/// <summary>
/// Use heaps to find a running median in an array of integers.
/// </summary>
/// <param name="input"></param>
/// <returns></returns>
public static double FindMedian(int[] input)
{
MaxHeap lowerHalfHeap = new MaxHeap(input.Length / 2);
Heap upperHalfHeap = new Heap(input.Length / 2);
foreach (int item in input)
{
if (lowerHalfHeap.Size <= upperHalfHeap.Size)
{
lowerHalfHeap.Add(item);
}
else
{
upperHalfHeap.Add(item);
}
Heap.Balance(lowerHalfHeap, upperHalfHeap);
}
if (input.Length % 2 == 0)
{
return((double)(lowerHalfHeap.Peek() + upperHalfHeap.Peek()) / 2);
}
else
{
return((double)lowerHalfHeap.Peek());
}
}
/// <summary>
/// Helper method to balance heaps after each addition.
/// </summary>
/// <param name="lowerHeap"></param>
/// <param name="upperHeap"></param>
public static void Balance(MaxHeap lowerHeap, Heap upperHeap)
{
while (lowerHeap.Size > 0 && upperHeap.Size > 0 && lowerHeap.Peek() > upperHeap.Peek())
{
int lowHead = lowerHeap.Poll();
int highHead = upperHeap.Poll();
upperHeap.Add(lowHead);
lowerHeap.Add(highHead);
}
}