a new Amazon delivery truck driver who is also new in town. He departs from Amazon warehouse and has to go through n houses by the end of his day (h1,h2,…,hn). Given that we know the distance between these houses (called dij = distance(hi, hj), and dsi = distance(s,hi) with s being the Amazon warehouse. At the end of the day, the truck will go back to the warehouse s. So a typical road would look like: s -> h2 -> h1 -> h3 ….-> hn-1 -> hn -> S. Please use genetic algorithm with the above framework to write a pseudo code to find a road that minimize the distance that he needs to travel. In your pseudocode, please feel free to suggest the size of the initial population, the fitness function, choose how you do cross-over and mutation. You don’t have to implement this pseudo code but will be graded on the details you could provide so that people who are implementing it would…Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. Item i is in basket b if and only if i divides b with no remainder. Thus, item 1 is in all the baskets, item 2 is in all fifty of the even-numbered baskets, and so on. Basket 12 consists of items {1, 2, 3, 4, 6, 12}, since these are all the integers that divide 12. Answer the following questions: a. If the support threshold is 5, which items are frequent? (4 marks) b. What is confidence when the association rule is {5, 7} → 2 (2 marks) c. Considering the support threshold as 4, what are the candidate item sets for size 2 (pairs) (i.e., C2) while applying the A-Priori Algorithm. (2 marks)
- 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.Using the image provided, please answer the following questions. (a). Find a path from a to g in the graph G using the search strategy of depth-first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal". (b). Find a path from a to g in the graph G using the search strategy of breadth-first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal".(c). Find a path from a to g in the graph G using the search strategy of least-cost first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal". (d). Find a path from a to g in the graph G using the search strategy of best-first search. The heuristics for these nodes are: h(a,25); h(b, 43); h(c,5); h(d, 64); h(g, 0). Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal or "why-non-optimal".…A seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p-s and the buyer's payoffis b-p. Suppose simultaneously the buyer makes an offer p1 and the seller makes an offer p2. A transaction occurs if p1>=p2, and the transaction price is 1/2 (p1 + p2). Suppose the buyer uses a strategy p1(b) = 1/12 + (2/3)b and the seller uses a strategy p2(s) = 1/4 + (2/3)s. Suppose the buyer's value is 3/4 and the seller's valuation is 1/4. Will there be a transaction? Explain. Is this strategy profile a Bayesian Nash equilibrium? Explain.