/// <summary> /// Chooses an arbitrary ordering of the sequence [0, 1, ... <paramref name="n"/> - 1] using <paramref name="i"/> to choose.
/// </summary>
/// <param name="n">The number of elements to permute</param>
/// <param name="i">The index of the permutation. This should be a nonnegative number less than
/// Factorial(<paramref name="n"/>).</param>
/// <returns>An array of indices between 0 and <paramref name="n"/> in an arbitrary order.</returns>
/// <exception cref="ArgumentException">Thrown if <paramref name="n"/>is out of range. The current
/// implementation allows
/// permutation of up to 16 elements.</exception>
/// <exception cref="ArgumentException">Thorwn if <paramref name="i"/>is not a nonnegative integer
/// less than Factorial(<paramref name="n"/>).</exception>
static int[] ChoosePermutation_1(int n, int i)
//^ requires 0 <= n && n <= 12 && 0 <= i && i < Combinatorics.Factorial(n);
{
// if (!(0 <= n && n <= 12)) throw new ArgumentException("ChoosePermutation: out of range. Must be between 0 and 16.");
// if (!(0 <= i && i < Combinatorics.Factorial(n))) throw new ArgumentException("ChoosePermutation: out of range. Must be in [0, Combinatorics.Factorial(16)).");
int[] result = new int[n];
Set <int> indicesToChoose = Set <int> .EmptySet;
for (int k = 0; k < n; k += 1)
{
indicesToChoose = indicesToChoose.Add(k);
}
int choice = i;
for (int l = n - 1; l >= 0; l -= 1)
{
int f = Combinatorics.Factorial(l);
int currentChoiceIndex = choice / f;
int currentChoice = indicesToChoose.Choose(currentChoiceIndex);
result[l] = currentChoice;
indicesToChoose = indicesToChoose.Remove(currentChoice);
choice = choice % f;
}
return(result);
}
/// <summary>
/// Chooses an arbitrary ordering of the sequence [0, 1, ... <paramref name="n"/> - 1] using <paramref name="i"/> to choose.
/// </summary>
/// <param name="n">The number of elements to permute</param>
/// <param name="i">The index of the permutation. If this is a nonnegative number less than
/// Factorial(<paramref name="n"/>) and <paramref name="n"/> <= 12, then the permutations are enumerated. In other words,
/// each of the possible permutations will correspond to exactly one integer in [0..Factorial(n)). Outside
/// of that range, the permutation will be chosen using the given integer as a random seed.</param>
/// <returns>An array of indices between 0 and <paramref name="n"/> in a chosen order.</returns>
public static int[] ChoosePermutation(int n, int i)
{
// for case of small numbers, use enumerated choice
if (0 <= n && n <= 12 && 0 <= i && i < Combinatorics.Factorial(n))
{
return(ChoosePermutation_1(n, i));
}
if (n < 0)
{
throw new ArgumentException("NModel.Combinatorics.ChoosePermutation: Parameter may not be negative", "n");
}
// otherwise use i as a random seed
int[] result = new int[n];
Set <int> indicesToChoose = Set <int> .EmptySet;
for (int k = 0; k < n; k += 1)
{
indicesToChoose = indicesToChoose.Add(k);
}
int choice = TypedHash <int> .ComputeHash(n, i);
for (int l = 0; l < n; l += 1)
{
//^ assume indicesToChoose.Count > 0;
int currentChoice = indicesToChoose.Choose(Math.Abs(choice) % indicesToChoose.Count);
result[l] = currentChoice;
indicesToChoose = indicesToChoose.Remove(currentChoice);
choice = TypedHash <int> .ComputeHash(choice, l);
}
return(result);
}