Problem 5. 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 01 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