随机加权选择 [英] Random weighted choice

问题描述

考虑下面代表 Broker 的类:

Consider the class below that represents a Broker:

public class Broker
{
    public string Name = string.Empty;
    public int Weight = 0;

    public Broker(string n, int w)
    {
        this.Name = n;
        this.Weight = w;
    }
}

我想从数组中随机选择一个 Broker，同时考虑到它们的权重.

I'd like to randomly select a Broker from an array, taking into account their weights.

你觉得下面的代码怎么样?

What do you think of the code below?

class Program
    {
        private static Random _rnd = new Random();

        public static Broker GetBroker(List<Broker> brokers, int totalWeight)
        {
            // totalWeight is the sum of all brokers' weight

            int randomNumber = _rnd.Next(0, totalWeight);

            Broker selectedBroker = null;
            foreach (Broker broker in brokers)
            {
                if (randomNumber <= broker.Weight)
                {
                    selectedBroker = broker;
                    break;
                }

                randomNumber = randomNumber - broker.Weight;
            }

            return selectedBroker;
        }


        static void Main(string[] args)
        {
            List<Broker> brokers = new List<Broker>();
            brokers.Add(new Broker("A", 10));
            brokers.Add(new Broker("B", 20));
            brokers.Add(new Broker("C", 20));
            brokers.Add(new Broker("D", 10));

            // total the weigth
            int totalWeight = 0;
            foreach (Broker broker in brokers)
            {
                totalWeight += broker.Weight;
            }

            while (true)
            {
                Dictionary<string, int> result = new Dictionary<string, int>();

                Broker selectedBroker = null;

                for (int i = 0; i < 1000; i++)
                {
                    selectedBroker = GetBroker(brokers, totalWeight);
                    if (selectedBroker != null)
                    {
                        if (result.ContainsKey(selectedBroker.Name))
                        {
                            result[selectedBroker.Name] = result[selectedBroker.Name] + 1;
                        }
                        else
                        {
                            result.Add(selectedBroker.Name, 1);
                        }
                    }
                }


                Console.WriteLine("A		" + result["A"]);
                Console.WriteLine("B		" + result["B"]);
                Console.WriteLine("C		" + result["C"]);
                Console.WriteLine("D		" + result["D"]);

                result.Clear();
                Console.WriteLine();
                Console.ReadLine();
            }
        }
    }

我没那么自信.当我运行这个时，Broker A 总是比 Broker D 获得更多的点击，并且它们具有相同的权重.

I'm not so confident. When I run this, Broker A always gets more hits than Broker D, and they have the same weight.

有更准确的算法吗?

谢谢！

推荐答案

你的算法几乎是正确的.但是，测试应该是 < 而不是 <=:

Your algorithm is nearly correct. However, the test should be < instead of <=:

if (randomNumber < broker.Weight)

这是因为 0 包含在随机数中，而 totalWeight 是不包含的.换句话说，权重为 0 的经纪人仍然有很小的机会被选中——根本不是你想要的.这说明经纪商 A 的点击量比经纪商 D 多.

This is because 0 is inclusive in the random number while totalWeight is exclusive. In other words, a broker with weight 0 would still have a small chance of being selected – not at all what you want. This accounts for broker A having more hits than broker D.

除此之外，您的算法很好，实际上是解决此问题的规范方法.

Other than that, your algorithm is fine and in fact the canonical way of solving this problem.

这篇关于随机加权选择的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！