Question

我有关于分数背包问题的编程任务。作为问题的解决方案，我们需要按照其利润/重量比的降序填充项目。我使用自定义Comparator对项目进行排序。

检查以下Item类中的profitByWeightComparator：

class Item {
  private int itemNumber;
  private int profit;
  private int weight;

  public Item() {
    profit=weight=0;
  }
  public Item(int itemNumber, int profit, int weight) {
    this.itemNumber = itemNumber;
    this.profit = profit;
    this.weight = weight;
  }
  public String toString() {
    return "("+this.getItemNumber()+", "+this.getProfit()+", "+this.getWeight()+")";
  }
  public static Comparator<Item> profitByWeightComparator = new Comparator<Item>() {
    @Override
    public int compare(Item item1, Item item2) {
      double item1Ratio = (double)(item1.getProfit()/item1.getWeight());
      double item2Ratio = (double)(item2.getProfit()/item2.getWeight());
      return new Double(item1Ratio).compareTo(new Double(item2Ratio));
    }
  };
  public int getItemNumber() {
    return this.itemNumber;
  }
  public int getProfit() {
    return this.profit;
  }
  public int getWeight() {
    return this.weight;
  }
}

我使用Comparator类的reversed()方法按降序排序。

检查下面KnapSack类中的fillGreedyByProfitPerWeight()方法：

class KnapSack {
  Item [] items;
  int capacity;
  KnapSack() {
    Scanner sc = new Scanner(System.in);
    System.out.println("Enter number of items: ");
    int n = sc.nextInt();
    items = new Item[n];
    System.out.println("Enter the capacity of the KnapSack: ");
    this.capacity = sc.nextInt();

    int profit = 0;
    int weight = 0;

    for(int i = 0; i < n; i++) {
      System.out.println("Enter Item "+(i+1)+" (Format - Profit<Space>Weight):");
      profit = sc.nextInt();
      weight = sc.nextInt();
      items[i] = new Item((i+1), profit, weight);
    }
    fillGreedyByProfitPerWeight();
  }
  public void fillGreedyByProfitPerWeight() {
    Arrays.sort(items,Item.profitByWeightComparator.reversed());
    fillKnapSack("Greedy by Profit Per Weight");
  }
  public void fillKnapSack(String strategy) {
    double totalProfit = 0d;
    int currItemProfit = 0, currItemWeight = 0, i=0, tempCapacity = capacity;
    ArrayList<Integer> filledItems = new ArrayList<Integer>();
    System.out.println(Arrays.toString(items));
    for(i = 0; i < items.length; i++) {
      currItemProfit = items[i].getProfit();
      currItemWeight = items[i].getWeight();
      if(currItemWeight <= tempCapacity) {
        filledItems.add(items[i].getItemNumber());
        totalProfit += currItemProfit;
        tempCapacity -= currItemWeight;
      }
      else {
        break;
      }
    }
    double fraction = (double)tempCapacity/currItemWeight;
    totalProfit += (double)(currItemProfit*fraction);
    System.out.println("KnapSack filled using strategy: "+strategy+".\nMaximum Profit: "+totalProfit);
    System.out.print("Items added: ");
    for(int k:filledItems) {
      System.out.print(k+" ");
    }
    if(fraction != 0d)
      System.out.print("and "+tempCapacity+"/"+currItemWeight+" of "+items[i].getItemNumber());
    System.out.println("\n");
  }

  public static void main(String[] args) {
    KnapSack obj = new KnapSack();
  }
}

然而，在某些情况下会导致奇怪的结果。对于例如当我尝试以下输入时：

No. of Items: 5
Capacity: 20
Item 1 (Format - Profit<space>Weight): 20 1
Item 2 (Format - Profit<space>Weight): 10 1
Item 3 (Format - Profit<space>Weight): 10 2
Item 4 (Format - Profit<space>Weight): 40 8
Item 5 (Format - Profit<space>Weight): 60 11

最大利润的预期输出为125（项目1，项目2，项目5，项目3和项目4的5/8），但获得的输出如下：（请检查链接，因为我不允许嵌入图片）

Output Screenshot

请注意，排序顺序混乱，因为第5项不应该是反向排序顺序的最后一个，它必须是第3个。什么可能是罪魁祸首？

Answer 1

您的比较器错误地执行除法：不是将int转换为double然后除以，而是先划分，然后将结果转换为double。那时分数消失了，所以结果没有正确排序。

按如下方式更改比较器：

public static Comparator<Item> profitByWeightComparator = new Comparator<Item>() {
    @Override
    public int compare(Item item1, Item item2) {
        double item1Ratio = ((double)item1.getProfit())/item1.getWeight();
        double item2Ratio = ((double)(item2.getProfit())/item2.getWeight();
        return Double.compare(item1Ratio, item2Ratio);
    }
};

现在，除法在double中完成，并且在不截断小数部分的情况下进行比较。

如果权重严格为正数且profit * weight不会溢出int，则可以完全跳过除法，比较这样的比率：

public static Comparator<Item> profitByWeightComparator = new Comparator<Item>() {
    @Override
    public int compare(Item item1, Item item2) {
        return Integer.compare(
            item1.getProfit() * item2.getWeight()
        ,   item2.getProfit() * item1.getWeight()
        );
    }
};

Java Comparator的reverse（）方法有很奇怪的结果

1 个答案: