从 C# 中的加权列表中选择 x 个随机元素(无需替换

问题描述

更新:我的问题已解决，我更新了问题中的代码源以与 Jason 的回答相匹配.请注意，rikitikitik 的答案是解决从样本中抽取卡片并替换的问题.

Update: my problem has been solved, I updated the code source in my question to match with Jason's answer. Note that rikitikitik answer is solving the issue of picking cards from a sample with replacement.

我想从加权列表中选择 x 个随机元素.采样是无更换的.我找到了这个答案:https://stackoverflow.com/a/2149533/57369 用 Python 实现.我在 C# 中实现了它并对其进行了测试.但是结果(如下所述)与我的预期不符.我对 Python 一无所知，所以我很确定我在将代码移植到 C# 时犯了一个错误，但我看不到 Pythong 中的代码在哪里有很好的文档记录.

I want to select x random elements from a weighted list. The sampling is without replacement. I found this answer: https://stackoverflow.com/a/2149533/57369 with an implementation in Python. I implemented it in C# and tested it. But the results (as described below) were not matching what I expected. I've no knowledge of Python so I'm quite sure I made a mistake while porting the code to C# but I can't see where as the code in Pythong was really well documented.

我选择了一张卡片 10000 次，这是我得到的结果(结果在执行中是一致的):

I picked one card 10000 times and this is the results I obtained (the result is consistent accross executions):

Card 1: 18.25 % (10.00 % expected)
Card 2: 26.85 % (30.00 % expected)
Card 3: 46.22 % (50.00 % expected)
Card 4: 8.68 % (10.00 % expected)

如您所见，卡片 1 和卡片 4 的权重均为 1，但卡片 1 的选择频率高于卡片 4(即使我选择 2 或 3 张卡片).

As you can see Card 1 and Card 4 have both a weigth of 1 but Card 1 is awlays picked way more often than card 4 (even if I pick 2 or 3 cards).

测试数据:

var cards = new List<Card>
{
    new Card { Id = 1, AttributionRate = 1 }, // 10 %
    new Card { Id = 2, AttributionRate = 3 }, // 30 %
    new Card { Id = 3, AttributionRate = 5 }, // 50 %
    new Card { Id = 4, AttributionRate = 1 }, // 10 %
};

这是我在 C# 中的实现

Here is my implementation in C#

public class CardAttributor : ICardsAttributor
{
    private static Random random = new Random();

    private List<Node> GenerateHeap(List<Card> cards)
    {
        List<Node> nodes = new List<Node>();
        nodes.Add(null);

        foreach (Card card in cards)
        {
            nodes.Add(new Node(card.AttributionRate, card, card.AttributionRate));
        }

        for (int i = nodes.Count - 1; i > 1; i--)
        {
            nodes[i>>1].TotalWeight += nodes[i].TotalWeight;
        }

        return nodes;
    }

    private Card PopFromHeap(List<Node> heap)
    {
        Card card = null;

        int gas = random.Next(heap[1].TotalWeight);
        int i = 1;

        while (gas >= heap[i].Weight)
        {
            gas -= heap[i].Weight;
            i <<= 1;

            if (gas >= heap[i].TotalWeight)
            {
                gas -= heap[i].TotalWeight;
                i += 1;
            }
        }

        int weight = heap[i].Weight;
        card = heap[i].Value;

        heap[i].Weight = 0;

        while (i > 0)
        {
            heap[i].TotalWeight -= weight;
            i >>= 1;
        }

        return card;
    }

    public List<Card> PickMultipleCards(List<Card> cards, int cardsToPickCount)
    {
        List<Card> pickedCards = new List<Card>();

        List<Node> heap = GenerateHeap(cards);

        for (int i = 0; i < cardsToPickCount; i++)
        {
            pickedCards.Add(PopFromHeap(heap));
        }

        return pickedCards;
    }
}

class Node
{
    public int Weight { get; set; }
    public Card Value { get; set; }
    public int TotalWeight { get; set; }

    public Node(int weight, Card value, int totalWeight)
    {
        Weight = weight;
        Value = value;
        TotalWeight = totalWeight;
    }
}

public class Card
{
    public int Id { get; set; }
    public int AttributionRate { get; set; }
}

推荐答案

程序中有两个小错误.首先，随机数的范围应该正好等于所有物品的总重量:

There are two minor bugs in the program. First, the range of the random number should be exactly equal to the total weight of all the items:

int gas = random.Next(heap[1].TotalWeight);

其次，将 gas > 的两个地方都改为 gas >=.

Second, change both places where it says gas > to say gas >=.

(原Python代码可以，因为gas是浮点数，所以>和>=的区别可以忽略不计.编写该代码是为了接受整数或浮点权重.)

(The original Python code is OK because gas is a floating-point number, so the difference between > and >= is negligible. That code was written to accept either integer or floating-point weights.)

更新:好的，您在代码中进行了建议的更改.我认为该代码现在是正确的！

Update: OK, you made the recommended changes in your code. I think that code is correct now!

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