Daily Programmer 261 Hard

using System;
using System.Collections.Generic;

namespace DailyProgrammer261Hard
{
    class Program
    {
        static void Main(string[] args)
        {
            int?[,] grid = new int?[4, 4];
            List<int[]> dominoes = new List<int[]>
            {
                new int[] { 1, 14 },
                new int[] { 2, 8 },
                new int[] { 3, 13 },
                new int[] { 4, 15 },
                new int[] { 5, 11 },
                new int[] { 6, 9 },
                new int[] { 7, 12 },
                new int[] { 10, 16 },
            };
            AddDominoAndValidate(ref grid, dominoes);

            PrintGrid(grid);
            Console.ReadLine();
        }

        static bool AddDominoAndValidate(ref int?[,] grid, List<int[]> dominoes)
        {
            // Where to start?
            int row = -1, col = -1;
            FindFirstEmptyCell(grid, ref row, ref col);

            // Try adding each domino
            bool horizontal = col != grid.GetLength(1) - 1 && !grid[row, col + 1].HasValue;
            bool vertical = row != grid.GetLength(0) - 1;

            foreach (int[] domino in dominoes)
            {
                List<int[]> fewerDominoes = RemoveDominoFromList(dominoes, domino);

                // Horizontal
                if (horizontal)
                {
                    // Unflipped
                    PutDownDomino(ref grid, domino, false, row, col, false);
                    if (VerifyGridMagic(grid))
                    {
                        if (IsGridFull(grid) || AddDominoAndValidate(ref grid, fewerDominoes))
                        {
                            return true;
                        }
                    }
                    PickUpDomino(ref grid, row, col, false);

                    // Flipped
                    PutDownDomino(ref grid, domino, true, row, col, false);
                    if (VerifyGridMagic(grid))
                    {
                        if (IsGridFull(grid) || AddDominoAndValidate(ref grid, fewerDominoes))
                        {
                            return true;
                        }
                    }
                    PickUpDomino(ref grid, row, col, false);
                }

                // Vertical
                if (vertical)
                {
                    // Unflipped
                    PutDownDomino(ref grid, domino, false, row, col, true);
                    if (VerifyGridMagic(grid))
                    {
                        if (IsGridFull(grid) || AddDominoAndValidate(ref grid, fewerDominoes))
                        {
                            return true;
                        }
                    }
                    PickUpDomino(ref grid, row, col, true);

                    // Flipped
                    PutDownDomino(ref grid, domino, true, row, col, true);
                    if (VerifyGridMagic(grid))
                    {
                        if (IsGridFull(grid) || AddDominoAndValidate(ref grid, fewerDominoes))
                        {
                            return true;
                        }
                    }
                    PickUpDomino(ref grid, row, col, true);
                }
            }

            return false;
        }

        private static void FindFirstEmptyCell(int?[,] grid, ref int row, ref int col)
        {
            for (int r = 0; r < grid.GetLength(0); r++)
            {
                for (int c = 0; c < grid.GetLength(1); c++)
                {
                    if (!grid[r, c].HasValue)
                    {
                        row = r;
                        col = c;
                        return;
                    }
                }
            }
        }

        private static List<int[]> RemoveDominoFromList(List<int[]> dominoes, int[] removed)
        {
            List<int[]> list = new List<int[]>();
            foreach (int[] domino in dominoes)
            {
                if (domino[0] != removed[0])
                {
                    list.Add(domino);
                }
            }
            return list;
        }

        private static void PutDownDomino(ref int?[,] grid, int[] domino, bool flipped, int row, int col, bool vertical)
        {
            //Console.WriteLine($"Placed {(flipped ? "flipped " : "")}domino [{domino[0]}, {domino[1]}] {(vertical ? "vertically" : "horizontally")} in row {row}, col {col}.");

            int domino1 = flipped ? domino[1] : domino[0];
            int domino2 = flipped ? domino[0] : domino[1];

            grid[row, col] = domino1;
            if (vertical)
            {
                grid[row + 1, col] = domino2;
            }
            else
            {
                grid[row, col + 1] = domino2;
            }
        }

        private static void PickUpDomino(ref int?[,] grid, int row, int col, bool vertical)
        {
            grid[row, col] = null;
            if (vertical)
            {
                grid[row + 1, col] = null;
            }
            else
            {
                grid[row, col + 1] = null;
            }
        }

        private static bool VerifyGridMagic(int?[,] grid)
        {
            int n = grid.GetLength(0);
            int m = (n / 2) * (n * n + 1);

            // Rows
            for (int r = 0; r < n; r++)
            {
                List<int?> items = new List<int?>();
                for (int c = 0; c < n; c++)
                {
                    items.Add(grid[r, c]);
                }
                if (!VerifyMagic(items, m)) { return false; }
            }

            // Cols
            for (int c = 0; c < n; c++)
            {
                List<int?> items = new List<int?>();
                for (int r = 0; r < n; r++)
                {
                    items.Add(grid[r, c]);
                }
                if (!VerifyMagic(items, m)) { return false; }
            }

            // Diag 1
            List<int?> d1Items = new List<int?>();
            for (int i = 0; i < n; i++)
            {
                d1Items.Add(grid[i, i]);
            }
            if (!VerifyMagic(d1Items, m)) { return false; }

            // Diag 2
            List<int?> d2Items = new List<int?>();
            for (int i = 0; i < n; i++)
            {
                d2Items.Add(grid[i, n - i - 1]);
            }
            if (!VerifyMagic(d2Items, m)) { return false; }

            return true;
        }

        private static bool VerifyMagic(List<int?> items, int magic)
        {
            int sum = 0;
            foreach (int? item in items)
            {
                if (item.HasValue)
                {
                    sum += item.Value;
                }
                else
                {
                    return true;
                }
            }
            if (sum == magic)
            {
                return true;
            }
            return false;
        }

        private static bool IsGridFull(int?[,] grid)
        {
            int n = grid.GetLength(0);
            for (int r = 0; r < n; r++)
            {
                for (int c = 0; c < n; c++)
                {
                    if (!grid[r, c].HasValue)
                    {
                        return false;
                    }
                }
            }
            return true;
        }

        static void PrintGrid(int?[,] grid)
        {
            int n = grid.GetLength(0);
            for (int r = 0; r < n; r++)
            {
                for (int c = 0; c < n; c++)
                {
                    Console.Write(NullableIntToString(grid[r, c]));
                    Console.Write(" ");
                }
                Console.Write("\r\n");
            }
        }

        static string NullableIntToString(int? value)
        {
            if (value.HasValue) return value.Value.ToString("00");
            else return "__";
        }
    }
}