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8. 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 reasonablo 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? O A Unreasonable algorithms may sometimes also be undecidable O B. Heuristics can be used to solve some problems for which no reasonable algorithm exsts O C. efficiency Two algorithms that solve the same problem must also have the same O B. Approximate solutions are often identical to optimal solutions

Question 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.

Develop a dynamic programming algorithm for the knapsack problem: given n items of know weights w1, . . . , wn and values v1, . . . ,vn and a knapsack of capacity W, find the most valuable subset of the items that fit into the knapsack. We assume that all the weights and the knapsack’s capacity are positive integers, while the item values are positive real numbers. (This is the 0-1 knapsack problem).  Analyze the structure of an optimal solution. Give the recursive solution. Give a solution to this problem by writing pseudo code procedures. Analyze the running time for your algorithms.

knapsack problem:   given the first table: c beeing value and w beeing weight, W max weight. I got table 2 as a solution to: 2 Solve the Knapsack problem with dynamic programming. To do this, enter the numbers Opt[k,V ] for k = 1,...,5 and V = 1,...,9 in a table. Here Opt[k, V ] is the partial solution obtained for the first k items with maximum weight V. " Can somebody explain me the values of the table? How do they get calculated?   Also how do i solve the followup-task: Using the values in the table, determine a solution OPTSOL(I)=(β1,β2,β3,β4), starting with β4. (Use backtracing to do this)

esc A Question 14 of 20: Select the best answer for the question. 14. Use Gauss-Jordan elimination to solve the following linear system: -3x + 4y = -6 5x - y = 10 O A. (2,0) O B. (2,-5) OC. (-6,2) OD. (2,2) O Mark for review (Will be highlighted on the review page) > 2 T W S #3 E D لم G $ 4 { R C 19 F % 50 F ف G Oll O O U *00 C 8 A

(b) One example of a greedy algorithm is the Dijkstra algorithm for finding the lowest cost path through a weighted graph. The diagram below shows two weighted graphs that a student wants to investigate using Dijkstra's algorithm. In each case the task it to find the lowest cost of reaching every node from v₁. Each graph has a single negative weight in it. ● V₁ ● 10 ● 12 V₂ V3 10 V4 V₁ 15 Graph (a) Graph (b) One of the graphs will yield a correct analysis of the lowest cost for all vertices, and the other will produce an incorrect analysis. Which of the two graphs will produce the incorrect analysis, and explain why the greedy nature of Dijkstra's algorithm is responsible for the incorrect analysis. Your answer should include the key concept of an invariant. V₂ (c) The priority queue is a widely used data structure. Priority queues may be implemented using binary heaps and simple linear arrays. For the basic priority queue operations of: 30 Building an initial queue Taking the highest…

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…

The best sequence is list of actions, called solution problem Path search The Optimal solution is : * a path from the initial state to a state satisfying the goal test This process of looking for the best sequence is called the solution with lowest path cost among all solutions none

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.

P is the set of problems that can be solved in polynomial time. More formally, P is the set of decision problems (e.g. given a graph G, does this graph G contain an odd cycle) for which there exists a polynomial-time algorithm to correctly output the answer to that problem. What is NP? Consider these five options and determine which option is correct. O NP is the set of problems that cannot be solved in polynomial time. NP is the set of problems whose answer can be found in polynomial time. O NP is the set of problems whose answer cannot be found in polynomial time. O NP is the set of problems that can be verified in polynomial time. O NP is the set of problems that cannot be verified in polynomial time.

The Optimal solution is : * a path from the initial state to a state satisfying the goal test This process of looking for the best sequence is called the solution with lowest path cost among all solutions none

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

P is the set of problems that can be solved in polynomial time. More formally, P is the set of decision problems (e.g. given a graph G, does this graph G contain an odd cycle) for which there exists a polynomial-time algorithm to correctly output the answer to that problem. What is NP? Consider these five options. A. NP is the set of problems that cannot be solved in polynomial time. B. NP is the set of problems whose answer can be found in polynomial time. C. NP is the set of problems whose answer cannot be found in polynomial time. D. NP is the set of problems that can be verified in polynomial time. E. NP is the set of problems that cannot be verified in polynomial time. Determine which option is correct. Answer either A, B, C, D, or E.

Gradient Descent Algorithm iii) Generate the graph of f(xk) vs k where k is the iteration number and xk is the current estimate of x at iteration k. This graph should convey the decreasing nature of function values. Deliverable(s) : The graph that is generated.

Question 14 of 20 : Select the best answer for the question. 14. Use Gauss-Jordan elimination to solve the following linear system: -3x + 4y = -6 5x - y = 10 O A. (2,0) о в. (2, -5) OC.(-6,2) O D. (2,2) O Mark for review (Will be highlighted on the review page) > esc $ % * 3 4 8 5 0 8 A W 3 E R ض U A S F D

Question 14 of 20 : Select the best answer for the question. 14. Use Gauss-Jordan elimination to solve the following linear system: -3x + 4y = -6 5x - y = 10 O A. (2,0) о в. (2, -5) O C.(-6,2) O D. (2,2) O Mark for review (Will be highlighted on the review page) > esc -> % * 4 8 50 8 A ض R U A S F D #3