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(Solved): Question 1:Question 2: (0.5) 0/1 Knapsack problem with Dynamic Programming. The following table has ...
Question 1:
Question 2:
![(0.5) Given the complexity function:
\[
T(n)=9 T\left(\frac{n}{2}\right)+n+1
\]
After applied the back substitution process,](https://media.cheggcdn.com/media/84e/84e8f459-6aee-44df-8d73-e3f64658d8e3/phpVtmHha)
(0.5) 0/1 Knapsack problem with Dynamic Programming. The following table has been computed for you to find the maximum profit with items . Which are the items that will be added to the Knapsack with a maximum capacity of ?. Show all your work to get credit.
(0.5) Given the complexity function: After applied the back substitution process, and after steps, (note that some steps are missing), we have arrived to the expression: Compute the solution for the above expresion as a function of . Show all your work including step by step the way you set up and solve your summations to get credit.
Expert Answer
Question 1The table represents the solution to the 0/1 Knapsack problem with dynamic programming, where the columns represent the different capacities of the knapsack (0 to 8 in this case) and the rows represent the different items that can be added to the knapsack (0 to 4 in this case).The 0/1 Knapsack problem is a classic optimization problem where a knapsack with a maximum weight capacity needs to be filled with items of different weights and values in a way that maximizes the total value of the items while not exceeding the capacity of the knapsack.The problem can be solved using dynamic programming, where a table is constructed to keep track of the maximum value that can be achieved for each weight capacity and each subset of items. The table is filled iteratively using the following recurrence relation: