Python Knapsack Problem: imagine you are carrying a knapsack with capacity to hold a total of weight C. You are selecting among n items with values A={a_1, a_2, ... , a_n} and associated weights W={w_1, w_2, ... , w_n}. Here the weights and values are all positive. You wish to maximize the total value of the items you select not exceeding the given weight capacity, example,maximize sum_{a in A} such that sum_{w in W} <= c. ="" note="" that="" you="" can="" only="" select="" your="" items="">
Reformulate this as a bottom-up dynamic programming problem as follows. Define K_{i,j} as the highest possible value sum considering items 1 through i and total weight capacity j (j <= c).="" what="" is="" the="" base="" case="" i.e.="" k_{0,j}="" for="" all="" j="" and="" k_{i,0}="" for="" all="" i.="" what="" is="" the="" loop="">
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