static IEnumerable <int> MedianMaintenance(IEnumerable <int> xs)
{
MaxPQ <int> lowValues = PQ <int> .CreateMaxPQ();
MinPQ <int> highValues = PQ <int> .CreateMinPQ();
int y = 0;
foreach (var x in xs) //lg(N!) + 4/3 lg (N!) == 7/3 lg (N!)
{
if (lowValues.Size > 0) //lg(N!)
{
if (x > lowValues.Top)
{
highValues.Push(x); //lg N
}
else
{
lowValues.Push(x); //lg N
}
}
else
{
lowValues.Push(x); //lg N
}
//TODO: Not a simple analysis, depends on order of data in xs
//Draft: Suppose 1/3 per branch and 2 lg N Push and Extract, the expected value would be 4/3 lg (N!)
if (lowValues.Size > highValues.Size + 1)
{
highValues.Push(ExtractMax(lowValues)); //2 lg N (Push + Extract)
}
else if (highValues.Size > lowValues.Size)
{
lowValues.Push(ExtractMin(highValues)); //2 lg N (Push + Extract)
}
//else { } //0
y = lowValues.Top;
yield return(y);
//DEBUG
//Console.WriteLine("Median of {0,4} = {1,4}", lowValues.Size + highValues.Size, y);
}
}