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PermutationPlainRank Property

Row index of the sequence in the plain ordered Permutation table.

Namespace:  Kaos.Combinatorics
Assembly:  KaosCombinatorics (in KaosCombinatorics.dll) Version: 6.0.0.0
Syntax
C#
Copy
public long PlainRank { get; set; }

Property Value

Type: Int64
Exceptions
ExceptionCondition
InvalidOperationExceptionWhen Choices not equal to Picks.
Remarks

Plain changes produces a table where adjacent rows differ by only a single swap of 2 adjacent elements. The table always begins with the same row that begins the lexicographically ordered table of the same Choices.

Any assigned value out of range will be normalized to (0..RowCount-1).

Examples
C#
Copy
using System;
using Kaos.Combinatorics;

namespace ExampleApp
{
    class PnExample07
    {
        static void Main()
        {
            var pn = new Permutation (4);

            Console.WriteLine ($"Plain changes, n={pn.Choices}:\n");

            foreach (var row in pn.GetRowsOfPlainChanges())
                Console.WriteLine ($"{row.PlainRank,2}: {row}  Swaps={row.Swaps}, Rank={row.Rank}");
        }

        /* Output:

        Plain changes, n=4:

         0: { 0, 1, 2, 3 }  Swaps=0, Rank=0
         1: { 0, 1, 3, 2 }  Swaps=1, Rank=1
         2: { 0, 3, 1, 2 }  Swaps=2, Rank=4
         3: { 3, 0, 1, 2 }  Swaps=3, Rank=18
         4: { 3, 0, 2, 1 }  Swaps=2, Rank=19
         5: { 0, 3, 2, 1 }  Swaps=1, Rank=5
         6: { 0, 2, 3, 1 }  Swaps=2, Rank=3
         7: { 0, 2, 1, 3 }  Swaps=1, Rank=2
         8: { 2, 0, 1, 3 }  Swaps=2, Rank=12
         9: { 2, 0, 3, 1 }  Swaps=3, Rank=13
        10: { 2, 3, 0, 1 }  Swaps=2, Rank=16
        11: { 3, 2, 0, 1 }  Swaps=3, Rank=22
        12: { 3, 2, 1, 0 }  Swaps=2, Rank=23
        13: { 2, 3, 1, 0 }  Swaps=3, Rank=17
        14: { 2, 1, 3, 0 }  Swaps=2, Rank=15
        15: { 2, 1, 0, 3 }  Swaps=1, Rank=14
        16: { 1, 2, 0, 3 }  Swaps=2, Rank=8
        17: { 1, 2, 3, 0 }  Swaps=3, Rank=9
        18: { 1, 3, 2, 0 }  Swaps=2, Rank=11
        19: { 3, 1, 2, 0 }  Swaps=1, Rank=21
        20: { 3, 1, 0, 2 }  Swaps=2, Rank=20
        21: { 1, 3, 0, 2 }  Swaps=3, Rank=10
        22: { 1, 0, 3, 2 }  Swaps=2, Rank=7
        23: { 1, 0, 2, 3 }  Swaps=1, Rank=6

        */
    }
}
See Also