Game.cs

using System;

namespace Game15
{
    class Game
    {
        int size;
        int[,] map;
        int space_x, space_y;
        static Random rand = new Random();

        public Game(int _size)
        {
            size = _size;
            map = new int[size, size];
        }

        /// <summary>
        /// Returns the tile numbers to initial position
        /// </summary>
        public void Start ()
        {
            for (int x = 0; x < size; x++)
            {
                for (int y = 0; y < size; y++)
                {
                    map[x, y] = Coords_to_position(x, y) + 1;
                }
            }
            space_x = size - 1;
            space_y = size - 1;
            map[space_x, space_y] = 0;
        }
        
        /// <summary>
        /// Ruturns the position of empty tile
        /// </summary>
        /// <returns></returns>
        public int Space_position()
        {
            return Coords_to_position(space_x, space_y);
        }

        /// <summary>
        /// Swaps the <position> tile with empty tile if possible
        /// </summary>
        /// <param name="position"></param>
        public void Shift (int position)
        {
            Position_to_coords(position, out int x, out int y);
            if (Math.Abs(space_x - x) + Math.Abs(space_y - y) != 1)
                return;

            map[space_x, space_y] = map[x, y];
            map[x, y] = 0;
            space_x = x;
            space_y = y;
        }

        /// <summary>
        /// Chooses a random tile next to empty tile and swaps them
        /// </summary>
        public void Shift_random ()
        {
            int x = space_x;
            int y = space_y;
            int a = rand.Next(0, 4);
            switch (a)
            {
                case 0: x--; break;
                case 1: x++; break;
                case 2: y--; break;
                case 3: y++; break;
            }
            Shift(Coords_to_position(x, y));
        }

        /// <summary>
        /// Checks if the puzzle is solved
        /// </summary>
        /// <returns></returns>
        public bool Check_numbers()
        {
            if (!(space_x == size - 1 && space_y == size - 1))
            {
                return false;
            }
            for (int x = 0; x < size; x++)
            {
                for (int y = 0; y < size; y++)
                {
                    if (!(x == size - 1 && y == size - 1))
                    {
                        if (map[x, y] != Coords_to_position(x, y) + 1)
                        {
                            return false;
                        }
                    }
                }
            }

            return true;
        }

        /// <summary>
        /// Returns the current number of <position> tile 
        /// </summary>
        /// <param name="position"></param>
        /// <returns></returns>
        public int Get_number (int position)
        {
            Position_to_coords(position, out int x, out int y);
            return map[x, y];
        }

        /// <summary>
        /// Converts matrix coordinates into array position
        /// </summary>
        /// <param name="x"></param>
        /// <param name="y"></param>
        /// <returns></returns>
        private int Coords_to_position(int x, int y)
        {
            if (x < 0)
            {
                x = 0;
            }
            if (x > size - 1)
            {
                x = size - 1;
            }
            if (y < 0)
            {
                y = 0;
            }
            if (y > size - 1)
            {
                y = size - 1;
            }
            return y * size + x;
        }

        /// <summary>
        /// Converts array position into matrix coordinates
        /// </summary>
        /// <param name="position"></param>
        /// <param name="x"></param>
        /// <param name="y"></param>
        public void Position_to_coords (int position, out int x, out int y)
        {
            if (position < 0) position = 0;
            if (position > size * size - 1)
            {
                position = size * size - 1;
            }

            x = position % size;
            y = position / size;
        }
    }
}