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- How would you modify the dynamic programming algorithm for the coin collecting problem if some cells on the board are inaccessible for the robot? Apply your algorithm to the board below, where the inaccessible cells are shown by X’s. How many optimal paths are there for this board? You need to provide 1) a modified recurrence relation, 2) a pseudo code description of the algorithm, and 3) a table that stores solutions to the subproblems.In your preferred programming language, code the Newton-Raphson method to find the stationary points of a nonlinear function. Please include your code with your hw submission. Use your implementation to find the stationary points of the following non-linear functions W:(x1, 82), W2(x1, T2), and W3(x1, 82): W: (x1, 2) = xỉ + x W2(x1, #2) = rỉ + x W3(x1, 2) = x} – x† + x3 – x3 + 0.1x,r2 %3| starting the following two initial guesses in each case: • x1 = 0.1, x2 = 0.1 • x1 = 1.0, x2 = 1.0 For W1(x1, x2), W2(x1, X2), and W3(x1, 02) and for each initial guess, please report: 1. The function value. 2. The coordinates x1 and x2 of the function stationary point. 3. The plot of the function value as a function of the Newton-Raphson iteration. Can anyone help me set this up? I will be using MATLAB but am new to this type of stuff so any help would be appreciatedQuestion 2: Consider the 0/1 knapsack problem. Given Nobjects where each object is specified by a weight and a profit, you are to put the objects in a bag of capacity C such that the sum of weights of the items in the bag does not exceed Cand the profits of the items is maximized. Note that you cannot use an item type more than once. a. Using dynamic programming, write an algorithm that finds the maximum total value according to the above constraints. b. What is the complexity of your algorithm? c. Show the dynamic programming table for the following data: W= { 2 ,7 , 1} , P={ 3 ,15 , 2 } and C=8.
- demonstrate the use of the periodic interval functions. Observe that since we have N points, and that we want points to be uniformly spaced throughout the interval including only the left end-point, then we must chose dr to be the length of the interval divided by N. Why only the left end- point? Recall that we want the domain to be periodic. Hence, the last point value should not be the right-hand end of the domain because this value is periodic with the left-hand value. So we chose da to be the length of the interval divided by N and not by (N-1).N.png ... If gcd(a, m) = 1, then the unique solution xo to ax = b (mod m) is equal to (1) xo = ab (mod m) (2) xo = ab (mod m), where b is the inverse of b. (3) xo = ām (mod m), where ā is the inverse of a. (4) xo = āb (mod m), where ā is the inverse of a. A Choice (2) (B) Choice (1) Choice (4) (D) Choice (3)Machine Learning Problem Perform the optimization problem of finding the minimum of J(x) = (2x-3)2 by: (i) defining theta, J(theta), h(theta) as defined in the Stanford Machine Learning videos in Coursera; (ii) plotting J(theta) vs theta by hand then use a program (iii) determining its minimum using gradient descent approach starting from a random initial value of theta = 5. Perform the search for the minimum using the gradient descent approach by hand calculations, i.e., step 1, step 2, etc. showing your work completely
- Use a software program or a graphing utility with matrix capabilities to write v as a linear combination of u1, u2, U3, U4, and u5. Then verify your solution. (Enter your answer in terms of u1, u2, u3, U4, and u5.) v = (5, 2, -12, 13, 6) u1 = (1, 2, -3, 4, –1) u2 = (1, 2, 0, 2, 1) Uз 3D (0, 1, 1, 1, —4) U4 = (2, 1, -1, 2, 1) u5 = (0, 2, 2, -1, -1) V =There are n ≥ 2 married couples who need to cross a river. They have a boat that can hold no more than two people at a time. To complicate matters, all the husbands are jealous and will not agree on any crossing procedure that would put a wife on the same bank of the river with another woman's husband without the wife's husband being there too, even if there are other people on the same bank. Can they cross the river under such constraints? Solve the problem for n = 2.Maximum weight = 20The above problem is a 0/1 Knapsack problem. Here there are 7 different objects labelled from A to G. The objective of this problem is to carry the different objects in your bag in such a way such that the profit is maximized. But you have to make sure that your bag does not exceed the maximum weight i.e. the maximum weight that this bag can carry is less than or equal to 15. Remember you can carry an object exactly once. Now it is your job to use Genetic Algorithm to solve this problem. 1. Encode the problem and create an initial population of 4 different chromosomes 2. Think of an appropriate fitness function to this problem and give proper justification. 3. Use the fitness function to calculate the fitness level of all the chromosomes in your population 4. Perform natural selection and select the two fittest chromosomes 5. Use the parents from (4) and perform crossover to get 2 offspring 6. Perform mutation and check the fitness of the final offspring. Comment…