selection based on percentage weighting


Question

I have a set of values, and an associated percentage for each:

a: 70% chance
b: 20% chance
c: 10% chance

I want to select a value (a, b, c) based on the percentage chance given.

how do I approach this?


my attempt so far looks like this:

r = random.random()
if r <= .7:
    return a
elif r <= .9:
    return b
else: 
    return c

I'm stuck coming up with an algorithm to handle this. How should I approach this so it can handle larger sets of values without just chaining together if-else flows.


(any explanation or answers in pseudo-code are fine. a python or C# implementation would be especially helpful)

1
27
9/7/2010 2:52:10 AM

Here is a complete solution in C#:

public class ProportionValue<T>
{
    public double Proportion { get; set; }
    public T Value { get; set; }
}

public static class ProportionValue
{
    public static ProportionValue<T> Create<T>(double proportion, T value)
    {
        return new ProportionValue<T> { Proportion = proportion, Value = value };
    }

    static Random random = new Random();
    public static T ChooseByRandom<T>(
        this IEnumerable<ProportionValue<T>> collection)
    {
        var rnd = random.NextDouble();
        foreach (var item in collection)
        {
            if (rnd < item.Proportion)
                return item.Value;
            rnd -= item.Proportion;
        }
        throw new InvalidOperationException(
            "The proportions in the collection do not add up to 1.");
    }
}

Usage:

var list = new[] {
    ProportionValue.Create(0.7, "a"),
    ProportionValue.Create(0.2, "b"),
    ProportionValue.Create(0.1, "c")
};

// Outputs "a" with probability 0.7, etc.
Console.WriteLine(list.ChooseByRandom());
36
9/7/2010 3:22:32 AM

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