Knight tour - dynamic programming - March 15, 2018

KnightTour_DynamicProgramming.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace knightTour
{
    /// <summary>
    /// problem statement:
    /// https://stackoverflow.com/questions/2893470/generate-10-digit-number-using-a-phone-keypad
    /// </summary>
    class knightTour
    {
        static void Main(string[] args)
        {
            var result   = CountDifferentPhoneNumbers(1, 1);
            var result2  = CountDifferentPhoneNumbers(2, 1);
            var result10 = CountDifferentPhoneNumbers(10, 1);
            var result10B = CountDifferentPhoneNumbers(10, 6);
        }

        public static int CountDifferentPhoneNumbers(int kSteps, int start)
        {
            var knights = prepareKnightTable();

            var previousStep = new int[10];
            previousStep[start] = 1; 

            var currentStep  = new int[10]; 

            for (int step = 0; step < kSteps; step++)
            {
                for (int number = 0; number <= 9; number++)
                {
                    var count = previousStep[number];
                    foreach (var item in knights[number])
                    {
                        currentStep[item] += count;
                    }
                }

                arrayCopy(previousStep, currentStep);
                initalizeCurrentStep(currentStep);
            }

            return previousStep.Sum(); 
        }

        private static void arrayCopy(int[] copyTo, int[] copyFrom)
        {
            var length = copyFrom.Length;
            for (int i = 0; i < length; i++)
            {
                copyTo[i] = copyFrom[i];
            }
        }

        private static void initalizeCurrentStep(int[] numbers)
        {
            for (int i = 0; i < numbers.Length; i++)
            {
                numbers[i] = 0; 
            }
        }

        private static int[][] prepareKnightTable()
        {
            var knights = new int[10][];
            knights[0] = new int[] { 4, 6 };
            knights[1] = new int[] { 8, 6 };
            knights[2] = new int[] { 7, 9 };
            knights[3] = new int[] { 4, 8 };
            knights[4] = new int[] { 3, 9 };
            knights[5] = new int[] { };
            knights[6] = new int[] { 0, 1, 7 };
            knights[7] = new int[] { 2, 6 };
            knights[8] = new int[] { 1, 3 };
            knights[9] = new int[] { 2, 4 };

            return knights;
        }
    }
}

Two issues:

1. First the calculation of knights[4] = new int[]{0, 3, 9}, 0 is missing in my code line 74;
2. All possible numbers, I need to set start number from 0 to 9, 10 of them.