Random weighted choice


Question

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;
    }
}

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

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

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

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

Is there a more accurate algorithm?

Thanks!

1
53
9/11/2008 2:34:11 PM

Accepted Answer

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

if (randomNumber < broker.Weight)

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.

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

34
9/11/2008 2:45:27 PM

How about something a little more generic, that can be used for any data type?

using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;

public static class IEnumerableExtensions {

    public static T RandomElementByWeight<T>(this IEnumerable<T> sequence, Func<T, float> weightSelector) {
        float totalWeight = sequence.Sum(weightSelector);
        // The weight we are after...
        float itemWeightIndex =  new Random().NextDouble * totalWeight;
        float currentWeightIndex = 0;

        foreach(var item in from weightedItem in sequence select new { Value = weightedItem, Weight = weightSelector(weightedItem) }) {
            currentWeightIndex += item.Weight;

            // If we've hit or passed the weight we are after for this item then it's the one we want....
            if(currentWeightIndex >= itemWeightIndex)
                return item.Value;

        }

        return default(T);

    }

}

Simply call by

    Dictionary<string, float> foo = new Dictionary<string, float>();
    foo.Add("Item 25% 1", 0.5f);
    foo.Add("Item 25% 2", 0.5f);
    foo.Add("Item 50%", 1f);

    for(int i = 0; i < 10; i++)
        Console.WriteLine(this, "Item Chosen {0}", foo.RandomElementByWeight(e => e.Value));

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