Daily Programmer 259 Hard

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

namespace DailyProgrammer259Hard
{
    class Program
    {
        static void Main(string[] args)
        {
            Stopwatch sw = new Stopwatch();
            sw.Start();
            for (int i = 1; i <= 500; i++)
            {
                Console.WriteLine($"{i} --> {DecToNos(i)}");
            }
            Console.WriteLine(sw.ElapsedMilliseconds);

            Console.ReadLine();
        }

        public static int NosToDec(string nos)
        {
            int dec = 0;

            for (int i = 0; i < nos.Length; i++)
            {
                switch (nos[i])
                {
                    case '0':
                        dec += i + 1;
                        break;
                    case '1':
                        dec -= i + 1;
                        break;
                    case '2':
                        dec *= i + 1;
                        break;
                }
            }

            return dec;
        }

        public static string DecToNos(int dec)
        {
            // Find shortest solutions
            List<string> solutions = new List<string>();
            string guess = "0";
            while (true)
            {
                if (NosToDec(guess) == dec)
                {
                    solutions.Add(guess);
                }

                string guess2 = IterateNosString(guess);
                if (guess2.Length != guess.Length && solutions.Count > 0)
                {
                    break;
                }
                guess = guess2;
            }

            // Tiebreaker #1: Most zeros
            List<string> tiebreaker1 = new List<string>();
            int peakZeros = -1;

            foreach (string solution in solutions)
            {
                int zeros = solution.Count(c => c == '0');

                if (zeros == peakZeros)
                {
                    tiebreaker1.Add(solution);
                }
                else if (zeros > peakZeros)
                {
                    tiebreaker1.Clear();
                    tiebreaker1.Add(solution);
                    peakZeros = zeros;
                }
            }

            // Tiebreaker #2: Lowest
            string winner = tiebreaker1[0];

            foreach(string solution in tiebreaker1)
            {
                if (String.CompareOrdinal(solution, winner) < 0)
                {
                    winner = solution;
                }
            }

            // Return
            return winner;
        }

        private static string IterateNosString(string nos)
        {
            StringBuilder sb = new StringBuilder(nos);

            for (int i = nos.Length - 1; i >= 0; i--)
            {
                char c = sb[i];
                if (c == '0')
                {
                    sb[i] = '1';
                    break;
                }
                if (c == '1')
                {
                    sb[i] = '2';
                    break;
                }
                if (c == '2')
                {
                    sb[i] = '0';
                    if (i == 0)
                    {
                        sb.Insert(0, '0');
                    }
                }
            }

            return sb.ToString();
        }
    }
}