背包问题：用值替换所有项目

Question

I am trying to solve the knapsack problem by applying my own algorithm. I give each item a score (values[i] - weights[i]) and add high score items to my knapsack. But this code replaces each item with the first item of values (5).

def knapsack(weights, values, capacity):
  knapsack = []
  scores = []
  for i in range(len(values)):
    score = values[i] - weights[i]
    scores.append(score)
  weight = 0
  while weight < capacity:
    if len(scores) != 0:
      valuable = max(scores)
      knapsack.append(values[scores.index(valuable)])
      weight += weights[scores.index(valuable)]
      scores.pop(scores.index(valuable))
    else:
      break
  return knapsack

weights = [1, 2, 4, 2, 5]
values  = [5, 3, 5, 3, 2]
capacity = 10

print(knapsack(weights, values, capacity))

What is wrong with this code?

Edit: I fixed it but there seems to be a logical error. If:

weights = [8, 2,  6,  7, 9]
values  = [3, 11, 13, 7, 4]
capacity = 24

Then there are two items with the same score (8, 3 and 9, 4), but 9, 4 is better since it fits exactly into the knapsack and it has higher value. Even changing line 8 to <= does not help.

Answer 1

You are not removing the appended values from the list as well. Try adding

values.pop(scores.index(valuable))
weights.pop(scores.index(valuable))

to the line before scores.pop(...) .

Additionally, you need to break out of the loop if the added item would make you over capacity, eg:

if (weight + weights[scores.index(valuable)]) > capacity:
    break

You need code to deal with tie-breakers, which reassigns the score index to the highest-valued item which fits under the capacity, eg:

ties = [i for i, x in enumerate(scores) if x == valuable]
if len(ties) > 1:
    most_valuable = -1
    for idx in ties:
        if values[idx] > most_valuable and (weight + weights[idx]) <= capacity:
            most_valuable = values[idx]
            scores_idx = idx

Full code:

def knapsack(weights, values, capacity):
    knapsack = []
    scores = []
    for i in range(len(values)):
        score = values[i] - weights[i]
        scores.append(score)
    weight = 0
    while weight < capacity:
        if len(scores) != 0:
            valuable = max(scores)
            scores_idx = scores.index(valuable)
            ties = [i for i, x in enumerate(scores) if x == valuable]
            if len(ties) > 1:
                most_valuable = -1
                for idx in ties:
                    if values[idx] > most_valuable and (weight + weights[idx]) <= capacity:
                        most_valuable = values[idx]
                        scores_idx = idx
            if (weight + weights[scores_idx]) > capacity:
                break
            knapsack.append(values[scores_idx])
            weight += weights[scores_idx]
            values.pop(scores_idx)
            weights.pop(scores_idx)
            scores.pop(scores_idx)
        else:
            break
    return knapsack

#  weights = [1, 2, 4, 2, 5]
#  values  = [5, 3, 5, 3, 2]
#  capacity = 10
weights = [8, 2, 6, 7, 9]
values = [3, 11, 13, 7, 4]
capacity = 24

print(knapsack(weights, values, capacity))