C#实现基于权重的随机算法

一、线性扫描

最简单常用的算法，获取随机值，直接遍历。

public static int GetRandomIndexLinear(int[] list, int totalWeight)
{
    var value = random.Next(0, totalWeight);
    for (int i = 0; i < list.Length; i++)
    {
        value -= list[i];
        if (value <= 0)
        {
            return i;
        }
    }
    return -1;
}

二、预处理

首先对权重进行处理，填充PrepareAdRewardWeight。

public static (float, int)[] PrepareAdRewardWeight;

设置n个空桶，空桶容量为平均权重，按平均权重区分大权重与小权重，依次将小权重填入桶中，剩余部分由大权重的一部分填满，大权重减去填充部分后，如果小于平均值，则后续当做小权重处理。
一轮遍历后，填充好的数据为小权重的占比和大权重的索引。

public static void InitAdRewardWeight(int[] weightList)
{
    var total = weightList.Sum();
    int length = weightList.Length;
    var avg = 1f * total / length;
    List<(float, int)> smallAvg = new List<(float, int)>();
    List<(float, int)> bigAvg = new List<(float, int)>();
    for (int i = 0; i < weightList.Length; i++)
    {
        (weightList[i] > avg ? bigAvg : smallAvg).Add((weightList[i], i));
    }
    PrepareAdRewardWeight = new (float, int)[weightList.Length];
    for (int i = 0; i < weightList.Length; i++)
    {
        if (smallAvg.Count > 0)
        {
            if (bigAvg.Count > 0)
            {
                PrepareAdRewardWeight[smallAvg[0].Item2] = (smallAvg[0].Item1 / avg, bigAvg[0].Item2);
                bigAvg[0] = (bigAvg[0].Item1 - avg + smallAvg[0].Item1, bigAvg[0].Item2);
                if (avg - bigAvg[0].Item1 > 0.0000001f)
                {
                    smallAvg.Add(bigAvg[0]);
                    bigAvg.RemoveAt(0);
                }
            }
            else
            {
                PrepareAdRewardWeight[smallAvg[0].Item2] = (smallAvg[0].Item1 / avg, smallAvg[0].Item2);
            }
            smallAvg.RemoveAt(0);
        }
        else
        {
            PrepareAdRewardWeight[bigAvg[0].Item2] = (bigAvg[0].Item1 / avg, bigAvg[0].Item2);
            bigAvg.RemoveAt(0);
        }
    }
}

预处理结束后，获取随机值的复杂度为O(1)。

public static int GetRandomIndex()
{
    var randomNum = random.NextDouble() * PrepareAdRewardWeight.Length;
    int intRan = (int)Math.Floor(randomNum);
    var p = PrepareAdRewardWeight[intRan];
    if (p.Item1 > randomNum - intRan)
    {
        return intRan;
    }
    else
    {
        return p.Item2;
    }
}

三、总结

随机目标的数量越大，第二种方法越高效。

参考

https://zhuanlan.zhihu.com/p/146216606