Lattice Paths

Problem 15.cs

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

namespace EulerProject
{
    class Program
    {
        private const long gridSize = 20;

        private static long[,] Grid;
        
        [STAThread]
        static void Main(string[] args)
        {
            // Create the grid and assign the start point
            Grid = new long[gridSize + 1, gridSize + 1];
            Grid[0, 0] = 1;

            // For each grid depth
            for (long i = 0; i < gridSize * 2; i++)
            {
                Console.WriteLine("Depth {0}", i);

                // For each point at the specified grid depth
                for (long j = 0; j <= i; j++)
                {
                    long x = j;
                    long y = -(j - i);

                    // Only use cells from within the grid boundaries
                    if (x <= gridSize && y <= gridSize)
                    {
                        // If on the right edge
                        if (x == gridSize)
                        {
                            // All routes go down
                            Grid[x, y + 1] += Grid[x, y];
                        }
                        else
                        {
                            // If on the bottom edge
                            if (y == gridSize)
                            {
                                // All routes go right
                                Grid[x + 1, y] += Grid[x, y];
                            }
                            else
                            {
                                // Both directions free, thus move in both;
                                Grid[x, y + 1] += Grid[x, y];
                                Grid[x + 1, y] += Grid[x, y];
                            }
                        }
                        Console.WriteLine("Cell ({0}, {1}) - Count: {2}", x, y, Grid[x,y]);
                    }
                }
            }

            Console.WriteLine("Depth {0}", (gridSize * 2)+1);
            Console.WriteLine("Cell ({0}, {1}) - Count: {2}", gridSize, gridSize, Grid[gridSize, gridSize]);

            System.Windows.Forms.Clipboard.SetText(Grid[gridSize, gridSize].ToString()); // 137846528820

            Console.ReadLine();
        }
    }
}