Given items of different values and volumes, find the most valuable set of items that fit in a knapsack of fixed volume. Formal Definition: There is a knapsack of capacity c > 0 and N items. Each item has value v_i > 0 and weight w_i > 0. Find the selection of items (δ_i = 1 if selected, 0 if not) that fit, ∑_i=1^N δ_iw_i ≤ c, and the total value, ∑_i=1^N δ_iv_i, is maximized.