背包问题：用值替换所有项目

Question

我正在尝试通过应用我自己的算法来解决背包问题。我给每个项目一个分数（值[i] - 权重[i]）并将高分项目添加到我的背包中。但是此代码将每个项目替换为值 (5) 的第一项。

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))

这段代码有什么问题？

编辑：我修复了它，但似乎存在逻辑错误。如果：

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

然后有两个项目得分相同（8, 3 和 9, 4），但 9, 4 更好，因为它正好适合背包并且具有更高的价值。即使将第 8 行更改为 <= 也无济于事。

Answer 1

您也没有从列表中删除附加值。尝试添加

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

到 scores.pop(...).

之前的行

此外，如果添加的项目会使您超出容量，则需要跳出循环，例如：

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

您需要代码来处理决胜局，它将分数索引重新分配给适合容量的最高值项目，例如：

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

完整代码：

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))

背包问题：用值替换所有项目

Knapsack Problem: Replaces all items with value

python

classification

knapsack-problem