a) Implement the bottom-up dynamic programming algorithm for the knapsack problem in python. The program should read inputs from a file called data.txt, and the output will be written to screen, indicating the optimal subset(s).

b) For the bottom-up dynamic programming algorithm, prove that its time efficiency is in (nW), its space efficiency is in (nW) and the time needed to find the composition of an optimal subset from a filled dynamic programming table is in O(n).

Consider the following instance of the knapsack problem with capacity W = 6 Item Weight Value 3 $25 $20 $15 $40 $50