Question

2 Knapsack Problem In a Knapsack problem, given n items {11, I2, -.., In} with weight {wi, w2, -.., wn) and value fvi, v2, ..., vn], 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 W. Tt i=1 In this question, we will consider two different ways to represent a solution to the Knapsack problem using an array with size n: X-[x1,22,--. ,z, » 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 I5, the binary array representation will be [O, 1, 1, 0, 1, 0, . . . , 이 and the linked list representation will be head → 2 → 3 → 5 (a) [4 marks] You decide to use a Monte Carlo-style simulation approach to investigate possible solutions to the Knapsack problem. In this approach, you randomly generate m feasible solu- tions {Xi, X2, ..., Xm) with objective values {V, V2, ..., Vm), where X, can be represented using either an array or list as described above Write a function CoMPUTEMEAN(argument list) to calculate the mean value of each variable rj (j = 1,2, . . . ,n) in the given m samples: zj = m Σǐni ii. 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(5%. LI) time, where | Lil denotes the size of the linked list representation of X, (b) [2 marksl 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

Answer 1

Mothol nisation Pablr means a pblo wohich seinus mien Sol:I can go by toalt. to receive the destination e Sol 2 1 Cam )o buǐ Bike -to Yeach.destinalen cAn 니 12 hrs iblu tiaSo But he taio onby atupts a tthe veo Stme knoun as desibe Sol'h →fasble Sdn means that Akich auerta th given Cerdilan the ithm bult a Sol' pat by put chesing hat ive an iik the ophouten rlm Sohve Thi approach i manly eaul to soaue n prtin

o nan netr wd to choke the bast Cand det to ade Pt means that, hich auwh that-anven Cenotto nblm. ㄗ ben Reached

x Phoble is, bog hag given and bas(5 -15 15.1 /Q 9-5 3 15K 3-122. 2-2 = 0 hain total ceght tess than (ot squal ta 115 ase diiSable

カrst cor have to take ushich obiedf, hanna high Prso 2 4215+041t 1x3 4xt Piz LK 1012/3#5AW15-t l86+1a@+D3