Coin Counting Problem

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;

namespace Z5_BuyGraphs
{
    class Program
    {
        // Dynamic programming, bottoms-up approach
        // Ref: [http://www.ccs.neu.edu/home/jaa/CSG713.04F/Information/Handouts/dyn_prog.pdf]

        public static int[] denoms = { 1, 8, 9, 27, 28, 31, 36 };
        public static int[] BigC;
        public static int[] BigS;

        static void Main(string[] args)
        {
            int money = 46;
            Console.WriteLine(CoinCounting(money));
            while (money > 0)
            {
                Console.Write(denoms[BigS[money]] + ", ");
                money -= denoms[BigS[money]];
            }
        }

        // O(NlogN + NK) //Sort + 2 loops
        private static int CoinCounting(int changeThis)
        {
            int coinsNeededMin = 0;
            int firstCoin = 0;
            BigC = new int[changeThis + 1];
            BigS = new int[changeThis + 1];

            Array.Sort(denoms);

            for (int i = 1; i <= changeThis; i++)
            {
                coinsNeededMin = int.MaxValue;
                for (int j = 0; j < denoms.Length && denoms[j] <= i; j++)
                {
                    int result = 1 + BigC[i - denoms[j]];
                    if (result < coinsNeededMin)
                    {
                        coinsNeededMin = result;
                        firstCoin = j;
                    }
                }
                BigC[i] = coinsNeededMin;
                BigS[i] = firstCoin;
            }
            return coinsNeededMin;
        }
    }
}