How do I calculate the “median of five” in C#?

Question

The median of five is sometimes used as an exercise in algorithm design and is known to be computable using only 6 comparisons.

What is the best way

Answer 1

Just to check how many comparisons:

    class MyComparable : IComparable
{

    public static int NumberOfComparisons = 0;

    public int NumPart { get; set; }

    #region IComparable Members

    public int CompareTo(object obj)
    {
        NumberOfComparisons++; //I know, not thread safe but just for the sample
        MyComparable mc = obj as MyComparable;
        if (mc == null)
            return -1;
        else
            return NumPart.CompareTo(mc.NumPart);
    }

    #endregion
}

class Program
{
    static void Main(string[] args)
    {
        List<MyComparable> list = new List<MyComparable>();
        list.Add(new MyComparable() { NumPart = 5 });
        list.Add(new MyComparable() { NumPart = 4 });
        list.Add(new MyComparable() { NumPart = 3 });
        list.Add(new MyComparable() { NumPart = 2 });
        list.Add(new MyComparable() { NumPart = 1 });
        list.Sort();


        Console.WriteLine(MyComparable.NumberOfComparisons);
    }
}

the result is 13.

Answer 2

This should do it

private Double medianofFive(double[] input)
{
    Double temp;
if (input[0] > input[1])//#1 - sort First and Second
{
    temp = input[0];
    input[0] = input[1];
    input[1] = temp;
}
if (input[2] > input[3])//#2 sort Third and Fourth
{
    temp = input[2];
    input[2] = input[3];
    input[3] = temp;
}

// replace the smaller of first and third with 5th, then sort
int smallerIndex = input[0] < input[2] ? 0 : 2;//#3
input[smallerIndex] = input[4];

//sort the new pair
if(input[smallerIndex]>input[smallerIndex+1])//#4
{
    temp = input[smallerIndex];
    input[smallerIndex] = input[smallerIndex+1];
    input[smallerIndex+1] = temp;
}

//compare the two smaller numbers
// then compare the smaller of the two's partner with larger of the two
// the smaller of THOSE two is the median
if (input[2] > input[0])
//#5
{
    temp = input[2] > input[1] ? input[1] : input[2];//#6
}
else
{
    temp = input[0] > input[3] ? input[3] : input[0];//#6
}
    return temp;
}

Answer 3

Interesting how many comparisons in MSDN sample...

public static double Median(this IEnumerable<double> source) {
        if (source.Count() == 0)  throw new InvalidOperationException("Cannot compute median for an empty set.");

        var sortedList = from number in source
                         orderby number
                         select number;

        int itemIndex = (int)sortedList.Count() / 2;

        if (sortedList.Count() % 2 == 0) {
            // Even number of items.
            return (sortedList.ElementAt(itemIndex) + sortedList.ElementAt(itemIndex - 1)) / 2; } else {
            // Odd number of items.
            return sortedList.ElementAt(itemIndex); }
    }

Answer 4

This is basically just factoring out the swapping and sorting code from your C++ example:

private static void Swap(ref double a, ref double b) {
    double t = a;
    a = b;
    b = t;
}

private static void Sort(ref double a, ref double b) {
    if (a > b) {
        double t = a;
        a = b;
        b = t;
    }
}

private static double MedianOfFive(double a, double b, double c, double d, double e){
    // makes a < b and c < d
    Sort(ref a, ref b);
    Sort(ref c, ref d);

    // eleminate the lowest
    if (c < a) {
        Swap(ref b, ref d);
        c = a;
    }

    // gets e in
    a = e;

    // makes a < b
    Sort(ref a, ref b);

    // eliminate another lowest
    // remaing: a,b,d
    if (a < c) {
        Swap(ref b, ref d);
        a = c;
    }

    return Math.Min(d, a);
}