Question

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.

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.

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)

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).

Test data:

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 %
};

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; }
}

Answer 1

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);

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

(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.)

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