Unbounded knapsack

Given list of N items where each item has some [weight, value] associated with it, put the items into a knapsack of capacity W to maximize the sum of values associated with the items. Repetition of items is allowed.

Hint

This algorithm recursively explores all possible combinations of items, considering the weight constraint at each step, to find the selection that yields the maximum total profit. At each step, compare and take the maximum profit achievable from the two choices:

• Include the item if this chosen item weight is less than the target weight. Add its profit to the maximum profit that can be obtained from items with reduced weight capacity (W - weight of the selected item).
• Exclude the item. Calculate the maximum profit that can be obtained from the remaining items with the current weight capacity (W).

• Python
• Javascript
•  Run

def pick(ls, w):
  if len(ls) <= 0 or w <= 0:
    return 0

  take = 0

  if ls[0][1] <= w:
    take = ls[0][0] + pick(ls, w - ls[0][1]);

  skip = pick(ls[1:], w)

  return max(take, skip)

ls = [[10, 1], [40, 3], [50, 4], [70, 5]]
W = 8

print(pick(ls, W))

function pick(list, w) {
  if (list.length <= 0 || w <= 0) {
    return 0;
  }

  let take = 0;

  if (list[0][1] <= w) {
    take = list[0][0] + pick(list, w - list[0][1]);
  }

  let skip = pick(list.slice(1), w);

  return Math.max(take, skip);
}

const list = [[10, 1], [40, 3], [50, 4], [70, 5]];
const W = 8;

console.log(pick(list, W));