Question

A 0-1 Knapsack problem is as below: 4 items Max weight is 5 Item 1: weight 5; benefit 6 Item 2: weight 3; benefit 4 Item 3: weight 4; benefit 5 Item 4: weight 2; benefit 3 (1) What is the recursive formula that can be used to solve 0-1 Knapsack problem? (10 points) (2) What is the sub-problem of the green cell in the table? (20 points) (3) Please fill out the table to solve this given 0-1 Knapsack problem and show what items should be selected. (40 points) i\W 0 1 2 3 4 5 0 0 0 0 0 0 0 1 2 3

          A 0-1 Knapsack problem is as below:
4 items
Max weight is 5
Item 1: weight 5; benefit 6
Item 2: weight 3; benefit 4
Item 3: weight 4; benefit 5
Item 4: weight 2; benefit 3
(1) What is the recursive formula that can be used to solve 0-1 Knapsack problem? (10
points)
(2) What is the sub-problem of the green cell in the table? (20 points)
(3) Please fill out the table to solve this given 0-1 Knapsack problem and show what
items should be selected. (40 points)
i\W 0
1
2
3
4
5
0
0
0
0
0
0
0
1
2
3

Show more…

A 0-1 Knapsack problem is as below:
4 items
Max weight is 5
Item 1: weight 5; benefit 6
Item 2: weight 3; benefit 4
Item 3: weight 4; benefit 5
Item 4: weight 2; benefit 3
(1) What is the recursive formula that can be used to solve 0-1 Knapsack problem? (10
points)
(2) What is the sub-problem of the green cell in the table? (20 points)
(3) Please fill out the table to solve this given 0-1 Knapsack problem and show what
items should be selected. (40 points)
i0
1
2
3
4
5
0
0
0
0
0
0
0
1
2
3

Added by Clara A.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Ravindra Yadav

Step 1

We can define a function K(W, n) that represents the maximum value that can be obtained by selecting items from 1 to n, considering the weight constraint. The recursive formula is as follows: K(W, n) = 0, if W = 0 or n = 0 (base case) K(W, n) = K(W, n-1), if Show more…

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A 0-1 Knapsack problem is as below: items Max weight is 5 Item I: weight 5; benefit 6 Item 2: weight 3; benefit 4 Item 3: weight 4; benefit 5 Item 4: weight 2; benefit 3 (1) What is the recursive formula that can be used to solve 0-1 Knapsack problem? (10 points) What is the sub-problem of the green cell in the table? (20 points) (3 Please fill out the table to solve this given 0-1 Knapsack problem and show what items should be selected. (40 points) IW 0 0 0 0 0 1 2 3

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