Leetcode 18 4 sum - practice with hashmap prepared on visited elements only

Leetcode18_4sum.cs

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

namespace Leetcode18_4sum
{
    class Program
    {
        /// <summary>
        /// Leetcode 18: 4 sum
        /// https://leetcode.com/problems/4sum/description/
        /// May 1, 2018
        /// </summary>
        /// <param name="args"></param>
        static void Main(string[] args)
        {
            var quardruplets = FourSum(new int[]{3, 2, 1, 4, 6}, 12); 
        }

        public static IList<IList<int>> FourSum(int[] numbers, int target)
        {
            var quadruplets = new List<IList<int>>();

            if (numbers == null || numbers.Length == 0)
            {
                return quadruplets;
            }

            Array.Sort(numbers);

            var firstTwoNumbersSums = new Dictionary<int, IList<int[]>>();
            var quadrupletsUnique = new HashSet<string>();

            int length = numbers.Length;            

            for (int third = 0; third < length - 1; third++)
            {
                var thirdNumber = numbers[third];

                for (int fourth = third + 1; fourth < length; fourth++)
                {
                    var fourthNumber = numbers[fourth];
                    var lastTwoSum = thirdNumber + fourthNumber;

                    var search = target - lastTwoSum;

                    if (!firstTwoNumbersSums.ContainsKey(search))
                    {
                        continue;
                    }

                    foreach(var item in firstTwoNumbersSums[search])
                    {
                        var firstNumber  = numbers[item[0]];
                        var secondNumber = numbers[item[1]];

                        var quadruplet = new int[] { firstNumber, secondNumber, thirdNumber, fourthNumber };
                        var key = string.Join(",", quadruplet);
                        if (!quadrupletsUnique.Contains(key))
                        {
                            quadrupletsUnique.Add(key); 
                            quadruplets.Add(new List<int>(new int[] { firstNumber, secondNumber, thirdNumber, fourthNumber }));                            
                        }
                    }
                }

                // It is time to add visited element into two sum dictionary.
                // Argue that no need to add any two indexes smaller than third, why?            
                for (int firstId = 0; firstId < third; firstId++)
                {
                    var firstNumber = numbers[firstId];
                    var firstTwoSum = firstNumber + thirdNumber;

                    var newItems = new int[] { firstId, third };

                    if (!firstTwoNumbersSums.ContainsKey(firstTwoSum))
                    {
                        var items = new List<int[]>();                        

                        firstTwoNumbersSums.Add(firstTwoSum, items); 
                     
                    }
                    
                    firstTwoNumbersSums[firstTwoSum].Add(newItems);                     
                }
            }

            return quadruplets;
        }       
    }
}