Question

2 Knapsack Problem În al Knapsack problem. given n items(11-12. . . . . 1"} with weight {w1·W2. . . . . ux) and value (n 2, .., nJ, the goal is to select a combination of items such that the total value V is maximized and the total weight is less or equal to a given capacity In this question, we will consider two different ways to represent a solution to the Knapsack problem using . an array with size n: X-r1.z2····.znl . linked list L that stores the indices of items that are included in a solution. For example, if a solution only includes items I2, I3 and Is, the binary array representation will be 0, 1, 1,0, 1,0,0 and the linked list representation will be head-2+3-+5 [4 marks You decide to use a Monte Carlo-style simulation approach to invest igate possible solutions to the Knapsack problem. In this approach, you randomly generate m feasible solu- tions {X1 , X2, . . . , Xm) with objective values {Vi, 2, . .. , V..), where X, can be represented using either an array or list as described above. (a) Write a function CoMPUTEMEAN(argument list) to calculate the mean value of each variable Tj (j-: 1, 2, . . . ,n) in the given m samples: j,-m Σml XiLi]. Note the format of the argument list will depend on the representation you have selected Full marks will be given if your algorithm runs in 0(Σ㈡ ,I) time, where L1 denotes the size of the linked list representation of X (b) 2 marks Briefly describe how a greedy algorithm (heuristic) could be developed for solving the Knapsack problem using the COMPUTEMEAN) function. ·You do not have to write an algorithm in pseudo code to answer part (b) of this ques- tion. We are expecting that you write a short paragraph or a short list of bullet points describing the important steps of the algorithm . You should also comment on whether such a greedy approach would be effective.

solution is required in pseudo code please.

Answer 1

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