Find an optimal solution to the fractional knapsack problem for an instance with number of items 5, Capacity of the sack W=15, profit associated with the items (p1,p2,…,p5)= (15,7,6,18,3) and weight associated with each item (w1,w2,…,w7)= (2,3,5,7,4, ).
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. Find an optimal solution to the fractional knapsack problem for an instance
with number of items 5, Capacity of the sack W=15, profit associated with
the items (p1,p2,…,p5)= (15,7,6,18,3) and weight associated with each item
(w1,w2,…,w7)= (2,3,5,7,4, ).
Step by step
Solved in 3 steps with 4 images
- a. Given n items, where each item has a weight and a value, and a knapsack that can carry at most W You are expected to fill in the knapsack with a subset of items in order to maximize the total value without exceeding the weight limit. For instance, if n = 6 and items = {(A, 10, 40), (B, 50, 30), (C, 40, 80), (D, 20, 60), (E, 40, 10), (F, 10, 60)} where each entry is represented as (itemIdi, weighti, valuei). Use greedy algorithm to solve the fractional knapsack problem. b. Given an array of n numbers, write a java or python program to find the k largest numbers using a comparison-based algorithm. We are not interested in the relative order of the k numbers and assuming that (i) k is a small constant (e.g., k = 5) independent of n, and (ii) k is a constant fraction of n (e.g., k = n/4). Provide the Big-Oh characterization of your algorithm.Find an optimal solution to the fractional knapsack problem for an Instance with number of items i.e n= 3, Capacity of the sack M=20, profit associated with the items (p1,p2,p3)= (25,24,15) and weight associated with each item (w1,w2,w3)= (18,15,10).A given Knapsack with maximal Weight capacity is 8Kg. There are some items can be chosen and taken into Knapsack. Each item has own weight and profit shown as follows. Please find the maximal profit of Knapsack after some items are selected and put into this Knapsack and its maximal Weight capacity isn't exceeded. item ID Weight 4Kg 5Kg 2Kg 1kg 6Kg A B с D E Profit 4500 5700 2250 1100 8700 The maximal profit of this Knapsack to taken some items and total weight is no exceeded the weight capacity : The last item is taken and put into this Knapsack is: The second item is taken and put into this Knapsack is : The first item is taken and put into this Knapsack is:
- Let S = {a, b, c, d, e, f, g} be a collection of objects with benefit-weight values, a: (12, 4), b: (10, 6), c: (8, 5), d: (11, 7), e: (14, 3), f : (7, 1), g: (9, 6). What is an optimal solution to the fractional knapsack problem for S assuming we have a sack that can hold objects with total weight 18? Show your work.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.please solve step py step no code . Find an optimal solution to the fractional knapsack problem for an instancewith number of items 5, Capacity of the sack W=15, profit associated withthe items (p1,p2,…,p5)= (15,7,6,18,3) and weight associated with each item(w1,w2,…,w7)= (2,3,5,7,4, ).
- 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.)Consider the knapsack problem: given n items of known weights w,., w, and values v,., v, and a knapsack of capacity W, find the most valuable subset of the items that fit int the knapcak . In order to design a dynamic programming algorithm, we have driven the recurrence relation below that expresses a solution to an instance of the knapsack problem in terms of solutions to its smaller subinstances. For 1 0 if j-w 0 and F[i,0] = 0 for i > 0 2.1) Solve the knapsack instance given below using the recurrence given above. Apply the dynamic programming to the following instance of the knapsack problem where the capacity W = 4. Fill out the cells in the table using the recurrence given. You will not receive any credit if you do not use the recurrence relation. Write your results to the table below. сараcity j item weight i 1 2 3 value $25 $22 1 1 2 2 25 25 25 25 $26 $27 3 1 25 25 47 47 4 26 51 4 26 i = 3 j= 3 F[3,3] = i = 3 j= 4 F[3,4] = i = 4 j = 2 F[4, 2] = i = 4 j= 3 F[4, 3] = i = 4 j= 4…Consider the knapsack problem: given n items of known weights w,., w, and values v,., v, and a knapsack of capacity W, find the most valuable subset of the items that fit int the knapcak . In order to design a dynamic programming algorithm, we have driven the recurrence relation below that expresses a solution to an instance of the knapsack problem in terms of solutions to its smaller subinstances. For 1 0 if j-w¿ 0 and F[i,0] = 0 for i > 0 2.1) Solve the knapsack instance given below using the recurrence given above. Apply the dynamic programming to the following instance of the knapsack problem where the capacity W = 4. Fill out the cells in the table using the recurrence given. Write your results to the table below. сараcity j item weight i 1 2 3 value $25 $22 1 1 2 2 25 25 25 25 $26 $27 3 1 25 25 47 47 4 26 51 4 26 i = 3 j= 3 F[3,3] = i = 3 j= 4 F[3,4] = i = 4 j = 2 F[4, 2] = i = 4 j= 3 F[4, 3] = i = 4 j= 4 F[4, 4] = 1. 2. 3.
- please i need corect answear Instance with number of items i.e n= 3, Capacity of the sack M=20, profit associated with the items (p1,p2,p3)= (25,24,15) and weight associated with each item (w1,w2,w3)= (18,15,10). Find an optimal solution to the fractional knapsack problem for anFirst, build a DP table for the 0-1 Knapsack problem with knapsack capacity W = 8, and a list of items A = { (2,5), (4, 10), (5, 9), (4, 7), (3, 12) } of (weight, value) pairs. 0 12 34 56 7 8 Wt. Val 5 005 4 10 9 4 7 3 12 Then enter the optimal solution of items for the knapsack with W = 8. For example, enter (2, 5), (4, 7) if those two items are selected What's the total value for fractional knapsack problem with W = 8? For example, enter 12.5 if the total value of selected items is 12.5 2.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.