In a 0-1 knapsack problem, how could you implement a repair mutation to transform infeasible solutions into feasible ones (Le, make the sum of costs of the selected items go below the budget)?
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- Answer the given question with a proper explanation and step-by-step solution. You are asked to pick up a project on building highways to connect all cities in the country. The cost of building a highway between two cites i and j is c(i, j) > 0. If you were in charge from the beginning, this would have been a minimum spanning tree problem and could be solve easily with the algorithms covered in class. Since you pick it up halfway, however, some suboptimal choices have already been made by your predecessor. In other words, highways were already built between some pairs of cities. Design an algorithm to find a cost minimizing set of highways to built subject to the choices already made. Do not copy others.The problem states that there are five philosophers sitting around a circular table. The philosophers must alternatively think and eat. Each philosopher has a bowl of food in front of them, and they require a fork in each hand to eat. However, there are only five forks available. You need to design a solution where each philosopher can eat their food without causing a deadlock.The Knapsack Problem is a famous computer science problem that is defined as follows: imagine you are carrying a knapsack with capacity to hold a total of weight C. You are selecting among n items with values A={a_1, a_2, ... , a_n} and associated weights W={w_1, w_2, ... , w_n}. Here the weights and values are all positive (but not necessarily unique). You wish to maximize the total value of the items you select not exceeding the given weight capacity, i.e. maximize sum_{a in A} such that sum_{w in W} <= C. Please note that you can only select your items once. a) We can reformulate this as a 2D bottom-up dynamic programming problem as follows. Define T_{i,j} as the highest possible value sum considering items 1 through i and total weight capacity j (j <= C). What is the base case i.e. T_{0,j} for all j and T_{i,0} for all i?, and What is the loop statement?
- If we want to prove P = NP, we only need to pick up any one NPC problem and design a polynomial-time algorithm for the problem. If you want to prove P = NP, select one NPC problem based on your preference and describe your idea of a polynomial-time algorithm that solves the problem. It does not have to be a formal algorithm or pseudo-code, a description of your idea of designing such an algorithm would be fine.We mentioned that if we want to prove P = NP, we only need to pick up any one NPC problem and design a polynomial-time algorithm for the problem. If you want to prove P = NP, select one NPC problem based on your preference and describe your idea of a polynomial-time algorithm that solves the problem. It does not have to be a formal algorithm or pseudo-code, a description of your idea of designing such an algorithm would be fine.implement Bresenham line drawing algorithm:For Slope |m|<1:Either value of x is increasedOR both x and y is increased using decision parameter.
- How might NPT's multiple possibilities minimize overhead?Consider the following design problem. A farmer is building a wire fence on his land. He has planted N wooden posts into the ground but has not put wire between them yet. The positions of these wooden posts are final; they cannot be moved. Wire placed between posts follows a straight line, and the farmer must place wire between the posts such that it forms an enclosure. The farmer is smart and will not allow the wires to cross. See the figure below, where the posts are the circles, and the lines are the wire (ignore the post numbering). However, the farmer would like the fence to enclose as much land as possible. He is willing to let some of his posts go unused (that is, not be part of the wire fence), so long as it maximizes the amount of land that the fence encloses. What algorithm would you use to solve this problem? Give a brief description of how it would work and the asymptotic run time as a function of N.Correct answer will be upvoted else downvoted. Computer science. You are given a grid a comprising of positive integers. It has n lines and m segments. Develop a framework b comprising of positive integers. It ought to have a similar size as a, and the accompanying conditions ought to be met: 1≤bi,j≤106; bi,j is a various of ai,j; the outright worth of the contrast between numbers in any nearby pair of cells (two cells that share a similar side) in b is equivalent to k4 for some integer k≥1 (k isn't really something similar for all sets, it is own for each pair). We can show that the appropriate response consistently exists. Input The primary line contains two integers n and m (2≤n,m≤500). Every one of the accompanying n lines contains m integers. The j-th integer in the I-th line is ai,j (1≤ai,j≤16). Output The output ought to contain n lines each containing m integers. The j-th integer in the I-th line ought to be bi,j.
- In the context of evolutionary computing the goal function is known as the fitnessfunction and the problem is to maximize it. The typical formulation has to be changedin a simple way.min f (x) = − max[− f (x)] (4.9)Another requirement is that the goal function is positive.Phenotype evolution treats x as a phenotype and the goal function as the fitnessfunction. The typical framework for the method is as follows:Starting from a randomly generated state of the 15-puzzle game , steepest-ascent hill-climbing (the vanilla version of hill-climbing search) gets stuck 76% of the time, i.e., solving only 24% of problem instances. But it works very quickly, i.e., it takes just 6 steps on average when it succeeds and 5 steps when it gets stuck. In contrast, if sideways moves are allowed, this raises the percentage of problem instances solved by hill-climbing from 24% to 81%, with the success at a cost: the algorithm averages roughly 7 steps for each successful instance and 32 steps for each failure. Now suppose that we are implementing random-restart hill climbing (i.e., if a search fails, it keeps to try, and try, until it gets a success) by the following two versions: one uses vanilla steepest-ascent hill climbing, and the other one uses hill climbing with sideways moves. Can you please tell which version of random-restart hill-climbing listed above runs faster on average? Please justify your…Wireless sensor networks are a special kind of network that facilitates communication. Sensor nodes in WSNs relay information to and from a central base station. The computing resources and storage space of a sensor node are limited. Take, for example, an algorithm that can be solved by solving subproblems. Is it preferable to use dynamic programming or divide and conquer to solve these subproblems independently at various sensor nodes? Try to keep your writing short and sweet.