3 Consider the following knapsacu problem. The size of Knap Sack is 60. Compute the maximum profit using the the bag Greedy algorithm and Identity the objects placed in 1 2 3 405 Object 5 Profit 30 40 45 77 90 5 22 Weight 25 10 15
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- Consider the following version of Knapsack. Given are two weight limits W1 and W2, whereW1 ≤ W2. Given are also n items (w1, c1),(w2, c2), . . . ,(wn, cn), where wiis the weight and cithe cost of the i-th item. We want to find a subset of these items of the highest cost, wherethe subset weights at least W1 and at most W2. Give an O(nW2) algorithm for this problem.(Recall that the cost (respectively weight) of a subset is the sum of the costs (respectivelyweights) of the items in the subset.)I will leave multiple likes Please help answering the following (all parts if possible): a.) Define real and integer valued knapsack problem b.) Provide greedy solution to real valuedknapsack problem, provide performance estimate for that method. c.) Provide python code and test driver in the separate .py file. d.) Explain brute force algorithm and why in the case of integervalued knapsack brute force algorithm takes exponential time.Given a knapsack of capacity W = 1.5Kg, solve the following 0/1 knapsack problem using DP. Illustrate the procedure and determine the subset of items.
- Two users can establish a shared secret key using the Diffie-Hellman algorithm, even if they have never met, share nosecrets, and have no certificatesa. Explain how this algorithm is susceptible to a man-inthe-middle attack.b. How would this susceptibility change if n or g weresecret?Algorithm of 0/1 - Knapsack problem, [dynamic programming and set method]=====================================================================Object(s): | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |Benefit(s): | 3 | 4 | 5 | 6 | 5 | *1 | 8 | *2 | (unit)Weight(s): | 2 | 4 | 6 | 7 | 9 | 10 | 12 | 13 | (unit)*1 = Last digit of your Stud_ID number*2 = Summation of first and last digit of your Stud_ID numberCapacity of the storage or bag (C) = 30 (unit)Carry objects by using the given storage or bag (C) and find out the maximum benefit(s) with these limitations by 'Algorithm of 0/1 - Knapsack problem'.Consider E: y2=x3+15x+17 mod 97 List all elements of the group. Verify if Hasse’s bound is satisfied. Pick any point P in the group that is not “0” Pick 2 random integers a and b (what range will you use?) Compute A=a.P and B=b.P and show the answers Find the shared key that can be computed using A and b (also show your answer using B and a)
- Consider a Diffie-Hellman scheme with a common prime q = 17 and a primitive root α = 3. a) If user A has a private key XA=4, what is A’s public key, YA? b) A sends YA to B. If B has a private key XB=6, what is the shared secret key, K that B can calculate and share with A? c) If B computes YB and sends it to A, what is the shared secret Key, K computed by A?A Mining pools does what? A. Let members earn more rewards, on average, than they would by mining alone B. Typically make all their members search for blocks with the same coinbase address (the address that receives mining rewards) C. Evenly divides up block rewards between all members of the pool, regardless of their computing power D. Might undermine the security of Bitcoin's consensus algorithm, but this isn't a problem in practice since the majority of miners aren't part of poolsConsider the following version of Knapsack. Given are two weight limits Wi and W2, where WW2. Given are also n items (wi, ci), (W2, C2)..... (Wn, Cn), where w, is the weight and c the cost of the i-th item. We want to find a subset of these items of the highest cost, where the subset weights at least W₁ and at most W2. Give an O(nW₂) algorithm for this problem. (Recall that the cost (respectively weight) of a subset is the sum of the costs (respectively weights) of the items in the subset.)
- Q: Apply the dynamic algorithm of Knapsack problem for the following inputs. Knapsack of capacity W = 10 item weight value 1 1 $10 2 2 $40 3 1 $20 4 3 $20 5 5 $60Apply the bottom-up dynamic programming algorithm to the followinginstance of the knapsack problem: Item Weight Value 1 3 $25 2 2 $30 3 1 $15 4 4 $40 5 5 $50 Capacity W = 8.Proposition Q. ( Generic shortest-paths algorithm) Initialize distTo[s] to 0 andall other distTo[] values to infinity, and proceed as follows: Relax any edge in G, continuing until no edge is eligible. For all vertices w reachable from s, the value of distTo[w] after this computation is the length of a shortest path from s to w (and the value of edgeTo[] is the last edge on that path).