Bestimmen Sie begründet die Anzahl der Permutationen von [6] mit höchstens drei Fixpunkten.

Permutation with a maximum of 3 fixed points.cs

var unchaged = new int[] { 1, 2, 3, 4, 5, 6 };
var perms = GetPermutations(unchaged, 6);
int counter = 0;
var tolerances = new int[] { 0, 0, 0, 0 };
foreach (var perm in perms)
{
    var list = perm.ToList();
    var text = "";
    int tolerance = 0;
    for (int i = 0; i < list.Count; i++)
    {
        var item = list[i];
        if (item == unchaged[i])
        {
            if (tolerance < 4)
            {
                tolerance++;
            }
            else
            {
                text = "";
                break;
            }
        }
        text += item + " ";
    }
    if (text != "")
    {
        if (tolerance < 4)
        {
            tolerances[tolerance]++;
            counter++;
            Console.WriteLine(text + "Fixed points " + tolerance);
        }
    }
}
Console.WriteLine(counter);
for (int i = 0; i < 4; i++)
{
    Console.WriteLine("Tolerance " + i + " " + tolerances[i]);
}

static IEnumerable<IEnumerable<T>> GetPermutations<T>(IEnumerable<T> list, int length)
{
    if (length == 1) return list.Select(t => new T[] { t });
    return GetPermutations(list, length - 1).SelectMany(t => list.Where(o => !t.Contains(o)), (t1, t2) => t1.Concat(new T[] { t2 }));
}