Pick random element from list with probability

Question

I Have a list that contains four item (A, B, C, D). Every item has a probability to be chosen. Let's say for example A has 74% of chance to be picked, B 15%, C 7% ,and D 4%.

I want to create a function that choose randomly an item according to its probability.

Any help please?

Answer 1

Define a class for your items like this:

class Items<T>
{
    public double Probability { get; set; }
    public T Item { get; set; }
}

then initialize it

var initial = new List<Items<string>>
{
    new Items<string> {Probability = 74 / 100.0, Item = "A"},
    new Items<string> {Probability = 15 / 100.0, Item = "B"},
    new Items<string> {Probability = 7 / 100.0, Item = "C"},
    new Items<string> {Probability = 4 / 100.0, Item = "D"},
};

then you need to convert it to aggregate a sum of probabilities from 0 to 1

var converted = new List<Items<string>>(initial.Count);
var sum = 0.0;
foreach (var item in initial.Take(initial.Count - 1))
{
    sum += item.Probability;
    converted.Add(new Items<string> {Probability = sum, Item = item.Item});
}
converted.Add(new Items<string> {Probability = 1.0, Item = initial.Last().Item});

now you can pick an item from converted collection with respect to probability:

var rnd = new Random();
while (true)
{
    var probability = rnd.NextDouble();
    var selected = converted.SkipWhile(i => i.Probability < probability).First();
    Console.WriteLine($"Selected item = {selected.Item}");
}

NOTE: my implementation have O(n) complexity. You can optimize it with binary search (because values in converted collection are sorted)