the knapsack problem

The knapsack problem: Suppose that we have a knapsack with total capacity W. We also have n items where item ; has value v; >0 and weight 0 02/W, 2... > Un/un, and pack items greedily as long as possible (i.e., take the first k items where k 0. (b) Consider the following modified algorithm: compute the greedy solution as before and find the item of maximum value = max, us. Output the maximum of the greedy algorithm and 4). Show that this new algorithm gives a 1/2-approximation algorithm. The knapsack problem: Suppose that we have a knapsack with total capacity W. We also have n items where item ; has value v; >0 and weight 0 02/W, 2... > Un/un, and pack items greedily as long as possible (i.e., take the first k items where k 0. (b) Consider the following modified algorithm: compute the greedy solution as before and find the item of maximum value = max, us. Output the maximum of the greedy algorithm and 4). Show that this new algorithm gives a 1/2-approximation algorithm